Package 'vcd'

Title: Visualizing Categorical Data
Description: Visualization techniques, data sets, summary and inference procedures aimed particularly at categorical data. Special emphasis is given to highly extensible grid graphics. The package was package was originally inspired by the book "Visualizing Categorical Data" by Michael Friendly and is now the main support package for a new book, "Discrete Data Analysis with R" by Michael Friendly and David Meyer (2015).
Authors: David Meyer [aut, cre] , Achim Zeileis [aut] , Kurt Hornik [aut] , Florian Gerber [ctb], Michael Friendly [aut]
Maintainer: David Meyer <[email protected]>
License: GPL-2
Version: 1.4-13
Built: 2024-11-16 06:53:57 UTC
Source: CRAN

Help Index


Bangdiwala's Observer Agreement Chart

Description

Representation of a k×kk \times k confusion matrix, where the observed and expected diagonal elements are represented by superposed black and white rectangles, respectively. The function also computes a statistic measuring the strength of agreement (relation of respective area sums).

Usage

## Default S3 method:
agreementplot(x, reverse_y = TRUE, main = NULL,
              weights = c(1, 1 - 1/(ncol(x) - 1)^2), margins = par("mar"),
              newpage = TRUE, pop = TRUE, 
              xlab = names(dimnames(x))[2],
              ylab = names(dimnames(x))[1],
              xlab_rot = 0, xlab_just = "center",
              ylab_rot = 90, ylab_just = "center",
              fill_col = function(j) gray((1 - (weights[j]) ^ 2) ^ 0.5),
              line_col = "red", xscale = TRUE, yscale = TRUE,
              return_grob = FALSE,
              prefix = "", ...)
## S3 method for class 'formula'
agreementplot(formula, data = NULL, ..., subset)

Arguments

x

a confusion matrix, i.e., a table with equal-sized dimensions.

reverse_y

if TRUE, the y axis is reversed (i.e., the rectangles' positions correspond to the contingency table).

main

user-specified main title.

weights

vector of weights for successive larger observed areas, used in the agreement strength statistic, and also for the shading. The first element should be 1.

margins

vector of margins (see par).

newpage

logical; if TRUE, the plot is drawn on a new page.

pop

logical; if TRUE, all newly generated viewports are popped after plotting.

return_grob

logical. Should a snapshot of the display be returned as a grid grob?

xlab, ylab

labels of x- and y-axis.

xlab_rot, ylab_rot

rotation angle for the category labels.

xlab_just, ylab_just

justification for the category labels.

fill_col

a function, giving the fill colors used for exact and partial agreement

line_col

color used for the diagonal reference line

formula

a formula, such as y ~ x. For details, see xtabs.

data

a data frame (or list), or a contingency table from which the variables in formula should be taken.

subset

an optional vector specifying a subset of the rows in the data frame to be used for plotting.

xscale, yscale

logicals indicating whether the marginals should be added on the x-axis/y-axis, respectively.

prefix

character string used as prefix for the viewport name

...

further graphics parameters (see par).

Details

Weights can be specified to allow for partial agreement, taking into account contributions from off-diagonal cells. Partial agreement is typically represented in the display by lighter shading, as given by fill_col(j), corresponding to weights[j].

A weight vector of length 1 means strict agreement only, each additional element increases the maximum number of disagreement steps.

cotabplot can be used for stratified analyses (see examples).

Value

Invisibly returned, a list with components

Bangdiwala

the unweighted agreement strength statistic.

Bangdiwala_Weighted

the weighted statistic.

weights

the weight vector used.

Author(s)

David Meyer [email protected]

References

Bangdiwala, S. I. (1988). The Agreement Chart. Department of Biostatistics, University of North Carolina at Chapel Hill, Institute of Statistics Mimeo Series No. 1859, https://repository.lib.ncsu.edu/bitstreams/fea554e9-8750-4f1a-8419-ee126ce1a790/download

Bangdiwala, S. I., Ana S. Haedo, Marcela L. Natal, and Andres Villaveces. The agreement chart as an alternative to the receiver-operating characteristic curve for diagnostic tests. Journal of Clinical Epidemiology, 61 (9), 866-874.

Michael Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("SexualFun")
agreementplot(t(SexualFun))

data("MSPatients")
## Not run: 
## best visualized using a resized device, e.g. using:
## get(getOption("device"))(width = 12)
pushViewport(viewport(layout = grid.layout(ncol = 2)))
pushViewport(viewport(layout.pos.col = 1))
agreementplot(t(MSPatients[,,1]), main = "Winnipeg Patients",
              newpage = FALSE)
popViewport()
pushViewport(viewport(layout.pos.col = 2))
agreementplot(t(MSPatients[,,2]), main = "New Orleans Patients",
              newpage = FALSE)
popViewport(2)
dev.off()

## End(Not run)

## alternatively, use cotabplot:
cotabplot(MSPatients, panel = cotab_agreementplot)

Arthritis Treatment Data

Description

Data from Koch & Edwards (1988) from a double-blind clinical trial investigating a new treatment for rheumatoid arthritis.

Usage

data("Arthritis")

Format

A data frame with 84 observations and 5 variables.

ID

patient ID.

Treatment

factor indicating treatment (Placebo, Treated).

Sex

factor indicating sex (Female, Male).

Age

age of patient.

Improved

ordered factor indicating treatment outcome (None, Some, Marked).

Source

Michael Friendly (2000), Visualizing Categorical Data: http://euclid.psych.yorku.ca/ftp/sas/vcd/catdata/arthrit.sas

References

G. Koch & S. Edwards (1988), Clinical efficiency trials with categorical data. In K. E. Peace (ed.), Biopharmaceutical Statistics for Drug Development, 403–451. Marcel Dekker, New York.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("Arthritis")
art <- xtabs(~ Treatment + Improved, data = Arthritis, subset = Sex == "Female")
art

mosaic(art, gp = shading_Friendly)
mosaic(art, gp = shading_max)

Extended Association Plots

Description

Produce an association plot indicating deviations from a specified independence model in a possibly high-dimensional contingency table.

Usage

## Default S3 method:
assoc(x, row_vars = NULL, col_vars = NULL, compress = TRUE,
  xlim = NULL, ylim = NULL,
  spacing = spacing_conditional(sp = 0), spacing_args = list(),
  split_vertical = NULL, keep_aspect_ratio = FALSE, 
  xscale = 0.9, yspace = unit(0.5, "lines"), main = NULL, sub = NULL,
  ..., residuals_type = "Pearson", gp_axis = gpar(lty = 3))
## S3 method for class 'formula'
assoc(formula, data = NULL, ..., subset = NULL, na.action = NULL, main = NULL, sub = NULL)

Arguments

x

a contingency table in array form with optional category labels specified in the dimnames(x) attribute, or an object inheriting from the "ftable" class (such as "structable" objects).

row_vars

a vector of integers giving the indices, or a character vector giving the names of the variables to be used for the rows of the association plot.

col_vars

a vector of integers giving the indices, or a character vector giving the names of the variables to be used for the columns of the association plot.

compress

logical; if FALSE, the space between the rows (columns) are chosen such that the total heights (widths) of the rows (columns) are all equal. If TRUE, the space between rows and columns is fixed and hence the plot is more “compressed”.

xlim

a 2×k2 \times k matrix of doubles, kk number of total columns of the plot. The columns of xlim correspond to the columns of the association plot, the rows describe the column ranges (minimums in the first row, maximums in the second row). If xlim is NULL, the ranges are determined from the residuals according to compress (if TRUE: widest range from each column, if FALSE: from the whole association plot matrix).

ylim

a 2×k2 \times k matrix of doubles, kk number of total rows of the plot. The columns of ylim correspond to the rows of the association plot, the rows describe the column ranges (minimums in the first row, maximums in the second row). If ylim is NULL, the ranges are determined from the residuals according to compress (if TRUE: widest range from each row, if FALSE: from the whole association plot matrix).

spacing

a spacing object, a spacing function, or a corresponding generating function (see strucplot for more information). The default is the spacing-generating function spacing_conditional that is (by default) called with the argument list spacing_args (see spacings for more details).

spacing_args

list of arguments for the spacing-generating function, if specified (see strucplot for more information).

split_vertical

vector of logicals of length kk, where kk is the number of margins of x (default: FALSE). Values are recycled as needed. A TRUE component indicates that the corresponding dimension is folded into the columns, FALSE folds the dimension into the rows.

keep_aspect_ratio

logical indicating whether the aspect ratio should be fixed or not.

residuals_type

a character string indicating the type of residuals to be computed. Currently, only Pearson residuals are supported.

xscale

scale factor resizing the tile's width, thus adding additional space between the tiles.

yspace

object of class "unit" specifying additional space separating the rows.

gp_axis

object of class "gpar" specifying the visual aspects of the tiles' baseline.

formula

a formula object with possibly both left and right hand sides specifying the column and row variables of the flat table.

data

a data frame, list or environment containing the variables to be cross-tabulated, or an object inheriting from class table.

subset

an optional vector specifying a subset of observations to be used. Ignored if data is a contingency table.

na.action

an optional function which indicates what should happen when the data contain NAs. Ignored if data is a contingency table.

main, sub

either a logical, or a character string used for plotting the main (sub) title. If logical and TRUE, the name of the data object is used.

...

other parameters passed to strucplot

Details

Association plots have been suggested by Cohen (1980) and extended by Friendly (1992) and provide a means for visualizing the residuals of an independence model for a contingency table.

assoc is a generic function and currently has a default method and a formula interface. Both are high-level interfaces to the strucplot function, and produce (extended) association plots. Most of the functionality is described there, such as specification of the independence model, labeling, legend, spacing, shading, and other graphical parameters.

For a contingency table, the signed contribution to Pearson's χ2\chi^2 for cell {ijk}\{ij\ldots k\} is

dijk=(fijkeijk)eijkd_{ij\ldots k} = \frac{(f_{ij\ldots k} - e_{ij\ldots k})}{ \sqrt{e_{ij\ldots k}}}

where fijkf_{ij\ldots k} and eijke_{ij\ldots k} are the observed and expected counts corresponding to the cell. In the association plot, each cell is represented by a rectangle that has (signed) height proportional to dijkd_{ij\ldots k} and width proportional to eijk\sqrt{e_{ij\ldots k}}, so that the area of the box is proportional to the difference in observed and expected frequencies. The rectangles in each row are positioned relative to a baseline indicating independence (dijk=0d_{ij\ldots k} = 0). If the observed frequency of a cell is greater than the expected one, the box rises above the baseline, and falls below otherwise.

Additionally, the residuals can be colored depending on a specified shading scheme (see Meyer et al., 2003). Package vcd offers a range of residual-based shadings (see the shadings help page). Some of them allow, e.g., the visualization of test statistics.

Unlike the assocplot function in the graphics package, this function allows the visualization of contingency tables with more than two dimensions. Similar to the construction of ‘flat’ tables (like objects of class "ftable" or "structable"), the dimensions are folded into rows and columns.

The layout is very flexible: the specification of shading, labeling, spacing, and legend is modularized (see strucplot for details).

Value

The "structable" visualized is returned invisibly.

Author(s)

David Meyer [email protected]

References

Cohen, A. (1980), On the graphical display of the significant components in a two-way contingency table. Communications in Statistics—Theory and Methods, A9, 1025–1041.

Friendly, M. (1992), Graphical methods for categorical data. SAS User Group International Conference Proceedings, 17, 190–200. http://datavis.ca/papers/sugi/sugi17.pdf

Meyer, D., Zeileis, A., Hornik, K. (2003), Visualizing independence using extended association plots. Proceedings of the 3rd International Workshop on Distributed Statistical Computing, K. Hornik, F. Leisch, A. Zeileis (eds.), ISSN 1609-395X. https://www.R-project.org/conferences/DSC-2003/Proceedings/

Meyer, D., Zeileis, A., and Hornik, K. (2006), The strucplot framework: Visualizing multi-way contingency tables with vcd. Journal of Statistical Software, 17(3), 1-48. doi:10.18637/jss.v017.i03 and available as vignette ("strucplot", package = "vcd").

See Also

mosaic, strucplot, structable

Examples

data("HairEyeColor")
## Aggregate over sex:
(x <- margin.table(HairEyeColor, c(1, 2)))

## Ordinary assocplot:
assoc(x)
## and with residual-based shading (of independence)
assoc(x, main = "Relation between hair and eye color", shade = TRUE)

## Aggregate over Eye color:
(x <- margin.table(HairEyeColor, c(1, 3)))
chisq.test(x)
assoc(x, main = "Relation between hair color and sex", shade = TRUE)

# Visualize multi-way table
assoc(aperm(HairEyeColor), expected = ~ (Hair + Eye) * Sex,
      labeling_args = list(just_labels = c(Eye = "left"),
                           offset_labels = c(right = -0.5),
                           offset_varnames = c(right = 1.2),
                           rot_labels = c(right = 0),
                           tl_varnames = c(Eye = TRUE))
)

assoc(aperm(UCBAdmissions), expected = ~ (Admit + Gender) * Dept, compress = FALSE,
      labeling_args = list(abbreviate_labs = c(Gender = TRUE), rot_labels = 0)
)

Association Statistics

Description

Computes the Pearson chi-Squared test, the Likelihood Ratio chi-Squared test, the phi coefficient, the contingency coefficient and Cramer's V for possibly stratified contingency tables.

Usage

assocstats(x)

Arguments

x

a contingency table, with possibly more than 2 dimensions. In this case, all dimensions except the first two ones are considered as strata.

Value

In case of a 2-dimensional table, a list with components:

chisq_tests

a 2×32 \times 3 table with the chi-squared statistics.

phi

The absolute value of the phi coefficient (only defined for 2×22 \times 2 tables).

cont

The contingency coefficient.

cramer

Cramer's V.

In case of higher-dimensional tables, a list of the above mentioned structure, each list component representing one stratum defined by the combinations of all levels of the stratum dimensions.

Author(s)

David Meyer [email protected]

References

Michael Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Fleiss, J. L. (1981). Statistical methods for rates and proportions (2nd ed). New York: Wiley

Examples

data("Arthritis")
tab <- xtabs(~Improved + Treatment, data = Arthritis)
summary(assocstats(tab))

assocstats(UCBAdmissions)

Baseball Data

Description

Baseball data.

Usage

data("Baseball")

Format

A data frame with 322 observations and 25 variables.

name1

player's first name.

name2

player's last name.

atbat86

times at Bat: number of official plate appearances by a hitter. It counts as an official at-bat as long as the batter does not walk, sacrifice, get hit by a pitch or reach base due to catcher's interference.

hits86

hits.

homer86

home runs.

runs86

the number of runs scored by a player. A run is scored by an offensive player who advances from batter to runner and touches first, second, third and home base in that order without being put out.

rbi86

Runs Batted In: A hitter earns a run batted in when he drives in a run via a hit, walk, sacrifice (bunt or fly) fielder's choice, hit-batsman or on an error (when the official scorer rules that the run would have scored anyway).

walks86

A “walk” (or “base on balls”) is an award of first base granted to a batter who receives four pitches outside the strike zone.

years

Years in the Major Leagues. Seems to count all years a player has actually played in the Major Leagues, not necessarily consecutive.

atbat

career times at bat.

hits

career hits.

homeruns

career home runs.

runs

career runs.

rbi

career runs batted in.

walks

career walks.

league86

player's league.

div86

player's division.

team86

player's team.

posit86

player's position (see Hitters).

outs86

number of putouts (see Hitters)

assist86

number of assists (see Hitters)

error86

number of assists (see Hitters)

sal87

annual salary on opening day (in USD 1000).

league87

league in 1987.

team87

team in 1987.

Source

SAS System for Statistical Graphics, First Edition, page A2.3

References

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

See Also

Hitters

Examples

data("Baseball")

Binary Regression Plot

Description

Creates a display of observed and fitted values for a binary regression model with one numeric predictor, conditioned by zero or many co-factors.

Usage

binreg_plot(model, main = NULL, xlab = NULL, ylab = NULL,
            xlim = NULL, ylim = NULL,
            pred_var = NULL, pred_range = c("data", "xlim"),
            group_vars = NULL, base_level = NULL, subset,
            type = c("response", "link"), conf_level = 0.95, delta = FALSE,
            pch = NULL, cex = 0.6, jitter_factor = 0.1,
            lwd = 5, lty = 1, point_size = 0, col_lines = NULL, col_bands = NULL, 
            legend = TRUE, legend_pos = NULL, legend_inset = c(0, 0.1),
            legend_vgap = unit(0.5, "lines"),
            labels = FALSE, labels_pos = c("right", "left"),
            labels_just = c("left","center"), labels_offset = c(0.01, 0),
            gp_main = gpar(fontface = "bold", fontsize = 14),
            gp_legend_frame = gpar(lwd = 1, col = "black"),
            gp_legend_title = gpar(fontface = "bold"),
            newpage = TRUE, pop = FALSE, return_grob = FALSE)
grid_abline(a, b, ...)

Arguments

model

a binary regression model fitted with glm.

main

user-specified main title.

xlab

x-axis label. Defaults to the name of the (first) numeric predictor.

ylab

y-axis label. Defaults to the name of the response - within either 'P(...)' or 'logit(...)', depending on the response type.

xlim

Range of the x-axis. Defaults to the range of the numeric predictor.

ylim

Range of the y-axis. Defaults to the unit interval on probability scale or the fitted values range on the link scale, depending on type.

pred_var

character string of length 1 giving the name of the numeric predictor. Defaults to the first one found in the data set.

pred_range

"data", "xlim", or a numeric vector. If "data", the numeric predictor corresponds to the observed values. If "xlim", 100 values are taken from the "xlim" range. A numeric vector will be interpreted as the values to be predicted.

group_vars

optional character string of conditioning variables. Defaults to all factors found in the data set, response excluded. If FALSE, no variables are used for conditioning.

base_level

vector of length one. If the response is a vector, this specifies the base ('no effect') value of the response variable (e.g., "Placebo", 0, FALSE, etc.) and defaults to the first level for factor responses, or 0 for numeric/binary variables. This controls which observations will be plotted on the top or the bottom of the display. If the response is a matrix with success and failure column, this specifies the one to be interpreted as failure (default: 2), either as an integer, or as a string ("success" or "failure"). The proportions of successes will be plotted as observed values.

subset

an optional vector specifying a subset of the data rows. The value is evaluated in the data environment, so expressions can be used to select the data (see examples).

type

either "response" or "link" to select the scale of the fitted values. The y-axis will be adapted accordingly.

conf_level

confidence level used for calculating confidence bands.

delta

logical; indicates whether the delta method should be employed for calculating the limits of the confidence band or not (see details).

pch

character or numeric vector of symbols used for plotting the (possibly conditioned) observed values, recycled as needed.

cex

size of the plot symbols (in lines).

jitter_factor

argument passed to jitter used for the points representing the observed values.

lwd

Line width for the fitted values.

lty

Line type for the fitted values.

point_size

size of points for the fitted values in char units (default: 0, so no points are plotted).

col_lines, col_bands

character vector specifying the colors of the fitted lines and confidence bands, by default chosen with rainbow_hcl. The confidence bands are using alpha blending with alpha = 0.2.

legend

logical; if TRUE (default), a legend is drawn.

legend_pos

numeric vector of length 2, specifying x and y coordinates of the legend, or a character string (e.g., "topleft", "center" etc.). Defaults to "topleft" if the fitted curve's slope is positive, and "topright" else.

legend_inset

numeric vector or length 2 specifying the inset from the legend's x and y coordinates in npc units.

legend_vgap

vertical space between the legend's line entries.

labels

logical; if TRUE, labels corresponding to the factor levels are plotted next to the fitted lines.

labels_pos

either "right" or "left", determining on which side of the fitted lines (start or end) the labels should be placed.

labels_just

character vector of length 2, specifying the relative justification of the labels to their coordinates. See the documentation of the just parameter of grid.text for more details.

labels_offset

numeric vector of length 2, specifying the offset of the labels' coordinates in npc units.

gp_main

object of class "gpar" used for the main title.

gp_legend_frame

object of class "gpar" used for the legend frame.

gp_legend_title

object of class "gpar" used for the legend title.

newpage

logical; if TRUE, the plot is drawn on a new page.

pop

logical; if TRUE, all newly generated viewports are popped after plotting.

return_grob

logical. Should a snapshot of the display be returned as a grid grob?

a

intercept; alternatively, a regression model from which coefficients can be extracted via coef.

b

slope.

...

Further arguments passed to grid.abline.

Details

The primary purpose of binreg_plot() is to visualize observed and fitted values for binary regression models (like the logistic or probit regression model) with one numeric predictor. If one or more categorical predictors are used in the model, the fitted values are conditioned on them, i.e. separate curves are drawn corresponding to the factor level combinations. Thus, it shows a full-model plot, not a conditional plot where several models would be fit to data subsets.

The implementation relies on objects returned by glm, as it uses its "terms" and "model" components.

The function tries to determine suitable values for the legend and/or labels, but depending on the data, this might require some tweaking.

By default, the limits of the confidence band are determined for the linear predictor (i.e., on the link scale) and transformed to response scale (if this is the chosen plot type) using the inverse link function. If delta is TRUE, the limits are determined on the response scale. Note that the resulting band using the delta method is symmetric around the fitted mean, but may exceed the unit interval (on the response scale) and will be cut off.

grid_abline() is a simple convenience wrapper for grid.abline with similar behavior than abline in that it extracts coefficients from a regression model, if given instead of the intercept a.

Value

if return_grob is TRUE, a grob object corresponding to the plot. NULL (invisibly) else.

Author(s)

David Meyer [email protected]

References

Michael Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

## Simple model with no conditioning variables
art.mod0 <- glm(Improved > "None" ~ Age, data = Arthritis, family = binomial)

binreg_plot(art.mod0, "Arthritis Data")
binreg_plot(art.mod0, type = "link") ## logit scale

## one conditioning factor
art.mod1 <- update(art.mod0, . ~ . + Sex)
binreg_plot(art.mod1)
binreg_plot(art.mod1, legend = FALSE, labels = TRUE, xlim = c(20, 80))

## two conditioning factors
art.mod2 <- update(art.mod1, . ~ . + Treatment)
binreg_plot(art.mod2)
binreg_plot(art.mod2, subset = Sex == "Male") ## subsetting

## some tweaking
binreg_plot(art.mod2, gp_legend_frame = gpar(col = NA, fill = "white"), col_bands = NA)
binreg_plot(art.mod2, legend = FALSE, labels = TRUE,
            labels_pos = "left", labels_just = c("left", "top"))

## model with grouped response data
shuttle.mod <- glm(cbind(nFailures, 6 - nFailures) ~ Temperature,
                   data = SpaceShuttle, na.action = na.exclude, family = binomial)
binreg_plot(shuttle.mod, xlim = c(30, 81), pred_range = "xlim",
            ylab = "O-Ring Failure Probability", xlab = "Temperature (F)")

Broken Marriage Data

Description

Data from the Danish Welfare Study about broken marriages or permanent relationships depending on gender and social rank.

Usage

data("BrokenMarriage")

Format

A data frame with 20 observations and 4 variables.

Freq

frequency.

gender

factor indicating gender (male, female).

rank

factor indicating social rank (I, II, III, IV, V).

broken

factor indicating whether the marriage or permanent relationship was broken (yes, no).

Source

E. B. Andersen (1991), The Statistical Analysis of Categorical Data, page 177.

References

E. B. Andersen (1991), The Statistical Analysis of Categorical Data. 2nd edition. Springer-Verlag, Berlin.

Examples

data("BrokenMarriage")
structable(~ ., data = BrokenMarriage)

Ergebnisse der Fussball-Bundesliga

Description

Results from the first German soccer league (1963-2008).

Usage

data("Bundesliga")

Format

A data frame with 14018 observations and 7 variables.

HomeTeam

factor. Name of the home team.

AwayTeam

factor. Name of the away team.

HomeGoals

number of goals scored by the home team.

AwayGoals

number of goals scored by the away team.

Round

round of the game.

Year

year in which the season started.

Date

starting time of the game (in "POSIXct" format).

Details

The data comprises all games in the first German soccer league since its foundation in 1963. The data have been queried online from the official Web page of the DFB and prepared as a data frame in R by Daniel Dekic, Torsten Hothorn, and Achim Zeileis (replacing earlier versions of the data in the package containing only subsets of years).

Each year/season comprises 34 rounds (except 1963, 1964, 1991) so that all 18 teams play twice against each other (switching home court advantage). In 1963/64, there were only 16 teams, hence only 30 rounds. In 1991, after the German unification, there was one season with 20 teams and 38 rounds.

Source

Homepage of the Deutscher Fussball-Bund (DFB, German Football Association): https://www.dfb.de/index/

References

Leonhard Knorr-Held (1999), Dynamic rating of sports teams. SFB 386 “Statistical Analysis of Discrete Structures”, Discussion paper 98.

See Also

UKSoccer

Examples

data("Bundesliga")

## number of goals per game poisson distributed?
ngoals1 <- xtabs(~ HomeGoals, data = Bundesliga, subset = Year == 1995)
ngoals2 <- xtabs(~ AwayGoals, data = Bundesliga, subset = Year == 1995)
ngoals3 <- table(apply(subset(Bundesliga, Year == 1995)[,3:4], 1, sum))

gf1 <- goodfit(ngoals1)
gf2 <- goodfit(ngoals2)
gf3 <- goodfit(ngoals3)

summary(gf1)
summary(gf2)
summary(gf3)
plot(gf1)
plot(gf2)
plot(gf3)

Ord_plot(ngoals1)
distplot(ngoals1)

Votes in German Bundestag Election 2005

Description

Number of votes by province in the German Bundestag election 2005 (for the parties that eventually entered the parliament).

Usage

data("Bundestag2005")

Format

A 2-way "table" giving the number of votes for each party (Fraktion) in each of the 16 German provinces (Bundesland):

No Name Levels
1 Bundesland Schleswig-Holstein, Mecklenburg-Vorpommern, ...
2 Fraktion SPD, CDU/CSU, Gruene, FDP, Linke

Details

In the election for the German parliament “Bundestag”, five parties obtained enough votes to enter the parliament: the social democrats SPD, the conservative CDU/CSU, the liberal FDP, the green party “Die Gruenen” and the leftist party “Die Linke”. The table Bundestag2005 gives the number of votes for each party (Fraktion) in each of the 16 German provinces (Bundesland). The provinces are ordered from North to South.

The data have been obtained from the German statistical office (Statistisches Bundesamt) from the Web page given below.

Note that the number of seats in the parliament cannot be computed from the number of votes alone. The examples below show the distribution of seats that resulted from the election.

Source

Die Bundeswahlleiterin, Statistisches Bundesamt. https://www.bundeswahlleiterin.de/bundestagswahlen/2005.html

Examples

library(colorspace)
## The outcome of the election in terms of seats in the
## parliament was:
seats <- structure(c(226, 61, 54, 51, 222),
  .Names = c("CDU/CSU", "FDP",  "Linke", "Gruene", "SPD"))

## Hues are chosen as metaphors for the political parties
## CDU/CSU: blue, FDP: yellow, Linke: purple, Gruene: green, SPD: red
## using the respective hues from a color wheel with
## chroma = 60 and luminance = 75
parties <- rainbow_hcl(6, c = 60, l = 75)[c(5, 2, 6, 3, 1)]
names(parties) <- names(seats)
parties

## The pie chart shows that neither the SPD+Gruene coalition nor
## the opposition of CDU/CSU+FDP could assemble a majority.
## No party would enter a coalition with the leftists, leading to a
## big coalition.
pie(seats, clockwise = TRUE, col = parties)

## The regional distribution of the votes, stratified by province,
## is shown in a mosaic display: first for the 10 Western then the
## 6 Eastern provinces.
data("Bundestag2005")
votes <- Bundestag2005[c(1, 3:5, 9, 11, 13:16, 2, 6:8, 10, 12),
                       c("CDU/CSU", "FDP", "SPD", "Gruene", "Linke")]
mosaic(votes, gp = gpar(fill = parties[colnames(votes)]),
  spacing = spacing_highlighting, labeling = labeling_left,
  labeling_args = list(rot_labels = c(0, 90, 0, 0), pos_labels = "center",
  just_labels = c("center","center","center","right"), varnames = FALSE),
  margins = unit(c(2.5, 1, 1, 12), "lines"),
  keep_aspect_ratio = FALSE)

Butterfly Species in Malaya

Description

Data from Fisher et al. (1943) giving the number of tokens found for each of 501 species of butterflies collected in Malaya.

Usage

data("Butterfly")

Format

A 1-way table giving the number of tokens for 501 species of butterflies. The variable and its levels are

No Name Levels
1 nTokens 0, 1, ..., 24

Source

Michael Friendly (2000), Visualizing Categorical Data, pages 21–22.

References

R. A. Fisher, A. S. Corbet, C. B. Williams (1943), The relation between the number of species and the number of individuals, Journal of Animal Ecology, 12, 42–58.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("Butterfly")
Ord_plot(Butterfly)

Conditional Density Plots

Description

Computes and plots conditional densities describing how the distribution of a categorical variable y changes over a numerical variable x.

Usage

cd_plot(x, ...)
## Default S3 method:
cd_plot(x, y,
  plot = TRUE, ylab_tol = 0.05,
  bw = "nrd0", n = 512, from = NULL, to = NULL,
  main = "", xlab = NULL, ylab = NULL, margins = c(5.1, 4.1, 4.1, 3.1),
  gp = gpar(), name = "cd_plot", newpage = TRUE, pop = TRUE, return_grob = FALSE, ...)
## S3 method for class 'formula'
cd_plot(formula, data = list(),
  plot = TRUE, ylab_tol = 0.05,
  bw = "nrd0", n = 512, from = NULL, to = NULL,
  main = "", xlab = NULL, ylab = NULL, margins = c(5.1, 4.1, 4.1, 3.1),
  gp = gpar(), name = "cd_plot", newpage = TRUE, pop = TRUE, return_grob = FALSE, ...)

Arguments

x

an object, the default method expects either a single numerical variable.

y

a "factor" interpreted to be the dependent variable

formula

a "formula" of type y ~ x with a single dependent "factor" and a single numerical explanatory variable.

data

an optional data frame.

plot

logical. Should the computed conditional densities be plotted?

ylab_tol

convenience tolerance parameter for y-axis annotation. If the distance between two labels drops under this threshold, they are plotted equidistantly.

bw, n, from, to, ...

arguments passed to density

main, xlab, ylab

character strings for annotation

margins

margins when calling plotViewport

gp

a "gpar" object controlling the grid graphical parameters of the rectangles. It should specify in particular a vector of fill colors of the same length as levels(y). The default is to call gray.colors.

name

name of the plotting viewport.

newpage

logical. Should grid.newpage be called before plotting?

return_grob

logical. Should a snapshot of the display be returned as a grid grob?

pop

logical. Should the viewport created be popped?

Details

cd_plot computes the conditional densities of x given the levels of y weighted by the marginal distribution of y. The densities are derived cumulatively over the levels of y.

This visualization technique is similar to spinograms (see spine) but they do not discretize the explanatory variable, but rather use a smoothing approach. Furthermore, the original x axis and not a distorted x axis (as for spinograms) is used. This typically results in conditional densities that are based on very few observations in the margins: hence, the estimates are less reliable there.

Value

The conditional density functions (cumulative over the levels of y) are returned invisibly.

Author(s)

Achim Zeileis [email protected]

References

Hofmann, H., Theus, M. (2005), Interactive graphics for visualizing conditional distributions, Unpublished Manuscript.

See Also

spine, density

Examples

## Arthritis data
data("Arthritis")
cd_plot(Improved ~ Age, data = Arthritis)
cd_plot(Improved ~ Age, data = Arthritis, bw = 3)
cd_plot(Improved ~ Age, data = Arthritis, bw = "SJ")
## compare with spinogram
spine(Improved ~ Age, data = Arthritis, breaks = 3)

## Space shuttle data
data("SpaceShuttle")
cd_plot(Fail ~ Temperature, data = SpaceShuttle, bw = 2)

## scatter plot with conditional density
cdens <- cd_plot(Fail ~ Temperature, data = SpaceShuttle, bw = 2, plot = FALSE)
plot(I(-1 * (as.numeric(Fail) - 2)) ~ jitter(Temperature, factor = 2), data = SpaceShuttle,
  xlab = "Temperature", ylab = "Failure")
lines(53:81, cdens[[1]](53:81), col = 2)

Compute Conditional Tables

Description

For a contingency table in array form, compute a list of conditional tables given some margins.

Usage

co_table(x, margin, collapse = ".")

Arguments

x

a contingency table in array form.

margin

margin index(es) or corresponding name(s) of the conditioning variables.

collapse

character used when collapsing level names (if more than 1 margin is specified).

Details

This is essentially an interface to [ which is more convenient for arrays of arbitrary dimension.

Value

A list of the resulting conditional tables.

Author(s)

Achim Zeileis [email protected]

Examples

data("HairEyeColor")
co_table(HairEyeColor, 1)
co_table(HairEyeColor, c("Hair", "Eye"))
co_table(HairEyeColor, 1:2, collapse = "")

Breathlessness and Wheeze in Coal Miners

Description

Data from Ashford & Sowden (1970) given by Agresti (1990) on the association between two pulmonary conditions, breathlessness and wheeze, in a large sample of coal miners who were smokers with no radiological evidence of pneumoconlosis, aged between 20–64 when examined. This data is frequently used as an example of fitting models for bivariate, binary responses.

Usage

data("CoalMiners")

Format

A 3-dimensional table of size 2 x 2 x 9 resulting from cross-tabulating variables for 18,282 coal miners. The variables and their levels are as follows:

No Name Levels
1 Breathlessness B, NoB
2 Wheeze W, NoW
3 Age 20-24, 25-29, 30-34, ..., 60-64

Details

In an earlier version of this data set, the first group, aged 20-24, was inadvertently omitted from this data table and the breathlessness variable was called wheeze and vice versa.

Source

Michael Friendly (2000), Visualizing Categorical Data, pages 82–83, 319–322.

References

A. Agresti (1990), Categorical Data Analysis. Wiley-Interscience, New York, Table 7.11, p. 237

J. R. Ashford and R. D. Sowdon (1970), Multivariate probit analysis, Biometrics, 26, 535–546.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("CoalMiners")

ftable(CoalMiners, row.vars = 3)

## Fourfold display, both margins equated
fourfold(CoalMiners[,,2:9], mfcol = c(2,4))

## Fourfold display, strata equated
fourfold(CoalMiners[,,2:9], std = "ind.max", mfcol = c(2,4))


## Log Odds Ratio Plot
lor_CM <- loddsratio(CoalMiners)
summary(lor_CM)
plot(lor_CM)
lor_CM_df <- as.data.frame(lor_CM)

# fit linear models using WLS
age <- seq(20, 60, by = 5)
lmod <- lm(LOR ~ age, weights = 1 / ASE^2, data = lor_CM_df)
grid.lines(age, fitted(lmod), gp = gpar(col = "blue"))
qmod <- lm(LOR ~ poly(age, 2), weights = 1 / ASE^2, data = lor_CM_df)
grid.lines(age, fitted(qmod), gp = gpar(col = "red"))

Test for (Conditional) Independence

Description

Performs a test of (conditional) independence of 2 margins in a contingency table by simulation from the marginal distribution of the input table under (conditional) independence.

Usage

coindep_test(x, margin = NULL, n = 1000, 
  indepfun = function(x) max(abs(x)), aggfun = max,
  alternative = c("greater", "less"),
  pearson = TRUE)

Arguments

x

a contingency table.

margin

margin index(es) or corresponding name(s) of the conditioning variables. Each resulting conditional table has to be a 2-way table.

n

number of (conditional) independence tables to be drawn.

indepfun

aggregation function capturing independence in (each conditional) 2-way table.

aggfun

aggregation function aggregating the test statistics computed by indepfun.

alternative

a character string specifying the alternative hypothesis; must be either "greater" (default) or "less" (and may be abbreviated.)

pearson

logical. Should the table of Pearson residuals under independence be computed and passed to indepfun (default) or the raw table of observed frequencies?

Details

If margin is NULL this computes a simple independence statistic in a 2-way table. Alternatively, margin can give several conditioning variables and then conditional independence in the resulting conditional table is tested.

By default, this uses a (double) maximum statistic of Pearson residuals. By changing indepfun or aggfun a (maximum of) Pearson Chi-squared statistic(s) can be computed or just the usual Pearson Chi-squared statistics and so on. Other statistics can be computed by changing pearson to FALSE.

The function uses r2dtable to simulate the distribution of the test statistic under the null.

Value

A list of class "coindep_test" inheriting from "htest" with following components:

statistic

the value of the test statistic.

p.value

the pp value for the test.

method

a character string indicating the type of the test.

data.name

a character string giving the name(s) of the data.

observed

observed table of frequencies

expctd

expected table of frequencies

residuals

corresponding Pearson residuals

margin

the margin used

dist

a vector of size n with simulated values of the distribution of the statistic under the null.

qdist

the corresponding quantile function (for computing critical values).

pdist

the corresponding distribution function (for computing pp values).

Author(s)

Achim Zeileis [email protected]

See Also

chisq.test, fisher.test, r2dtable

Examples

library(MASS)
TeaTasting <- matrix(c(3, 1, 1, 3), nrow = 2,
                     dimnames = list(Guess = c("Milk", "Tea"),
                                     Truth = c("Milk", "Tea"))
)
## compute maximum statistic
coindep_test(TeaTasting)
## compute Chi-squared statistic
coindep_test(TeaTasting, indepfun = function(x) sum(x^2))
## use unconditional asymptotic distribution
chisq.test(TeaTasting, correct = FALSE)
chisq.test(TeaTasting)


data("UCBAdmissions")
## double maximum statistic
coindep_test(UCBAdmissions, margin = "Dept")
## maximum of Chi-squared statistics
coindep_test(UCBAdmissions, margin = "Dept", indepfun = function(x) sum(x^2))
## Pearson Chi-squared statistic
coindep_test(UCBAdmissions, margin = "Dept", indepfun = function(x) sum(x^2), aggfun = sum)
## use unconditional asymptotic distribution
loglm(~ Dept * (Gender + Admit), data = UCBAdmissions)

Panel-generating Functions for Contingency Table Coplots

Description

Panel-generating functions visualizing contingency tables that can be passed to cotabplot.

Usage

cotab_mosaic(x = NULL, condvars = NULL, ...)
cotab_assoc(x = NULL, condvars = NULL, ylim = NULL, ...)
cotab_sieve(x = NULL, condvars = NULL, ...)
cotab_loddsratio(x = NULL, condvars = NULL, ...)
cotab_agreementplot(x = NULL, condvars = NULL, ...)
cotab_fourfold(x = NULL, condvars = NULL, ...)
cotab_coindep(x, condvars,
  test = c("doublemax", "maxchisq", "sumchisq"),
  level = NULL, n = 1000, interpolate = c(2, 4),
  h = NULL, c = NULL, l = NULL, lty = 1,
  type = c("mosaic", "assoc"), legend = FALSE, ylim = NULL, ...)

Arguments

x

a contingency tables in array form.

condvars

margin name(s) of the conditioning variables.

ylim

y-axis limits for assoc plot. By default this is computed from x.

test

character indicating which type of statistic should be used for assessing conditional independence.

level, n, h, c, l, lty, interpolate

variables controlling the HCL shading of the residuals, see shadings for more details.

type

character indicating which type of plot should be produced.

legend

logical. Should a legend be produced in each panel?

...

further arguments passed to the plotting function (such as mosaic or assoc or sieve respectively).

Details

These functions of class "panel_generator" are panel-generating functions for use with cotabplot, i.e., they return functions with the interface

panel(x, condlevels)

required for cotabplot. The functions produced by cotab_mosaic, cotab_assoc and cotab_sieve essentially only call co_table to produce the conditioned table and then call mosaic, assoc or sieve respectively with the arguments specified.

The function cotab_coindep is similar but additionally chooses an appropriate residual-based shading visualizing the associated conditional independence model. The conditional independence test is carried out via coindep_test and the shading is set up via shading_hcl.

A description of the underlying ideas is given in Zeileis, Meyer, Hornik (2005).

Author(s)

Achim Zeileis [email protected]

References

Meyer, D., Zeileis, A., and Hornik, K. (2006), The strucplot framework: Visualizing multi-way contingency tables with vcd. Journal of Statistical Software, 17(3), 1-48. doi:10.18637/jss.v017.i03 and available as vignette("strucplot").

Zeileis, A., Meyer, D., Hornik K. (2007), Residual-based shadings for visualizing (conditional) independence, Journal of Computational and Graphical Statistics, 16, 507–525.

See Also

cotabplot, mosaic, assoc, sieve, co_table, coindep_test, shading_hcl

Examples

data("UCBAdmissions")

cotabplot(~ Admit + Gender | Dept, data = UCBAdmissions)
cotabplot(~ Admit + Gender | Dept, data = UCBAdmissions, panel = cotab_assoc)
cotabplot(~ Admit + Gender | Dept, data = UCBAdmissions, panel = cotab_fourfold)

ucb <- cotab_coindep(UCBAdmissions, condvars = "Dept", type = "assoc",
                     n = 5000, margins = c(3, 1, 1, 3))
cotabplot(~ Admit + Gender | Dept, data = UCBAdmissions, panel = ucb)

Coplot for Contingency Tables

Description

cotabplot is a generic function for creating trellis-like coplots (conditional plots) for contingency tables.

Usage

cotabplot(x, ...)
## Default S3 method:
cotabplot(x, cond = NULL,
  panel = cotab_mosaic, panel_args = list(),
  margins = rep(1, 4), layout = NULL,
  text_gp = gpar(fontsize = 12), rect_gp = gpar(fill = grey(0.9)),
  pop = TRUE, newpage = TRUE, return_grob = FALSE,
  ...)
## S3 method for class 'formula'
cotabplot(formula, data = NULL, ...)

Arguments

x

an object. The default method can deal with contingency tables in array form.

cond

margin index(es) or corresponding name(s) of the conditioning variables.

panel

panel function applied for each conditioned plot, see details.

panel_args

list of arguments passed to panel if this is a panel-generating function inheriting from class "grapcon_generator".

margins

either an object of class "unit" of length 4, or a numeric vector of length 4. The elements are recycled as needed. giving the margins around the whole plot.

layout

integer vector (of length two), giving the number of rows and columns for the panel.

text_gp

object of class "gpar" used for the text in the panel titles.

rect_gp

object of class "gpar" used for the rectangles with the panel titles.

pop

logical indicating whether the generated viewport tree should be removed at the end of the drawing or not.

newpage

logical controlling whether a new grid page should be created.

return_grob

logical. Should a snapshot of the display be returned as a grid grob?

...

further arguments passed to the panel-generating function.

formula

a formula specifying the variables used to create a contingency table from data. It has to be of type ~ x + y | z where z is/are the conditioning variable(s) used.

data

either a data frame, or an object of class "table" or "ftable".

Details

cotabplot is a generic function designed to create coplots or conditional plots (see Cleveland, 1993, and Becker, Cleveland, Shyu, 1996) similar to coplot but for contingency tables.

cotabplot takes on computing the conditioning information and setting up the trellis display, and then relies on a panel function to create plots from the full table and the conditioning information. A simple example would be a contingency table tab with margin names "x", "y" and "z". To produce this plot either the default interface can be used or the formula interface via

cotabplot(tab, "z") cotabplot(~ x + y | z, data = tab)

The panel function needs to be of the form

panel(x, condlevels)

where x is the full table (tab in the example above) and condlevels is a named vector with the levels (e.g., c(z = "z1") in the example above).

Alternatively, panel can also be a panel-generating function of class "grapcon_generator" which creates a function with the interface described above. The panel-generating function is called with the interface

panel(x, condvars, ...)

where again x is the full table, condvars is now only a vector with the names of the conditioning variables (and not their levels, e.g., "z" in the example above). Further arguments can be passed to the panel-generating function via ... which also includes the arguments set in panel_args.

Suitable panel-generating functions for mosaic, association and sieve plots can be found at cotab_mosaic.

A description of the underlying ideas is given in Zeileis, Meyer, Hornik (2005).

Author(s)

Achim Zeileis [email protected]

References

Becker, R.A., Cleveland, W.S., Shyu, M.-J. (1996), The visual design and control of trellis display. Journal of Computational and Graphical Statistics, 5, 123–155.

Cleveland, W.S. (1993), Visualizing Data, Summit, New Jersey: Hobart Press.

Meyer, D., Zeileis, A., and Hornik, K. (2006), The strucplot framework: Visualizing multi-way contingency tables with vcd. Journal of Statistical Software, 17(3), 1-48. doi:10.18637/jss.v017.i03 and available as vignette("strucplot").

Zeileis, A., Meyer, D., Hornik K. (2007), Residual-based shadings for visualizing (conditional) independence, Journal of Computational and Graphical Statistics, 16, 507–525.

See Also

cotab_mosaic, cotab_coindep, co_table, coindep_test

Examples

data("UCBAdmissions")

cotabplot(~ Admit + Gender | Dept, data = UCBAdmissions)
cotabplot(~ Admit + Gender | Dept, data = UCBAdmissions, panel = cotab_assoc)

ucb <- cotab_coindep(UCBAdmissions, condvars = "Dept", type = "assoc",
                     n = 5000, margins = c(3, 1, 1, 3))
cotabplot(~ Admit + Gender | Dept, data = UCBAdmissions, panel = ucb)

Danish Welfare Study Data

Description

Data from the Danish Welfare Study.

Usage

data("DanishWelfare")

Format

A data frame with 180 observations and 5 variables.

Freq

frequency.

Alcohol

factor indicating daily alcohol consumption: less than 1 unit (<1), 1-2 units (1-2) or more than 2 units (>2). 1 unit is approximately 1 bottle of beer or 4cl 40% alcohol.

Income

factor indicating income group in 1000 DKK (0-50, 50-100, 100-150, >150).

Status

factor indicating marriage status (Widow, Married, Unmarried).

Urban

factor indicating urbanization: Copenhagen (Copenhagen), Suburbian Copenhagen (SubCopenhagen), three largest cities (LargeCity), other cities (City), countryside (Country).

Source

E. B. Andersen (1991), The Statistical Analysis of Categorical Data, page 205.

References

E. B. Andersen (1991), The Statistical Analysis of Categorical Data. 2nd edition. Springer-Verlag, Berlin.

Examples

data("DanishWelfare")
ftable(xtabs(Freq ~ ., data = DanishWelfare))

Diagnostic Distribution Plots

Description

Diagnostic distribution plots: poissonness, binomialness and negative binomialness plots.

Usage

distplot(x, type = c("poisson", "binomial", "nbinomial"),
  size = NULL, lambda = NULL, legend = TRUE, xlim = NULL, ylim = NULL,
  conf_int = TRUE, conf_level = 0.95, main = NULL,
  xlab = "Number of occurrences", ylab = "Distribution metameter",
  gp = gpar(cex = 0.8), lwd=2, gp_conf_int = gpar(lty = 2),
  name = "distplot", newpage = TRUE,
  pop =TRUE, return_grob = FALSE, ...)

Arguments

x

either a vector of counts, a 1-way table of frequencies of counts or a data frame or matrix with frequencies in the first column and the corresponding counts in the second column.

type

a character string indicating the distribution.

size

the size argument for the binomial and negative binomial distribution. If set to NULL and type is "binomial", then size is taken to be the maximum count. If set to NULL and type is "nbinomial", then size is estimated from the data.

lambda

parameter of the poisson distribution. If type is "poisson" and lambda is specified a leveled poissonness plot is produced.

legend

logical. Should a legend be plotted?

xlim

limits for the x axis.

ylim

limits for the y axis.

conf_int

logical. Should confidence intervals be plotted?

conf_level

confidence level for confidence intervals.

main

a title for the plot.

xlab

a label for the x axis.

ylab

a label for the y axis.

gp

a "gpar" object controlling the grid graphical parameters of the points.

gp_conf_int

a "gpar" object controlling the grid graphical parameters of the confidence intervals.

lwd

line width for the fitted line

name

name of the plotting viewport.

newpage

logical. Should grid.newpage be called before plotting?

pop

logical. Should the viewport created be popped?

return_grob

logical. Should a snapshot of the display be returned as a grid grob?

...

further arguments passed to grid.points.

Details

distplot plots the number of occurrences (counts) against the distribution metameter of the specified distribution. If the distribution fits the data, the plot should show a straight line. See Friendly (2000) for details.

In these plots, the open points show the observed count metameters; the filled points show the confidence interval centers, and the dashed lines show the conf_level confidence intervals for each point.

Value

Returns invisibly a data frame containing the counts (Counts), frequencies (Freq) and other details of the computations used to construct the plot.

Author(s)

Achim Zeileis [email protected]

References

D. C. Hoaglin (1980), A poissonness plot, The American Statistican, 34, 146–149.

D. C. Hoaglin & J. W. Tukey (1985), Checking the shape of discrete distributions. In D. C. Hoaglin, F. Mosteller, J. W. Tukey (eds.), Exploring Data Tables, Trends and Shapes, chapter 9. John Wiley & Sons, New York.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

## Simulated data examples:
dummy <- rnbinom(1000, size = 1.5, prob = 0.8)
distplot(dummy, type = "nbinomial")

## Real data examples:
data("HorseKicks")
data("Federalist")
data("Saxony")
distplot(HorseKicks, type = "poisson")
distplot(HorseKicks, type = "poisson", lambda = 0.61)
distplot(Federalist, type = "poisson")
distplot(Federalist, type = "nbinomial", size = 1)
distplot(Federalist, type = "nbinomial")
distplot(Saxony, type = "binomial", size = 12)

Doubledecker Plot

Description

This function creates a doubledecker plot visualizing a classification rule.

Usage

## S3 method for class 'formula'
doubledecker(formula, data = NULL, ..., main = NULL)
## Default S3 method:
doubledecker(x, depvar = length(dim(x)),
  margins = c(1,4, length(dim(x)) + 1, 1),
  gp = gpar(fill = rev(gray.colors(tail(dim(x), 1)))),
  labeling = labeling_doubledecker,
  spacing = spacing_highlighting,
  main = NULL, keep_aspect_ratio = FALSE, ...)

Arguments

formula

a formula specifying the variables used to create a contingency table from data. The dependent variable is used last for splitting.

data

either a data frame, or an object of class "table" or "ftable".

x

a contingency table in array form, with optional category labels specified in the dimnames(x) attribute.

depvar

dimension index or character string specifying the dependent variable. That will be sorted last in the table.

margins

margins of the plot. Note that by default, all factor names (except the last one) and their levels are visualized as a block under the plot.

gp

object of class "gpar" used for the tiles of the last variable.

labeling

labeling function or corresponding generating generating function (see strucplot for details).

spacing

spacing object, spacing function or corresponding generating function (see strucplot for details).

main

either a logical, or a character string used for plotting the main title. If main is TRUE, the name of the data object is used.

keep_aspect_ratio

logical indicating whether the aspect ratio should be maintained or not.

...

Further parameters passed to mosaic.

Details

Doubledecker plots visualize the the dependence of one categorical (typically binary) variable on further categorical variables. Formally, they are mosaic plots with vertical splits for all dimensions (antecedents) except the last one, which represents the dependent variable (consequent). The last variable is visualized by horizontal splits, no space between the tiles, and separate colors for the levels.

Value

The "structable" visualized is returned invisibly.

Author(s)

David Meyer [email protected]

References

H. Hoffmann (2001), Generalized odds ratios for visual modeling. Journal of Computational and Graphical Statistics, 10, 4, 628–640.

Meyer, D., Zeileis, A., and Hornik, K. (2006), The strucplot framework: Visualizing multi-way contingency tables with vcd. Journal of Statistical Software, 17(3), 1-48. doi:10.18637/jss.v017.i03 and available as vignette("strucplot").

See Also

strucplot, mosaic

Examples

data("Titanic")
doubledecker(Titanic)
doubledecker(Titanic, depvar = "Survived")
doubledecker(Survived ~ ., data = Titanic)

Employment Status

Description

Data from a 1974 Danish study given by Andersen (1991) on the employees who had been laid off. The workers are classified by their employment status on 1975-01-01, the cause of their layoff and the length of employment before they were laid off.

Usage

data("Employment")

Format

A 3-dimensional array resulting from cross-tabulating variables for 1314 employees. The variables and their levels are as follows:

No Name Levels
1 EmploymentStatus NewJob, Unemployed
2 EmploymentLength <1Mo, 1-3Mo, 3-12Mo, 1-2Yr, 2-5Yr, >5Yr
3 LayoffCause Closure, Replaced

Source

Michael Friendly (2000), Visualizing Categorical Data, pages 126–129.

References

E. B. Andersen (1991), The Statistical Analysis of Categorical Data. Springer-Verlag, Berlin.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("Employment")

## Employment Status
mosaic(Employment,
       expected = ~ LayoffCause * EmploymentLength + EmploymentStatus,
       main = "Layoff*EmployLength + EmployStatus")

mosaic(Employment,
       expected = ~ LayoffCause * EmploymentLength + LayoffCause * EmploymentStatus,
       main = "Layoff*EmployLength + Layoff*EmployStatus")

## Stratified view

grid.newpage()
pushViewport(viewport(layout = grid.layout(ncol = 2)))
pushViewport(viewport(layout.pos.col = 1))

## Closure
mosaic(Employment[,,1], main = "Layoff: Closure", newpage = FALSE)

popViewport(1)
pushViewport(viewport(layout.pos.col = 2))

## Replaced
mosaic(Employment[,,2], main = "Layoff: Replaced", newpage = FALSE)
popViewport(2)

‘May’ in Federalist Papers

Description

Data from Mosteller & Wallace (1984) investigating the use of certain keywords (‘may’ in this data set) to identify the author of 12 disputed ‘Federalist Papers’ by Alexander Hamilton, John Jay and James Madison.

Usage

data("Federalist")

Format

A 1-way table giving the number of occurrences of ‘may’ in 262 blocks of text. The variable and its levels are

No Name Levels
1 nMay 0, 1, ..., 6

Source

Michael Friendly (2000), Visualizing Categorical Data, page 19.

References

F. Mosteller & D. L. Wallace (1984), Applied Bayesian and Classical Inference: The Case of the Federalist Papers. Springer-Verlag, New York, NY.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("Federalist")
gf <- goodfit(Federalist, type = "nbinomial")
summary(gf)
plot(gf)

Fourfold Plots

Description

Creates an (extended) fourfold display of a 2×2×k2 \times 2 \times k contingency table, allowing for the visual inspection of the association between two dichotomous variables in one or several populations (strata).

Usage

fourfold(x,
  color = c("#99CCFF", "#6699CC", "#FFA0A0", "#A0A0FF", "#FF0000", "#000080"),
  conf_level = 0.95, std = c("margins", "ind.max", "all.max"),
  margin = c(1, 2), space = 0.2, main = NULL, sub = NULL,
  mfrow = NULL, mfcol = NULL, extended = TRUE, ticks = 0.15,
  p_adjust_method = p.adjust.methods, newpage = TRUE,
  fontsize = 12, default_prefix = c("Row", "Col", "Strata"),
  sep = ": ", varnames = TRUE, return_grob = FALSE)

Arguments

x

a 2×2×k2 \times 2 \times k contingency table in array form, or a 2×22 \times 2 matrix if kk is 1. If length(dim(x)>3, dimensions 3:length(dim(x) are silently raveled into a combined strata dimension with k=prod(dim(x)[-(1:2)])).

color

a vector of length 6 specifying the colors to use for the smaller and larger diagonals of each 2×22 \times 2 table. The first pair is used for the standard (non-extended) plots, the other two for the extended version: the second/third pair is used for tables with non-significant/significant log-odds ratios, respectively, the latter being visualized in brighter colors.

conf_level

confidence level used for the confidence rings on the odds ratios. Must be a single non-negative number less than 1; if set to 0, confidence rings are suppressed.

std

a character string specifying how to standardize the table. Must be one of "margins", "ind.max", or "all.max", and can be abbreviated by the initial letter. If set to "margins", each 2×22 \times 2 table is standardized to equate the margins specified by margin while preserving the odds ratio. If "ind.max" or "all.max", the tables are either individually or simultaneously standardized to a maximal cell frequency of 1.

margin

a numeric vector with the margins to equate. Must be one of 1, 2, or c(1, 2) (the default), which corresponds to standardizing only the row, only column, or both row and column in each 2×22 \times 2 table. Only used if std equals "margins".

space

the amount of space (as a fraction of the maximal radius of the quarter circles) used for the row and column labels.

main, sub

character string for the fourfold plot title/subtitle.

mfrow, mfcol

a numeric vector with two components: nr and nc, indicating that the displays for the 2×22 \times 2 tables should be arranged in an nr by nc layout, filled by rows/columns. The defaults are calculated to give a collection of plots in landscape orientation when k is not a perfect square.

extended

logical; if TRUE, extended plots are plotted, i.e., colors are brighter for significant log-odds ratios, and ticks are plotted showing the direction of association for positive log-odds.

ticks

the length of the ticks. If set to 0, no ticks are plotted.

p_adjust_method

method to be used for p-value adjustments for multi-stratum plots, as provided by link[stats]{p.adjust}. Use p_adjust_method="none" to disable this adjustment. The p-values are used for the ‘visual’ significance tests of the odds ratios.

newpage

logical; if TRUE, grid.newpage() is called before plotting.

fontsize

fontsize of main title. Other labels are scaled relative to this.

default_prefix

character vector of length 3 with default labels for possibly missing row/column/strata variable names.

sep

default separator between variable names and levels for labels.

varnames

Logical; should the variable names be printed in the labeling of stratifed plots?

return_grob

Logical; shall a snapshot of the display be returned as a grob object?

Details

The fourfold display is designed for the display of 2×2×k2 \times 2 \times k tables.

Following suitable standardization, the cell frequencies fijf_{ij} of each 2×22 \times 2 table are shown as a quarter circle whose radius is proportional to fij\sqrt{f_{ij}} so that its area is proportional to the cell frequency. An association (odds ratio different from 1) between the binary row and column variables is indicated by the tendency of diagonally opposite cells in one direction to differ in size from those in the other direction; color is used to show this direction. Confidence rings for the odds ratio allow a visual test of the null of no association; the rings for adjacent quadrants overlap iff the observed counts are consistent with the null hypothesis.

Typically, the number kk corresponds to the number of levels of a stratifying variable, and it is of interest to see whether the association is homogeneous across strata. The fourfold display visualizes the pattern of association. Note that the confidence rings for the individual odds ratios are not adjusted for multiple testing.

References

Friendly, M. (1994), A fourfold display for 2 by 2 by kk tables. Technical Report 217, York University, Psychology Department, http://datavis.ca/papers/4fold/4fold.pdf.

Friendly, M. (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

See Also

mosaic, assoc

link[stats]{p.adjust} for methods of p value adjustment

Examples

data("UCBAdmissions")
## Use the Berkeley admission data as in Friendly (1995).
x <- aperm(UCBAdmissions, c(2, 1, 3))
dimnames(x)[[2]] <- c("Yes", "No")
names(dimnames(x)) <- c("Sex", "Admit?", "Department")
ftable(x)

## Fourfold display of data aggregated over departments, with
## frequencies standardized to equate the margins for admission
## and sex.
## Figure 1 in Friendly (1994).
fourfold(margin.table(x, c(1, 2)))

## Fourfold display of x, with frequencies in each table
## standardized to equate the margins for admission and sex.
## Figure 2 in Friendly (1994).
fourfold(x)
cotabplot(x, panel = cotab_fourfold)

## Fourfold display of x, with frequencies in each table
## standardized to equate the margins for admission. but not
## for sex.
## Figure 3 in Friendly (1994).
fourfold(x, margin = 2)

Goodness-of-fit Tests for Discrete Data

Description

Fits a discrete (count data) distribution for goodness-of-fit tests.

Usage

goodfit(x, type = c("poisson", "binomial", "nbinomial"),
  method = c("ML", "MinChisq"), par = NULL)
## S3 method for class 'goodfit'
predict(object, newcount = NULL, type = c("response", "prob"), ...)
## S3 method for class 'goodfit'
residuals(object, type = c("pearson", "deviance",
"raw"), ...)
## S3 method for class 'goodfit'
print(x, residuals_type = c("pearson", "deviance",
"raw"), ...)

Arguments

x

either a vector of counts, a 1-way table of frequencies of counts or a data frame or matrix with frequencies in the first column and the corresponding counts in the second column.

type

character string indicating: for goodfit, which distribution should be fit; for predict, the type of prediction (fitted response or probabilities); for residuals, either "pearson", "deviance" or "raw".

residuals_type

character string indicating the type of residuals: either "pearson", "deviance" or "raw".

method

a character string indicating whether the distribution should be fit via ML (Maximum Likelihood) or Minimum Chi-squared.

par

a named list giving the distribution parameters (named as in the corresponding density function), if set to NULL, the default, the parameters are estimated. If the parameter size is not specified if type is "binomial" it is taken to be the maximum count. If type is "nbinomial", then parameter size can be specified to fix it so that only the parameter prob will be estimated (see the examples below).

object

an object of class "goodfit".

newcount

a vector of counts. By default the counts stored in object are used, i.e., the fitted values are computed. These can also be extracted by fitted(object).

...

currently not used.

Details

goodfit essentially computes the fitted values of a discrete distribution (either Poisson, binomial or negative binomial) to the count data given in x. If the parameters are not specified they are estimated either by ML or Minimum Chi-squared.

To fix parameters, par should be a named list specifying the parameters lambda for "poisson" and prob and size for "binomial" or "nbinomial", respectively. If for "binomial", size is not specified it is not estimated but taken as the maximum count.

The corresponding Pearson Chi-squared or likelihood ratio statistic, respectively, is computed and given with their pp values by the summary method. The summary method always prints this information and returns a matrix with the printed information invisibly. The plot method produces a rootogram of the observed and fitted values.

In case of count distribtions (Poisson and negative binomial), the minimum Chi-squared approach is somewhat ad hoc. Strictly speaking, the Chi-squared asymptotics would only hold if the number of cells were fixed or did not increase too quickly with the sample size. However, in goodfit the number of cells is data-driven: Each count is a cell of its own. All counts larger than the maximal count are merged into the cell with the last count for computing the test statistic.

Value

A list of class "goodfit" with elements:

observed

observed frequencies.

count

corresponding counts.

fitted

expected frequencies (fitted by ML).

type

a character string indicating the distribution fitted.

method

a character string indicating the fitting method (can be either "ML", "MinChisq" or "fixed" if the parameters were specified).

df

degrees of freedom.

par

a named list of the (estimated) distribution parameters.

Author(s)

Achim Zeileis [email protected]

References

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

See Also

rootogram

Examples

## Simulated data examples:
dummy <- rnbinom(200, size = 1.5, prob = 0.8)
gf <- goodfit(dummy, type = "nbinomial", method = "MinChisq")
summary(gf)
plot(gf)

dummy <- rbinom(100, size = 6, prob = 0.5)
gf1 <- goodfit(dummy, type = "binomial", par = list(size = 6))
gf2 <- goodfit(dummy, type = "binomial", par = list(prob = 0.6, size = 6))
summary(gf1)
plot(gf1)
summary(gf2)
plot(gf2)

## Real data examples:
data("HorseKicks")
HK.fit <- goodfit(HorseKicks)
summary(HK.fit)
plot(HK.fit)

data("Federalist")
## try geometric and full negative binomial distribution
F.fit <- goodfit(Federalist, type = "nbinomial", par = list(size = 1))
F.fit2 <- goodfit(Federalist, type = "nbinomial")
summary(F.fit)
summary(F.fit2)
plot(F.fit)
plot(F.fit2)

Barplot

Description

Bar plots of 1-way tables in grid.

Usage

grid_barplot(height, width = 0.8, offset = 0,
  names = NULL, xlim = NULL, ylim = NULL, xlab = "", ylab = "", main = "",
  gp = gpar(fill = "lightgray"), name = "grid_barplot",
  newpage = TRUE, pop = FALSE, return_grob = FALSE)

Arguments

height

either a vector or a 1-way table of frequencies.

width

width of the bars (recycled if needed to the number of bars).

offset

offset of the bars (recycled if needed to the number of bars).

names

a vector of names for the bars, if set to NULL the names of height are used.

xlim

limits for the x axis.

ylim

limits for the y axis.

xlab

a label for the x axis.

ylab

a label for the y axis.

main

a title for the plot.

gp

a "gpar" object controlling the grid graphical parameters of the rectangles.

name

name of the plotting viewport.

newpage

logical. Should grid.newpage be called before plotting?

pop

logical. Should the viewport created be popped?

return_grob

logical. Shall the plot be returned as a grob object?

Details

grid_barplot mimics (some of) the features of barplot, but currently it only supports 1-way tables.

Author(s)

Achim Zeileis [email protected]

Examples

grid_barplot(sample(1:6), names = letters[1:6])

Legend Function for grid Graphics

Description

This function can be used to add legends to grid-based plots.

Usage

grid_legend(x, y, pch = NA, col = par('col'), labels, frame = TRUE,
            hgap = unit(0.8, "lines"), vgap = unit(0.8, "lines"),
            default_units = "lines", gp = gpar(), draw = TRUE,
            title = NULL, just = 'center', lwd = NA, lty = NA,
            size = 1,
            gp_title = NULL, gp_labels = NULL,
            gp_frame = gpar(fill = "transparent"),
            inset = c(0, 0))

Arguments

x

character string "topright", "topleft", "bottomright", "bottomleft", "top", "bottom", "left", "right", "center" or x coordinate of the legend.

y

y coordinates of the legend.

pch

integer vector of plotting symbols, if any.

col

character vector of colors for the symbols.

labels

character vector of labels corresponding to the symbols.

frame

logical indicating whether the legend should have a border or not.

hgap

object of class "unit" specifying the space between symbols and labels.

vgap

object of class "unit" specifying the space between the lines.

default_units

character string indicating the default unit.

gp

object of class "gpar" used for the legend.

draw

logical indicating whether the legend be drawn or not.

title

character string indicating the plot's title.

just

justification of the legend relative to its (x, y) location. see ?viewport for more details.

lwd

positive number to set the line width. if specified lines are drawn.

lty

line type. if specified lines are drawn.

size

size of the group symbols (in char units).

gp_title

object of class "gpar" used for the title.

gp_labels

object of class "gpar" used for the labels.

gp_frame

object of class "gpar" used for the frame.

inset

numeric vector of length 2 specifying the inset of the legend in npc units, relative to the specified x and y coordinates.

Value

Invisibly, the legend as a "grob" object.

Author(s)

David Meyer [email protected] Florian Gerber [email protected]

See Also

legend

Examples

data("Lifeboats")
attach(Lifeboats)
ternaryplot(Lifeboats[,4:6],
  pch = ifelse(side == "Port", 1, 19),
  col = ifelse(side == "Port", "red", "blue"),
  id  = ifelse(men / total > 0.1, as.character(boat), NA),
  prop_size = 2,
  dimnames_position = "edge",
  main = "Lifeboats on Titanic")
grid_legend(0.8, 0.9, c(1, 19), c("red", "blue"),
  c("Port", "Starboard"), title = "SIDE")


grid.newpage()
pushViewport(viewport(height = .9, width = .9 ))
grid.rect(gp = gpar(lwd = 2, lty = 2))

grid_legend(x = unit(.05,'npc'),
            y = unit(.05,'npc'),
            just = c(0,0),
            pch = c(1,2,3),
            col = c(1,2,3),
            lwd=NA, 
            lty=NA,
            labels = c("b",'r','g'),
            title = NULL,
            gp=gpar(lwd=2, cex=1),
            hgap = unit(.8, "lines"),
            vgap = unit(.9, "lines"))

grid_legend(x = unit(1,'npc'),
            y = unit(1,'npc'),
            just = c(1,1),
            pch = NA,
            col = c(1,2,3,4),
            lwd=c(1,1,1,3), 
            lty=c(1,2,1,3),
            labels = c("black",'red','green','blue'),
            gp_labels = list(gpar(col = 1), gpar(col = 2), gpar(col = 3), gpar(col = 4)),
            title = NULL,
            gp=gpar(lwd=2, cex=1),
            hgap = unit(.8, "lines"),
            vgap = unit(.9, "lines"))

grid_legend(x = 'topleft',
            pch = c(1,NA,2,NA),
            col = c(1,2,3,4),
            lwd=NA, 
            lty=c(NA,2,NA,3),
            labels = c("black",'red','green','blue'),
            title = 'Some LONG Title',
            gp_title = gpar(col = 3),
            gp_frame = gpar(col = 4, lty = 2, fill = "transparent"),
            gp_labels = gpar(col = 6),
            gp=gpar(lwd=2, cex=2, col = 1),
            hgap = unit(.8, "lines"),
            vgap = unit(.9, "lines"))

grid_legend(x = .7,
            y = .7,
            pch = c(1,NA,2,NA),
            col = c(1,2,3,4),
            lwd=1, 
            lty=c(NA,2,NA,3),
            labels = c("black",'red','green','blue'),
            title = 'short T',
            gp=gpar(lwd=1, cex=.7,col = 1),
            hgap = unit(.8, "lines"),
            vgap = unit(.9, "lines"))

grid_legend(x = 'bottomright',
            pch = c(1,NA,2,NA),
            col = c(2),
            lwd=NA, 
            lty=c(NA,2,NA,3),
            labels = c("black",'red','green','blue'),
            title = NULL,
            gp=gpar(lwd=2, cex=1,col = 1),
            hgap = unit(.8, "lines"),
            vgap = unit(.9, "lines"))

Hitters Data

Description

This data set is deduced from the Baseball fielding data set: fielding performance basically includes the numbers of Errors, Putouts and Assists made by each player. In order to reduce the number of observations, the was compressed by calculating the mean number of errors, putouts and assists for each team and for only 6 positions (1B, 2B, 3B, C, OF, SS and UT). In addition, each of these three variables was scaled to a common range by dividing each variable by the maximum of the variable.

Usage

data("Hitters")

Format

A data frame with 154 observations and 4 variables.

Positions

factor indicating the field position (1B=first baseman, 2B=second baseman, 3B=third baseman, C=catcher, OF=outfielder, SS=Short Stop, UT=Utility Players).

Putouts

occur when a fielder causes an opposing player to be tagged or forced out.

Assists

are credited to other fielders involved in making that putout.

Errors

count the errors made by a player.

Source

SAS System for Statistical Graphics, First Edition, Page A2.3

References

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("Hitters")
attach(Hitters)

colors <- c("black","red","green","blue","red","black","blue")
pch <- substr(levels(Positions), 1, 1)
ternaryplot(Hitters[,2:4],
  pch = as.character(Positions),
  col = colors[as.numeric(Positions)],
  main = "Baseball Hitters Data")
grid_legend(0.8, 0.9, pch, colors, levels(Positions),
  title = "POSITION(S)")

detach(Hitters)

HLS Color Specification

Description

Create a HLS color from specifying hue, luminance and saturation.

Usage

hls(h = 1, l = 0.5, s = 1)

Arguments

h

hue value in [0, 1].

l

luminance value in [0, 1].

s

saturation value in [0, 1].

Details

HLS colors are a similar specification of colors as HSV colors, but using hue/luminance/saturation rather that hue/saturation/value.

Author(s)

Achim Zeileis [email protected]

See Also

hsv, hcl2hex, polarLUV

Examples

## an HLS color wheel
pie(rep(1, 12), col = sapply(1:12/12, function(x) hls(x)))

Death by Horse Kicks

Description

Data from von Bortkiewicz (1898), given by Andrews & Herzberg (1985), on number of deaths by horse or mule kicks in 10 (of 14 reported) corps of the Prussian army. 4 corps were not considered by Fisher (1925) as they had a different organization. This data set is a popular subset of the VonBort data.

Usage

data("HorseKicks")

Format

A 1-way table giving the number of deaths in 200 corps-years. The variable and its levels are

No Name Levels
1 nDeaths 0, 1, ..., 4

Source

Michael Friendly (2000), Visualizing Categorical Data, page 18.

References

D. F. Andrews & A. M. Herzberg (1985), Data: A Collection of Problems from Many Fields for the Student and Research Worker. Springer-Verlag, New York, NY.

R. A. Fisher (1925), Statistical Methods for Research Workers. Oliver & Boyd, London.

L. von Bortkiewicz (1898), Das Gesetz der kleinen Zahlen. Teubner, Leipzig.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

See Also

VonBort

Examples

data("HorseKicks")
gf <- goodfit(HorseKicks)
summary(gf)
plot(gf)

Hospital data

Description

The table relates the length of stay (in years) of 132 long-term schizophrenic patients in two London mental hospitals with the frequency of visits.

Usage

data("Hospital")

Format

A 2-dimensional array resulting from cross-tabulating 132 patients. The variables and their levels are as follows:

No Name Levels
1 Visit Frequency Regular, Less than monthly, Never
2 Length of Stay 2--9 years, 10--19 years, 20+ years

Details

Wing (1962) who collected this data concludes that the longer the length of stay in hospital, the less frequent the visits.

Haberman (1974) notes that this pattern does not increase from the "Less than monthly" to the "Never" group, which are homogeneous.

Source

S.J Haberman (1974): Log-linear models for frequency tables with ordered classifications. Biometrics, 30:689–700.

References

J.K. Wing (1962): Institutionalism in mental hospitals. British Journal of Social Clinical Psychology, 1:38–51.

Examples

data("Hospital")

mosaic(t(Hospital), shade = TRUE)
mosaic(Hospital, shade = TRUE)
sieve(Hospital, shade = TRUE)
assoc(Hospital, shade = TRUE)

Independence Table

Description

Computes table of expected frequencies (under the null hypotheses of independence) from an nn-way table.

Usage

independence_table(x, frequency = c("absolute", "relative"))

Arguments

x

a table.

frequency

indicates whether absolute or relative frequencies should be computed.

Value

A table with either absolute or relative frequencies.

Author(s)

David Meyer [email protected]

Examples

data("MSPatients")
independence_table(MSPatients)
independence_table(MSPatients, frequency = "relative")

Job Satisfaction Data

Description

Data from Petersen (1968) about the job satisfaction of 715 blue collar workers, selected from Danish Industry in 1968.

Usage

data("JobSatisfaction")

Format

A data frame with 8 observations and 4 variables.

Freq

frequency.

management

factor indicating quality of management (bad, good).

supervisor

factor indicating supervisor's job satisfaction (low, high).

own

factor indicating worker's own job satisfaction (low, high).

Source

E. B. Andersen (1991), The Statistical Analysis of Categorical Data, Table 5.4.

References

E. B. Andersen (1991), The Statistical Analysis of Categorical Data. 2nd edition. Springer-Verlag, Berlin.

E. Petersen (1968), Job Satisfaction in Denmark. (In Danish). Mentalhygiejnisk Forlag, Copenhagen.

Examples

data("JobSatisfaction")
structable(~ ., data = JobSatisfaction)

mantelhaen.test(xtabs(Freq ~ own + supervisor + management,
                      data = JobSatisfaction))

Opinions About Joint Sports

Description

Data from a Danish study in 1983 and 1985 about sports activities and the opinion about joint sports with the other gender among 16–19 year old high school students.

Usage

data("JointSports")

Format

A data frame with 40 observations and 5 variables.

Freq

frequency.

opinion

factor indicating opinion about sports joint with the other gender (very good, good, indifferent, bad, very bad).

year

factor indicating year of study (1983, 1985).

grade

factor indicating school grade (1st, 3rd).

gender

factor indicating gender (Boy, Girl).

Source

E. B. Andersen (1991), The Statistical Analysis of Categorical Data, page 210.

References

E. B. Andersen (1991), The Statistical Analysis of Categorical Data. 2nd edition. Springer-Verlag, Berlin.

Examples

library(MASS)
data("JointSports")
tab <- xtabs(Freq ~ gender + opinion + grade + year, data = JointSports)
doubledecker(opinion ~ gender + year + grade, data = tab)
loglm(~ opinion* (gender + grade+ year) + gender*year*grade, data = tab)

Cohen's Kappa and Weighted Kappa

Description

Computes two agreement rates: Cohen's kappa and weighted kappa, and confidence bands.

Usage

Kappa(x, weights = c("Equal-Spacing", "Fleiss-Cohen"))
## S3 method for class 'Kappa'
print(x, digits=max(getOption("digits") - 3, 3),
CI=FALSE, level=0.95, ...)
## S3 method for class 'Kappa'
confint(object, parm, level = 0.95, ...)
## S3 method for class 'Kappa'
summary(object, ...)
## S3 method for class 'summary.Kappa'
print(x, ...)

Arguments

x

For Kappa: a confusion matrix. For the print methods: object of class "Kappa" or "summary.Kappa"

weights

either one of the character strings given in the default value, or a user-specified matrix with same dimensions as x.

digits

minimal number of significant digits.

CI

logical; shall confidence limits be added to the output?

level

confidence level between 0 and 1 used for the confidence interval.

object

object of class "Kappa".

parm

Currently, ignored.

...

Further arguments passed to the default print method.

Details

Cohen's kappa is the diagonal sum of the (possibly weighted) relative frequencies, corrected for expected values and standardized by its maximum value. The equal-spacing weights are defined by 1ij/(r1)1 - |i - j| / (r - 1), rr number of columns/rows, and the Fleiss-Cohen weights by 1ij2/(r1)21 - |i - j|^2 / (r - 1)^2. The latter one attaches greater importance to near disagreements.

Value

An object of class "Kappa" with three components:

Unweighted

numeric vector of length 2 with the kappa statistic (value component), along with Approximate Standard Error (ASE component)

Weighted

idem for the weighted kappa.

Weights

numeric matrix with weights used.

Note

The summary method also prints the weights.

There is a confint method for computing approximate confidence intervals.

Author(s)

David Meyer [email protected]

References

Cohen, J. (1960), A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20, 37–46.

Everitt, B.S. (1968), Moments of statistics kappa and weighted kappa. The British Journal of Mathematical and Statistical Psychology, 21, 97–103.

Fleiss, J.L., Cohen, J., and Everitt, B.S. (1969), Large sample standard errors of kappa and weighted kappa. Psychological Bulletin, 72, 332–327.

See Also

agreementplot, confint

Examples

data("SexualFun")
K <- Kappa(SexualFun)
K
confint(K)
summary(K)
print(K, CI = TRUE)

Labeling Functions for Strucplots

Description

These functions generate labeling functions used for strucplots.

Usage

labeling_border(labels = TRUE, varnames = labels,
  set_labels = NULL, set_varnames = NULL, 
  tl_labels = NULL, alternate_labels = FALSE, tl_varnames = NULL, 
  gp_labels = gpar(fontsize = 12),
  gp_varnames = gpar(fontsize = 12, fontface = 2),
  rot_labels = c(0, 90, 0, 90), rot_varnames = c(0, 90, 0, 90),
  pos_labels = "center", pos_varnames = "center",
  just_labels = "center", just_varnames = pos_varnames,
  boxes = FALSE, fill_boxes = FALSE,
  offset_labels = c(0, 0, 0, 0), offset_varnames = offset_labels,
  labbl_varnames = NULL, labels_varnames = FALSE, sep = ": ",
  abbreviate_labs = FALSE, rep = TRUE, clip = FALSE, ...)
labeling_values(value_type = c("observed", "expected", "residuals"),
                suppress = NULL, digits = 1, clip_cells = FALSE, ...)
labeling_residuals(suppress = NULL, digits = 1, clip_cells = FALSE, ...)
labeling_conditional(...)
labeling_left(rep = FALSE, pos_varnames = "left",
  pos_labels = "left", just_labels = "left", ...)
labeling_left2(tl_labels = TRUE, clip = TRUE, pos_varnames = "left",
  pos_labels = "left", just_labels = "left", ...)
labeling_cboxed(tl_labels = TRUE, boxes = TRUE, clip = TRUE,
  pos_labels = "center", ...)
labeling_lboxed(tl_labels = FALSE, boxes = TRUE, clip = TRUE,
  pos_labels = "left", just_labels = "left",
  labbl_varnames = FALSE, ...)
labeling_doubledecker(lab_pos = c("bottom", "top"), dep_varname = TRUE,
  boxes = NULL, clip = NULL, labbl_varnames = FALSE,
  rot_labels = rep.int(0, 4),
  pos_labels = c("left", "center", "left", "center"),
  just_labels = c("left", "left", "left", "center"),
  varnames = NULL, gp_varnames = gpar(fontsize = 12, fontface = 2),
  offset_varnames = c(0, -0.6, 0, 0), tl_labels = NULL, ...)

Arguments

labels

vector of logicals indicating whether labels should be drawn for a particular dimension.

varnames

vector of logicals indicating whether variable names should be drawn for a particular dimension.

set_labels

An optional character vector with named components replacing the so-specified variable names. The component names must exactly match the variable names to be replaced.

set_varnames

An optional list with named components of character vectors replacing the labels of the so-specified variables. The component names must exactly match the variable names whose labels should be replaced.

tl_labels

vector of logicals indicating whether labels should be positioned on top (column labels) / left (row labels) for a particular dimension.

alternate_labels

vector of logicals indicating whether labels should be alternated on the top/bottom (left/right) side of the plot for a particular dimension.

tl_varnames

vector of logicals indicating whether variable names should be positioned on top (column labels) / on left (row labels) for a particular dimension.

gp_labels

list of objects of class "gpar" used for drawing the labels.

gp_varnames

list of objects of class "gpar" used for drawing the variable names.

rot_labels

vector of rotation angles for the labels for each of the four sides of the plot.

rot_varnames

vector of rotation angles for the variable names for each of the four sides of the plot.

pos_labels

character string of label positions ("left", "center", "right") for each of the variables.

pos_varnames

character string of variable names positions ("left", "center", "right") for each of the four sides of the plot.

just_labels

character string of label justifications ("left", "center", "right") for each of the variables.

just_varnames

character string of variable names justifications ("left", "center", "right") for each of the four sides of the plot.

boxes

vector of logicals indicating whether boxes should be drawn around the labels for a particular dimension.

fill_boxes

Either a vector of logicals, or a vector of characters, or a list of such vectors, specifying the fill colors for the boxes. "TRUE" and "FALSE" values are transformed into "grey" and "white", respectively. If fill_boxes is atomic, each component specifies a basic color for the corresponding dimension. This color is transformed into its HSV representation, and the value is varied from 50% to 100% to give a sequential color palette for the levels. For NA components, no palette is produced (no fill color). If fill_boxes is a list of vectors, each vector specifies the level colors of the corresponding dimension.

offset_labels, offset_varnames

numeric vector of length 4 indicating the offset of the labels (variable names) for each of the four sides of the plot.

labbl_varnames

vector of logicals indicating whether variable names should be drawn on the left (column variables) / on top (row variables) of the corresponding labels.

labels_varnames

vector of logicals indicating, for each dimension, whether the variable name should be added to the corresponding labels or not.

sep

separator used if any component of "labels_varnames" is TRUE.

abbreviate_labs

vector of integers or logicals indicating, for each dimension, the number of characters the labels should be abbreviated to. TRUE means 1 character, FALSE causes no abbreviation. Values are recycled as needed.

rep

vector of logicals indicating, for each dimension, whether labels should be repeated for all conditioning strata, or appear only once.

clip

vector of integers indicating, for each dimension, whether labels should be clipped to not overlap.

lab_pos

character string switching between "top" or "bottom" position of the labels (only used for labeling_doubledecker).

dep_varname

logical or character string. If logical, this is indicating whether the name of the dependent variable should be printed or not. A character string will be printed instead of the variable name taken from the dimnames.

value_type

character string specifying which values should be displayed in the cells.

suppress

numeric vector of length 2 specifying an interval of values that are not displayed. 0 values are never displayed. A single number, k, is treated as c(-k, k). The default for labeling residuals is c(-2,2). Use suppress = 0 to show all non-zero values.

digits

integer specifying the number of digits used for rounding.

clip_cells

logical indicating whether the values should be clipped at the cell borders.

...

only used for labeling_conditional and labeling_doubledecker: parameters passed to labeling_cells and labeling_border.

Details

These functions generate labeling functions called by strucplot for their side-effect of adding labels to the plot. They suppose that a strucplot has been drawn and the corresponding viewport structure is pushed, since the positions of the viewports are used for the label positioning. Note that the functions can also be used ‘stand-alone’ as shown in the examples.

All values supplied to vectorized arguments can be ‘abbreviated’ by using named components which override the default component values. In addition, these defaults can be overloaded by the sequence of non-named components which are recycled as needed (see examples).

This help page only documents labeling_border and derived functions, more functions are described on the help page for labeling_cells and labeling_list.

labeling_left, labeling_left2, labeling_cboxed, and labeling_lboxed are really just wrappers to labeling_border, and good examples for the parameter usage.

labeling_residuals is a trivial wrapper for labeling_values, which in turn calls labeling_border by additionally adding the observed or expected frequencies or residuals to the cells.

Value

A function with arguments:

d

"dimnames" attribute from the visualized contingency table, or the visualized table itself from which the "dimnames" attributes will then be extracted.

split_vertical

vector of logicals indicating the split directions.

condvars

integer vector of conditioning dimensions.

Author(s)

David Meyer [email protected]

References

Meyer, D., Zeileis, A., and Hornik, K. (2006), The strucplot framework: Visualizing multi-way contingency tables with vcd. Journal of Statistical Software, 17(3), 1-48. doi:10.18637/jss.v017.i03 and available as vignette("strucplot").

See Also

labeling_cells, labeling_list, structable, grid.text

Examples

data("Titanic")

mosaic(Titanic)

mosaic(Titanic, labeling = labeling_left)
labeling_left

mosaic(Titanic, labeling = labeling_cboxed)
labeling_cboxed

mosaic(Titanic, labeling = labeling_lboxed)
labeling_lboxed

data("PreSex")
mosaic(~ PremaritalSex + ExtramaritalSex | Gender + MaritalStatus,
  data = PreSex, labeling = labeling_conditional)

## specification of vectorized arguments 
mosaic(Titanic, labeling_args = list(abbreviate_labs = c(Survived = TRUE)))

mosaic(Titanic, labeling_args = list(clip = TRUE, boxes = TRUE,
  fill_boxes = c(Survived = "green", "red")))

mosaic(Titanic, labeling_args = list(clip = TRUE, boxes = TRUE,
  fill_boxes = list(Sex = "red", "green")))

mosaic(Titanic, labeling_args = list(clip = TRUE, boxes = TRUE,
  fill_boxes = list(Sex = c(Male = "red", "blue"), "green")))

## change variable names
mosaic(Titanic, labeling_args = list(set_varnames = c(Sex = "Gender")))

## change labels
mosaic(Titanic, labeling_args = list(set_varnames = c(Survived = "Status"),
  set_labels = list(Survived = c("Survived", "Not Survived")), rep = FALSE))

## show frequencies
mosaic(Titanic, labeling = labeling_values)

Labeling Functions for Strucplots

Description

These functions generate labeling functions that produce labels for strucplots.

Usage

labeling_cells(labels = TRUE, varnames = TRUE,
  abbreviate_labels = FALSE, abbreviate_varnames = FALSE,
  gp_text = gpar(), lsep = ": ", lcollapse = "\n",
  just = "center", pos = "center", rot = 0,
  margin = unit(0.5, "lines"), clip_cells = TRUE,
  text = NULL, ...)
labeling_list(gp_text = gpar(), just = "left", pos = "left", lsep = ": ",
  sep = " ", offset = unit(c(2, 2), "lines"),
  varnames = TRUE, cols = 2, ...)

Arguments

labels

vector of logicals indicating, for each dimension, whether labels for the factor levels should be drawn or not. Values are recycled as needed.

varnames

vector of logicals indicating, for each dimension, whether variable names should be drawn. Values are recycled as needed.

abbreviate_labels

vector of integers or logicals indicating, for each dimension, the number of characters the labels should be abbreviated to. TRUE means 1 character, FALSE causes no abbreviation. Values are recycled as needed.

abbreviate_varnames

vector of integers or logicals indicating, for each dimension, the number of characters the variable (i.e., dimension) names should be abbreviated to. TRUE means 1 character, FALSE causes no abbreviation. Values are recycled as needed.

gp_text

object of class "gpar" used for the text drawn.

lsep

character that separates variable names from the factor levels.

sep

character that separates the factor levels (only used for labeling_list).

offset

object of class "unit" of length 2 specifying the offset in x- and y-direction of the text block drawn under the strucplot (only used for labeling_list).

cols

number of text columns (only used for labeling_list).

lcollapse

character that separates several variable name/factor level-combinations. Typically a line break. (Only used for labeling_cells.)

just, pos

character string of length 1 (labeling_list) or at most 2 (labeling_cells) specifying the labels' horizontal position and justification (horizontal and vertical for labeling_cells).

rot

rotation angle in degrees, used for all labels (only used for labeling_cells).

margin

object of class "unit" (a numeric value is converted to "lines") specifying an offset from the cell borders (only used for labeling_cells).

clip_cells

logical indicating whether text should be clipped at the cell borders (only used for labeling_cells).

text

Optionally, a character table of the same dimensions than the contingency table whose entries will then be used instead of the labels. NA entries are not drawn. This allows custom cell annotations (see examples). Only used for labeling_cells.

...

Currently not used.

Details

These functions generate labeling functions that can add different kinds of labels to an existing plot. Typically they are supplied to strucplot which then generates and calls the labeling function. They assume that a strucplot has been drawn and the corresponding viewport structure is pushed, so that by navigating through the viewport tree the labels can be positioned appropriately.

This help page only documents labeling_list and labeling_cells; more functions are described on the help page for labeling_border.

The functions can also be used ‘stand-alone’ as shown in the examples.

Using labeling_list will typically necessitate a bottom margin adjustment.

Value

A function with arguments:

d

"dimnames" attribute from the visualized contingency table, or the visualized table itself from which the "dimnames" attributes will then be extracted.

split_vertical

vector of logicals indicating the split directions.

condvars

integer vector of conditioning dimensions

Author(s)

David Meyer [email protected]

References

Meyer, D., Zeileis, A., and Hornik, K. (2006), The strucplot framework: Visualizing multi-way contingency tables with vcd. Journal of Statistical Software, 17(3), 1-48. doi:10.18637/jss.v017.i03 and available as vignette("strucplot").

See Also

labeling_border, structable, grid.text

Examples

data("Titanic")

mosaic(Titanic, labeling = labeling_cells)
mosaic(Titanic, labeling = labeling_list)

## A more complex example, adding the observed frequencies
## to a mosaic plot:
tab <- ifelse(Titanic < 6, NA, Titanic)
mosaic(Titanic, pop = FALSE)
labeling_cells(text = tab, margin = 0)(Titanic)

Legend Functions for Strucplots

Description

These functions generate legend functions for residual-based shadings.

Usage

legend_resbased(fontsize = 12, fontfamily = "",
  x = unit(1, "lines"), y = unit(0.1,"npc"),
  height = unit(0.8, "npc"),
  width = unit(0.7, "lines"),
  digits = 2, pdigits = max(1, getOption("digits") - 2),
  check_overlap = TRUE, text = NULL,
  steps = 200, ticks = 10, pvalue = TRUE,  range = NULL)
legend_fixed(fontsize = 12, fontfamily = "", x = unit(1, "lines"), y = NULL,
  height = NULL, width = unit(1.5, "lines"), steps = 200,
  digits = 1, space = 0.05, text = NULL, range = NULL)

Arguments

fontsize

fontsize of title and p-value text.

fontfamily

fontfamily of all text.

x, y

objects of class "unit" indicating the coordinates of the title. For legend_fixed, the default for y is computed as to leave enough space for the specified text.

height, width

object of class "unit" indicating the height/width of the legend. For legend_fixed, the default for y is computed as to align upper margins of legend and actual plot.

digits

number of digits for the scale labels.

pdigits

number of digits for the p-value.

check_overlap

logical indicating whether overlap of scale labels should be inhibited or not.

space

For legend_fixed only: proportion of space between the tiles.

text

character string indicating the title of the legend.

steps

granularity of the color gradient.

ticks

number of scale ticks.

pvalue

logical indicating whether the pp-value should be visualized under the scale or not.

range

Numeric vector of length 2 for setting the legend range. Computed from the residuals if omitted. NA values are replaced by the corresponding minimum / maximum of the residuals.

Details

These functions generate legend functions for residual-based shadings, visualizing deviations from expected values of an hypothesized independence model. Therefore, the legend uses a supplied shading function to visualize the color gradient for the residuals range. legend_fixed is inspired by the legend used in mosaicplot. For more details on the shading functions and their return values, see shadings.

Value

A function with arguments:

residuals

residuals from the fitted independence model to be visualized.

shading

shading function computing colors from residuals (see details).

autotext

character vector indicating the title to be used when no text argument is specified. Allows strucplot to generate sensible defaults depending on the residuals type.

Author(s)

David Meyer [email protected]

References

Meyer, D., Zeileis, A., and Hornik, K. (2006), The strucplot framework: Visualizing multi-way contingency tables with vcd. Journal of Statistical Software, 17(3), 1-48. doi:10.18637/jss.v017.i03 and available as vignette("strucplot").

Meyer, D., Zeileis, A., Hornik, K. (2003), Visualizing independence using extended association plots. Proceedings of the 3rd International Workshop on Distributed Statistical Computing, K. Hornik, F. Leisch, A. Zeileis (eds.), ISSN 1609-395X. https://www.R-project.org/conferences/DSC-2003/Proceedings/

See Also

structable, shadings

Examples

data("Titanic")

mosaic(Titanic, shade = TRUE, legend = legend_resbased)
mosaic(Titanic, shade = TRUE, legend = legend_fixed, gp = shading_Friendly)

Lifeboats on the Titanic

Description

Data from Mersey (1912) about the 18 (out of 20) lifeboats launched before the sinking of the S. S. Titanic.

Usage

data("Lifeboats")

Format

A data frame with 18 observations and 8 variables.

launch

launch time in "POSIXt" format.

side

factor. Side of the boat.

boat

factor indicating the boat.

crew

number of male crew members on board.

men

number of men on board.

women

number of women (including female crew) on board.

total

total number of passengers.

cap

capacity of the boat.

Source

M. Friendly (2000), Visualizing Categorical Data: http://euclid.psych.yorku.ca/ftp/sas/vcd/catdata/lifeboat.sas

References

L. Mersey (1912), Report on the loss of the “Titanic” (S. S.). Parliamentary command paper 6452.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("Lifeboats")
attach(Lifeboats)
ternaryplot(
  Lifeboats[,4:6],
  pch = ifelse(side == "Port", 1, 19),
  col = ifelse(side == "Port", "red", "blue"),
  id  = ifelse(men / total > 0.1, as.character(boat), NA),
  prop_size = 2,
  dimnames_position = "edge",
  main = "Lifeboats on the Titanic"
)
grid_legend(0.8, 0.9, c(1, 19), c("red", "blue"),
  c("Port", "Starboard"), title = "SIDE")
detach(Lifeboats)

Calculate Generalized Log Odds for Frequency Tables

Description

Computes (log) odds and their asymptotic variance covariance matrix for R (by strata) tables. Odds are calculated for pairs of levels of one array dimension (typically a response or focal variable) separately for each level of all stratifying dimensions. See Friendly et al. (2011) for a sketch of a general theory.

Usage

lodds(x, ...)
## Default S3 method:
lodds(x, response = NULL, strata = NULL, log = TRUE, 
  ref = NULL, correct = any(x == 0), ...)

## S3 method for class 'formula'
lodds(formula, data = NULL, ...,
subset = NULL, na.action = NULL)

odds(x, log = FALSE, ...)

## S3 method for class 'lodds'
coef(object, log = object$log, ...)
## S3 method for class 'lodds'
vcov(object, log = object$log, ...)
## S3 method for class 'lodds'
print(x, log = x$log, ...)
## S3 method for class 'lodds'
confint(object, parm, level = 0.95, log = object$log, ...)

## S3 method for class 'lodds'
dim(x, ...)
## S3 method for class 'lodds'
dimnames(x, ...)
## S3 method for class 'lodds'
as.array(x, log=x$log, ...)
## S3 method for class 'lodds'
t(x)
## S3 method for class 'lodds'
aperm(a, perm, ...)

Arguments

x

an object. For the default method a k-way matrix/table/array of frequencies. The number of margins has to be at least 2.

response

Numeric or character indicating the margin of a $k$-way table x (with $k$ greater than 2) that should be employed as the response variable. By default the first dimension is used.

strata

Numeric or character indicating the margins of a $k$-way table x (with $k$ greater than 2) that should be employed as strata. Ignored if response is specified. By default all dimensions except the first are used as strata.

ref

numeric or character. Reference categories for the (non-stratum) row and column dimensions that should be employed for computing the odds. By default, odds for profile contrasts (or sequential contrasts, i.e., successive differences of adjacent categories) are used. See details below.

formula

a formula specifying the variables used to create a contingency table from data. A conditioning formula can be specified; the conditioning variables will then be used as strata variables.

data

either a data frame, or an object of class "table" or "ftable".

subset

an optional vector specifying a subset of observations to be used.

na.action

a function which indicates what should happen when the data contain NAs. Ignored if data is a contingency table.

log

logical. Should the results be displayed on a log scale or not? All internal computations are always on the log-scale but the results are transformed by default if log = TRUE.

correct

logical or numeric. Should a continuity correction be applied before computing odds? If TRUE, 0.5 is added to all cells; if numeric (or an array conforming to the data) that value is added to all cells. By default, this not employed unless there are any zero cells in the table, but this correction is often recommended to reduce bias when some frequencies are small (Fleiss, 1981).

a, object

an object of class lodds as computed by lodds.

perm

numeric or character vector specifying a permutation of strata.

...

arguments passed to methods.

parm

a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.

level

the confidence level required for the confint method.

Details

For an n-way table with the response variable containing R levels, (log) odds are formed (by default) for the set of (R-1) contrasts among the response levels. The ref argument allows these to be specified in a general way.

ref = NULL (default) corresponds to “profile contrasts” (or sequential contrasts or successive differences) for ordered categories, i.e., R1–R2, R2–R3, R3–R4, etc., and similarly for the column categories. These are sometimes called “local odds” or “adjacent odds”.

ref = 1 gives contrasts with the first category; ref = dim(x) gives contrasts with the last category.

Note that all such parameterizations are equivalent, in that one can derive all other possible odds from any non-redundant set, but the interpretation of these values depends on the parameterization.

See the help page of plot.loddsratio for related visualization methods. There is as yet no plot method for lodds objects.

Value

An object of class lodds, with the following components:

coefficients

A named vector, of length (R-1) x (C-1) x prod(dim(x)[strata]) containing the log odds. Use the coef method to extract these from the object, and the confint method for confidence intervals. For a two-way table, the names for the log oddsare constructed in the form Ri:Rj using the table names for rows and columns. For a stratified table, the names are constructed in the form Ri:Rj|Lk.

vcov

Variance covariance matrix of the log odds.

dimnames

Dimension names for the log odds, considered as a table of size (R-1, C-1, dim(x)[strata]). Use the dim and dimnames methods to extract these and manipulate the log odds in relation to the original table.

dim

Corresponding dimension vector.

contrasts

A matrix C, such that C %*% as.vector(log(x)) gives the log odds ratios. Each row corresponds to one log odds, and is all zero, except for 2 elements of c(1, -1) for a given 2 x 1 subtable.

log

A logical, indicating the value of log in the original call.

Note

The method of calculation is an example of the use of the delta method described by Agresti (2013), Section 16.1.6, giving estimates of log odds ratios and their asymptotic covariance matrix.

The coef method returns the coefficients component as a vector of length (R-1) x prod(dim(x)[strata]). The dim and dimnames methods provide the proper attributes for treating the coefficients vector as an (R-1) x strata array. as.matrix and as.array methods are also provided for this purpose.

The confint method computes confidence intervals for the log odds (or for odds, with log = FALSE). The coeftest method (summary is an alias) prints the asymptotic standard errors, z tests (standardized log odds), and the corresponding p values.

Structural zeros: In addition to the options for zero cells provided by correct, the function allows for structural zeros to be represented as NA in the data argument. NA in the data yields NA as the LOR estimate, but does not affect other cells.

odds is just an alias to lodds with the default log=FALSE for convenience.

Author(s)

Achim Zeileis, Michael Friendly and David Meyer.

References

A. Agresti (2013), Categorical Data Analysis, 3rd Ed. New York: Wiley.

Fleiss, J. L. (1981). Statistical Methods for Rates and Proportions. 2nd Edition. New York: Wiley.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Friendly, M., Turner, H,, Firth, D., Zeileis, A. (2011). Advances in Visualizing Categorical Data Using the vcd, gnm and vcdExtra Packages in R. Correspondence Analysis and Related Methods (CARME 2011). http://www.datavis.ca/papers/adv-vcd-4up.pdf

See Also

loddsratio for log odds ratios; confint for confidence intervals; coeftest for z-tests of significance

Examples

## artificial example
set.seed(1)
x <- matrix(rpois(5 * 3, 7), ncol = 5, nrow = 3)
dimnames(x) <- list(Row = head(letters, 3), Col = tail(letters, 5))

x_lodds <- lodds(x)
coef(x_lodds)
x_lodds
confint(x_lodds)
summary(x_lodds)

### 2 x 2 x k cases
##data(CoalMiners, package = "vcd")
#lor_CM <- loddsratio(CoalMiners)
#lor_CM
#coef(lor_CM)
#confint(lor_CM)
#confint(lor_CM, log = FALSE)
#
### 2 x k x 2
#lor_Emp <-loddsratio(Employment)
#lor_Emp
#confint(lor_Emp)
#
### 4 way tables 
#data(Punishment, package = "vcd")
#lor_pun <- loddsratio(Freq ~ memory + attitude | age + education, data = Punishment)
#lor_pun
#confint(lor_pun)
#summary(lor_pun)
#
## fit linear model using WLS
#lor_pun_df <- as.data.frame(lor_pun)
#pun_mod1 <- lm(LOR ~ as.numeric(age) * as.numeric(education),
#               data = lor_pun_df, weights = 1 / ASE^2)
#anova(pun_mod1)
#
### illustrate ref levels
#VA.fem <- xtabs(Freq ~ left + right, subset=gender=="female", data=VisualAcuity)
#VA.fem
#loddsratio(VA.fem)                  # profile contrasts
#loddsratio(VA.fem, ref=1)           # contrasts against level 1
#loddsratio(VA.fem, ref=dim(VA.fem)) # contrasts against level 4
#

Calculate Generalized Log Odds Ratios for Frequency Tables

Description

Computes (log) odds ratios and their asymptotic variance covariance matrix for R x C (x strata) tables. Odds ratios are calculated for two array dimensions, separately for each level of all stratifying dimensions. See Friendly et al. (2011) for a sketch of a general theory.

Usage

loddsratio(x, ...)
## Default S3 method:
loddsratio(x, strata = NULL, log = TRUE, 
  ref = NULL, correct = any(x == 0L), ...)

## S3 method for class 'formula'
loddsratio(formula, data = NULL, ...,
subset = NULL, na.action = NULL)

oddsratio(x, stratum = NULL, log = TRUE)

## S3 method for class 'loddsratio'
coef(object, log = object$log, ...)
## S3 method for class 'loddsratio'
vcov(object, log = object$log, ...)
## S3 method for class 'loddsratio'
print(x, log = x$log, ...)
## S3 method for class 'loddsratio'
confint(object, parm, level = 0.95, log = object$log, ...)

## S3 method for class 'loddsratio'
as.array(x, log=x$log, ...)
## S3 method for class 'loddsratio'
t(x)
## S3 method for class 'loddsratio'
aperm(a, perm, ...)

Arguments

x

an object. For the default method a k-way matrix/table/array of frequencies. The number of margins has to be at least 2.

strata, stratum

Numeric or character indicating the margins of a $k$-way table x (with $k$ greater than 2) that should be employed as strata. By default all dimensions except the first two are used.

ref

numeric or character. Reference categories for the (non-stratum) row and column dimensions that should be employed for computing the odds ratios. By default, odds ratios for profile contrasts (or sequential contrasts, i.e., successive differences of adjacent categories) are used. See details below.

formula

a formula specifying the variables used to create a contingency table from data. A conditioning formula can be specified; the conditioning variables will then be used as strata variables.

data

either a data frame, or an object of class "table" or "ftable".

subset

an optional vector specifying a subset of observations to be used.

na.action

a function which indicates what should happen when the data contain NAs. Ignored if data is a contingency table.

log

logical. Should the results be displayed on a log scale or not? All internal computations are always on the log-scale but the results are transformed by default if log = TRUE.

correct

logical or numeric. Should a continuity correction be applied before computing odds ratios? If TRUE, 0.5 is added to all cells; if numeric (or an array conforming to the data) that value is added to all cells. By default, this not employed unless there are any zero cells in the table, but this correction is often recommended to reduce bias when some frequencies are small (Fleiss, 1981).

a, object

an object of class loddsratio as computed by loddsratio.

perm

numeric or character vector specifying a permutation of strata.

...

arguments passed to methods.

parm

a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.

level

the confidence level required for the confint method.

Details

For an R x C table, (log) odds ratios are formed for the set of (R-1) x (C-1) 2 x 2 tables, corresponding to some set of contrasts among the row and column variables. The ref argument allows these to be specified in a general way.

ref = NULL (default) corresponds to “profile contrasts” (or sequential contrasts or successive differences) for ordered categories, i.e., R1–R2, R2–R3, R3–R4, etc., and similarly for the column categories. These are sometimes called “local odds ratios”.

ref = 1 gives contrasts with the first category; ref = dim(x) gives contrasts with the last category; ref = c(2, 4) or ref = list(2, 4) corresponds to the reference being the second category in rows and the fourth in columns.

Combinations like ref = list(NULL, 3) are also possible, as are character vectors, e.g., ref = c("foo", "bar") also works ("foo" pertaining again to the row reference and "bar" to column reference).

Note that all such parameterizations are equivalent, in that one can derive all other possible odds ratios from any non-redundant set, but the interpretation of these values depends on the parameterization.

Note also that these reference level parameterizations only have meaning when the primary (non-strata) table dimensions are larger than 2x2. In the 2x2 case, the odds ratios are defined by the order of levels of those variables in the table, so you can achieve a desired interpretation by manipulating the table.

See the help page of plot.loddsratio for visualization methods.

Value

An object of class loddsratio, with the following components:

coefficients

A named vector, of length (R-1) x (C-1) x prod(dim(x)[strata]) containing the log odds ratios. Use the coef method to extract these from the object, and the confint method for confidence intervals. For a two-way table, the names for the log odds ratios are constructed in the form Ri:Rj/Ci:Cj using the table names for rows and columns. For a stratified table, the names are constructed in the form Ri:Rj/Ci:Cj|Lk.

vcov

Variance covariance matrix of the log odds ratios.

dimnames

Dimension names for the log odds ratios, considered as a table of size (R-1, C-1, dim(x)[strata]). Use the dim and dimnames methods to extract these and manipulate the log odds ratios in relation to the original table.

dim

Corresponding dimension vector.

contrasts

A matrix C, such that C %*% as.vector(log(x)) gives the log odds ratios. Each row corresponds to one log odds ratio, and is all zero, except for 4 elements of c(1, -1, -1, 1) for a given 2 x 2 subtable.

log

A logical, indicating the value of log in the original call.

Note

The method of calculation is an example of the use of the delta method described by Agresti (2013), Section 16.1.6, giving estimates of log odds ratios and their asymptotic covariance matrix.

The coef method returns the coefficients component as a vector of length (R-1) x (C-1) x prod(dim(x)[strata]). The dim and dimnames methods provide the proper attributes for treating the coefficients vector as an (R-1) x (C-1) x strata array. as.matrix and as.array methods are also provided for this purpose.

The confint method computes confidence intervals for the log odds ratios (or for odds ratios, with log = FALSE). The coeftest method (summary is an alias) prints the asymptotic standard errors, z tests (standardized log odds ratios), and the corresponding p values.

Structural zeros: In addition to the options for zero cells provided by correct, the function allows for structural zeros to be represented as NA in the data argument. NA in the data yields NA as the LOR estimate, but does not affect other cells.

oddsratio is just an alias to loddsratio for backward compatibility.

Author(s)

Achim Zeileis, Michael Friendly and David Meyer.

References

A. Agresti (2013), Categorical Data Analysis, 3rd Ed. New York: Wiley.

Fleiss, J. L. (1981). Statistical Methods for Rates and Proportions. 2nd Edition. New York: Wiley.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Friendly, M., Turner, H,, Firth, D., Zeileis, A. (2011). Advances in Visualizing Categorical Data Using the vcd, gnm and vcdExtra Packages in R. Correspondence Analysis and Related Methods (CARME 2011). http://www.datavis.ca/papers/adv-vcd-4up.pdf

See Also

plot.loddsratio for some plotting methods; confint for confidence intervals; coeftest for z-tests of significance

Examples

## artificial example
set.seed(1)
x <- matrix(rpois(5 * 3, 7), ncol = 5, nrow = 3)
dimnames(x) <- list(Row = head(letters, 3), Col = tail(letters, 5))

x_lor <- loddsratio(x)
coef(x_lor)
x_lor
confint(x_lor)
summary(x_lor)

## 2 x 2 x k cases
#data(CoalMiners, package = "vcd")
lor_CM <- loddsratio(CoalMiners)
lor_CM
coef(lor_CM)
confint(lor_CM)
confint(lor_CM, log = FALSE)

## 2 x k x 2
lor_Emp <-loddsratio(Employment)
lor_Emp
confint(lor_Emp)

## 4 way tables 
data(Punishment, package = "vcd")
lor_pun <- loddsratio(Freq ~ memory + attitude | age + education, data = Punishment)
lor_pun
confint(lor_pun)
summary(lor_pun)

# fit linear model using WLS
lor_pun_df <- as.data.frame(lor_pun)
pun_mod1 <- lm(LOR ~ as.numeric(age) * as.numeric(education),
               data = lor_pun_df, weights = 1 / ASE^2)
anova(pun_mod1)

## illustrate ref levels
VA.fem <- xtabs(Freq ~ left + right, subset=gender=="female", data=VisualAcuity)
VA.fem
loddsratio(VA.fem)                  # profile contrasts
loddsratio(VA.fem, ref=1)           # contrasts against level 1
loddsratio(VA.fem, ref=dim(VA.fem)) # contrasts against level 4

Table with Marginal Sums

Description

Adds row and column sums to a two-way table.

Usage

mar_table(x)

Arguments

x

a two-way table.

Value

A table with row and column totals added.

Author(s)

David Meyer [email protected]

Examples

data("SexualFun")
mar_table(SexualFun)

Extended Mosaic Plots

Description

Plots (extended) mosaic displays.

Usage

## Default S3 method:
mosaic(x, condvars = NULL,
  split_vertical = NULL, direction = NULL, spacing = NULL,
  spacing_args = list(), gp = NULL, expected = NULL, shade = NULL,
  highlighting = NULL, highlighting_fill = rev(gray.colors(tail(dim(x), 1))),
  highlighting_direction = NULL,
  zero_size = 0.5, zero_split = FALSE, zero_shade = NULL,
  zero_gp = gpar(col = 0), panel = NULL, main = NULL, sub = NULL, ...)
## S3 method for class 'formula'
mosaic(formula, data, highlighting = NULL,
  ..., main = NULL, sub = NULL, subset = NULL, na.action = NULL)

Arguments

x

a contingency table in array form, with optional category labels specified in the dimnames(x) attribute, or an object of class "structable".

condvars

vector of integers or character strings indicating conditioning variables, if any. The table will be permuted to order them first.

formula

a formula specifying the variables used to create a contingency table from data. For convenience, conditioning formulas can be specified; the conditioning variables will then be used first for splitting. If any, a specified response variable will be highlighted in the cells.

data

either a data frame, or an object of class "table" or "ftable".

subset

an optional vector specifying a subset of observations to be used.

na.action

a function which indicates what should happen when the data contain NAs. Ignored if data is a contingency table.

zero_size

size of the bullets used for zero entries (if 0, no bullets are drawn).

zero_split

logical controlling whether zero cells should be further split. If FALSE and zero_shade is FALSE, only one bullet is drawn (centered) for unsplit zero cells. If FALSE and zero_shade is TRUE, a bullet for each zero cell is drawn to allow, e.g., residual-based shadings to be effective also for zero cells.

zero_shade

logical controlling whether zero bullets should be shaded. The default is TRUE if shade is TRUE or expected is not null or gp is not null, and FALSE otherwise.

zero_gp

object of class "gpar" used for zero bullets in case they are not shaded.

split_vertical

vector of logicals of length kk, where kk is the number of margins of x (default: FALSE). Values are recycled as needed. A TRUE component indicates that the tile(s) of the corresponding dimension should be split vertically, FALSE means horizontal splits. Ignored if direction is not NULL.

direction

character vector of length kk, where kk is the number of margins of x (values are recycled as needed). For each component, a value of "h" indicates that the tile(s) of the corresponding dimension should be split horizontally, whereas "v" indicates vertical split(s).

spacing

spacing object, spacing function, or corresponding generating function (see strucplot for more information). The default is spacing_equal if x has two dimensions, spacing_increase for more dimensions, and spacing_conditional if conditioning variables are specified using condvars or the formula interface.

spacing_args

list of arguments for the generating function, if specified (see strucplot for more information).

gp

object of class "gpar", shading function or a corresponding generating function (see details and shadings). Components of "gpar" objects are recycled as needed along the last splitting dimension. Ignored if shade = FALSE.

shade

logical specifying whether gp should be used or not (see gp). If TRUE and expected is unspecified, a default model is fitted: if condvars (see strucplot) is specified, a corresponding conditional independence model, and else the total independence model.

expected

optionally, an array of expected values of the same dimension as x, or alternatively the corresponding independence model specification as used by loglin or loglm (see strucplot).

highlighting

character vector or integer specifying a variable to be highlighted in the cells.

highlighting_fill

color vector or palette function used for a highlighted variable, if any.

highlighting_direction

Either "left", "right", "top", or "bottom" specifying the direction of highlighting in the cells.

panel

Optional function with arguments: residuals, observed, expected, index, gp, and name called by the struc_mosaic workhorse for each tile that is drawn in the mosaic. index is an integer vector with the tile's coordinates in the contingency table, gp a gpar object for the tile, and name a label to be assigned to the drawn grid object.

main, sub

either a logical, or a character string used for plotting the main (sub) title. If logical and TRUE, the name of the data object is used.

...

Other arguments passed to strucplot

Details

Mosaic displays have been suggested in the statistical literature by Hartigan and Kleiner (1984) and have been extended by Friendly (1994). mosaicplot is a base graphics implementation and mosaic is a much more flexible and extensible grid implementation.

mosaic is a generic function which currently has a default method and a formula interface. Both are high-level interfaces to the strucplot function, and produce (extended) mosaic displays. Most of the functionality is described there, such as specification of the independence model, labeling, legend, spacing, shading, and other graphical parameters.

A mosaic plot is an area proportional visualization of a (possibly higher-dimensional) table of expected frequencies. It is composed of tiles (corresponding to the cells) created by recursive vertical and horizontal splits of a square. The area of each tile is proportional to the corresponding cell entry, given the dimensions of previous splits.

An extended mosaic plot, in addition, visualizes the fit of a particular log-linear model. Typically, this is done by residual-based shadings where color and/or outline of the tiles visualize sign, size and possibly significance of the corresponding residual.

The layout is very flexible: the specification of shading, labeling, spacing, and legend is modularized (see strucplot for details).

In contrast to the mosaicplot function in graphics, the splits start with the horizontal direction by default to match the printed output of structable.

Value

The "structable" visualized is returned invisibly.

Author(s)

David Meyer [email protected]

References

Hartigan, J.A., and Kleiner, B. (1984), A mosaic of television ratings. The American Statistician, 38, 32–35.

Emerson, J. W. (1998), Mosaic displays in S-PLUS: A general implementation and a case study. Statistical Computing and Graphics Newsletter (ASA), 9, 1, 17–23.

Friendly, M. (1994), Mosaic displays for multi-way contingency tables. Journal of the American Statistical Association, 89, 190–200.

Meyer, D., Zeileis, A., and Hornik, K. (2006), The strucplot framework: Visualizing multi-way contingency tables with vcd. Journal of Statistical Software, 17(3), 1-48. doi:10.18637/jss.v017.i03 and available as vignette("strucplot", package = "vcd").

The home page of Michael Friendly (http://datavis.ca) provides information on various aspects of graphical methods for analyzing categorical data, including mosaic plots. In particular, there are many materials for his course “Visualizing Categorical Data with SAS and R” at http://datavis.ca/courses/VCD/.

See Also

assoc, strucplot, mosaicplot, structable, doubledecker

Examples

library(MASS)
data("Titanic")
mosaic(Titanic)

## Formula interface for tabulated data plus shading and legend:
mosaic(~ Sex + Age + Survived, data = Titanic,
  main = "Survival on the Titanic", shade = TRUE, legend = TRUE)

data("HairEyeColor")
mosaic(HairEyeColor, shade = TRUE)
## Independence model of hair and eye color and sex.  Indicates that
## there are significantly more blue eyed blond females than expected
## in the case of independence (and too few brown eyed blond females).

mosaic(HairEyeColor, shade = TRUE, expected = list(c(1,2), 3))
## Model of joint independence of sex from hair and eye color.  Males
## are underrepresented among people with brown hair and eyes, and are
## overrepresented among people with brown hair and blue eyes, but not
## "significantly".

## Formula interface for raw data: visualize crosstabulation of numbers
## of gears and carburettors in Motor Trend car data.
data("mtcars")
mosaic(~ gear + carb, data = mtcars, shade = TRUE)

data("PreSex")
mosaic(PreSex, condvars = c(1,4))
mosaic(~ ExtramaritalSex + PremaritalSex | MaritalStatus + Gender,
       data = PreSex)

## Highlighting:
mosaic(Survived ~ ., data = Titanic)

data("Arthritis")
mosaic(Improved ~ Treatment | Sex, data = Arthritis, zero_size = 0)
mosaic(Improved ~ Treatment | Sex, data = Arthritis, zero_size = 0,
       highlighting_direction = "right")

Multiple Grid plots

Description

combines severals grid-based plots in a multi-panel-layout.

Usage

mplot(..., .list = list(),
      layout = NULL, cex = NULL,
      main = NULL, gp_main = gpar(fontsize = 20),
      sub = NULL, gp_sub = gpar(fontsize = 15),
      keep_aspect_ratio = TRUE)

Arguments

..., .list

A list of objects inheriting from class "grob", or having a "grob" attribute containing such an object.

layout

integer vector of length 2 giving the number of rows and columns. If NULL, the values will be guessed using some heuristics from the number of objects supplied in ....

cex

Scaling factor for the fonts in the subplots. If NULL, the value is calculated as the inverse square root of the row number.

main, sub

Optional main and sub title, respectively.

gp_main, gp_sub

Optional objects of class "gpar" specifying the graphical parameters for the main and sub title, respectively.

keep_aspect_ratio

logical; should the aspect ratio of the plots be fixed?

Details

This is a convenience function for producing multi-panel plots from grid-based displays, especially those produced by the vcd methods. The layout (number of rows and columns) is guessed from the amount of supplied objects, if not supplied. Currently, the vcd plotting functions do not return grob objects by default—this might change in the future. Also, some of them will return the grob object as a "grob" attribute, attached to the currently returned object.

Value

None.

Author(s)

David Meyer [email protected]

Examples

mplot(mosaic(Titanic, return_grob = TRUE),
      assoc(Titanic), return_grob = TRUE)

A = mosaic(Titanic, return_grob = TRUE)
B = mosaic(Titanic, type = "expected", return_grob = TRUE)
mplot(A, B)

mplot(sieve(SexualFun, return_grob = TRUE),
      agreementplot(SexualFun, return_grob = TRUE),
      main = "Sexual Fun")

mplot(A, grid.circle())

Diagnosis of Multiple Sclerosis

Description

Data from Westlund & Kurland (1953) on the diagnosis of multiple sclerosis (MS): two samples of patients, one from Winnipeg and one from New Orleans, were each rated by two neurologists (one from each city) in four diagnostic categories.

Usage

data("MSPatients")

Format

A 3-dimensional array resulting from cross-tabulating 218 observations on 3 variables. The variables and their levels are as follows:

No Name Levels
1 New Orleans Neurologist Certain, Probable, Possible, Doubtful
2 Winnipeg Neurologist Certain, Probable, Possible, Doubtful
3 Patients Winnipeg, New Orleans

Source

M. Friendly (2000), Visualizing Categorical Data: http://euclid.psych.yorku.ca/ftp/sas/vcd/catdata/msdiag.sas

References

K. B. Westlund & L. T. Kurland (1953), Studies on multiple sclerosis in Winnipeg, Manitoba and New Orleans, Louisiana, American Journal of Hygiene, 57, 380–396.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("MSPatients")
## Not run: 
## best visualized using a resized device, e.g. using:
## get(getOption("device"))(width = 12)
pushViewport(viewport(layout = grid.layout(ncol = 2)))
pushViewport(viewport(layout.pos.col = 1))
popViewport()
pushViewport(viewport(layout.pos.col = 2))
popViewport(2)
dev.off()

## End(Not run)

## alternative, more convenient way
mplot(
  agreementplot(t(MSPatients[,,1]), return_grob = TRUE,
    main = "Winnipeg Patients"),
  agreementplot(t(MSPatients[,,2]), return_grob = TRUE,
    main = "New Orleans Patients")
)

## alternatively, use cotabplot:
cotabplot(MSPatients, panel = cotab_agreementplot)

Non-Response Survey Data

Description

Data about non-response for a Danish survey in 1965.

Usage

data("NonResponse")

Format

A data frame with 12 observations and 4 variables.

Freq

frequency.

residence

factor indicating whether residence was in Copenhagen, in a city outside Copenhagen or at the countryside (Copenhagen, City, Country).

response

factor indicating whether a response was given (yes, no).

gender

factor indicating gender (male, female).

Source

E. B. Andersen (1991), The Statistical Analysis of Categorical Data, Table 5.17.

References

E. B. Andersen (1991), The Statistical Analysis of Categorical Data. 2nd edition. Springer-Verlag, Berlin.

Examples

data("NonResponse")
structable(~ ., data = NonResponse)

Ord Plots

Description

Ord plots for diagnosing discrete distributions.

Usage

Ord_plot(obj, legend = TRUE, estimate = TRUE, tol = 0.1, type = NULL,
  xlim = NULL, ylim = NULL, xlab = "Number of occurrences",
  ylab = "Frequency ratio", main = "Ord plot", gp = gpar(cex = 0.5),
  lwd = c(2,2), lty=c(2,1), col=c("black", "red"),
  name = "Ord_plot", newpage = TRUE, pop = TRUE,
  return_grob = FALSE, ...)
Ord_estimate(x, type = NULL, tol = 0.1)

Arguments

obj

either a vector of counts, a 1-way table of frequencies of counts or a data frame or matrix with frequencies in the first column and the corresponding counts in the second column.

legend

logical. Should a legend be plotted?.

estimate

logical. Should the distribution and its parameters be estimated from the data? See details.

tol

tolerance for estimating the distribution. See details.

type

a character string indicating the distribution, must be one of "poisson", "binomial", "nbinomial" or "log-series" or NULL. In the latter case the distribution is estimated from the data. See details.

xlim

limits for the x axis.

ylim

limits for the y axis.

xlab

a label for the x axis.

ylab

a label for the y axis.

main

a title for the plot.

gp

a "gpar" object controlling the grid graphical parameters of the points.

lwd, lty

vectors of length 2, giving the line width and line type used for drawing the OLS line and the WLS lines.

col

vector of length 2 giving the colors used for drawing the OLS and WLS lines.

name

name of the plotting viewport.

newpage

logical. Should grid.newpage be called before plotting?

pop

logical. Should the viewport created be popped?

return_grob

logical. Should a snapshot of the display be returned as a grid grob?

...

further arguments passed to grid.points.

x

a vector giving intercept and slope for the (fitted) line in the Ord plot.

Details

The Ord plot plots the number of occurrences against a certain frequency ratio (see Friendly (2000) for details) and should give a straight line if the data comes from a poisson, binomial, negative binomial or log-series distribution. The intercept and slope of this straight line conveys information about the underlying distribution.

Ord_plot fits a usual OLS line (black) and a weighted OLS line (red). From the coefficients of the latter the distribution is estimated by Ord_estimate as described in Table 2.10 in Friendly (2000). To judge whether a coefficient is positive or negative a tolerance given by tol is used. If none of the distributions fits well, no parameters are estimated. Be careful with the conclusions from Ord_estimate as it implements just some simple heuristics!

Value

A vector giving the intercept and slope of the weighted OLS line.

Author(s)

Achim Zeileis [email protected]

References

J. K. Ord (1967), Graphical methods for a class of discrete distributions, Journal of the Royal Statistical Society, A 130, 232–238.

Michael Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

## Simulated data examples:
dummy <- rnbinom(1000, size = 1.5, prob = 0.8)
Ord_plot(dummy)

## Real data examples:
data("HorseKicks")
data("Federalist")
data("Butterfly")
data("WomenQueue")

## Not run: 
grid.newpage()
pushViewport(viewport(layout = grid.layout(2, 2)))

pushViewport(viewport(layout.pos.col=1, layout.pos.row=1))
Ord_plot(HorseKicks, main = "Death by horse kicks", newpage = FALSE)
popViewport()

pushViewport(viewport(layout.pos.col=1, layout.pos.row=2))
Ord_plot(Federalist, main = "Instances of 'may' in Federalist papers", newpage = FALSE)
popViewport()

pushViewport(viewport(layout.pos.col=2, layout.pos.row=1))
Ord_plot(Butterfly, main = "Butterfly species collected in Malaya", newpage = FALSE)
popViewport()

pushViewport(viewport(layout.pos.col=2, layout.pos.row=2))
Ord_plot(WomenQueue, main = "Women in queues of length 10", newpage = FALSE)
popViewport(2)

## End(Not run)

## same
mplot(
  Ord_plot(HorseKicks, return_grob = TRUE, main = "Death by horse kicks"),
  Ord_plot(Federalist, return_grob = TRUE, main = "Instances of 'may' in Federalist papers"),
  Ord_plot(Butterfly, return_grob = TRUE, main = "Butterfly species collected in Malaya"),
  Ord_plot(WomenQueue, return_grob = TRUE, main = "Women in queues of length 10")
)

Ovary Cancer Data

Description

Data from Obel (1975) about a retrospective study of ovary cancer carried out in 1973. Information was obtained from 299 women, who were operated for ovary cancer 10 years before.

Usage

data("OvaryCancer")

Format

A data frame with 16 observations and 5 variables.

Freq

frequency.

stage

factor indicating the stage of the cancer at the time of operation (early, advanced).

operation

factor indicating type of operation (radical, limited).

survival

factor indicating survival status after 10 years (yes, no).

xray

factor indicating whether X-ray treatment was received (yes, no).

Source

E. B. Andersen (1991), The Statistical Analysis of Categorical Data, Table 6.4.

References

E. B. Obel (1975), A Comparative Study of Patients with Cancer of the Ovary Who Have Survived More or Less Than 10 Years. Acta Obstetricia et Gynecologica Scandinavica, 55, 429-439.

E. B. Andersen (1991), The Statistical Analysis of Categorical Data. 2nd edition. Springer-Verlag, Berlin.

Examples

data("OvaryCancer")
tab <- xtabs(Freq ~ xray + survival + stage + operation, data = OvaryCancer)
ftable(tab, col.vars = "survival", row.vars = c("stage", "operation", "xray"))

## model: ~ xray * operation * stage + survival * stage
## interpretation: treat xray, operation, stage as fixed margins,
##   the survival depends on stage, but not xray and operation.
doubledecker(survival ~ stage + operation + xray, data = tab)
mosaic(~ stage + operation + xray + survival,
  split_vertical = c(FALSE, TRUE, TRUE, FALSE), data = tab, keep_aspect_ratio = FALSE,
  gp = gpar(fill = rev(grey.colors(2))))
mosaic(~ stage + operation + xray + survival,
  split_vertical = c(FALSE, TRUE, TRUE, FALSE), data = tab, keep_aspect_ratio = FALSE,
  expected = ~ xray * operation * stage + survival*stage)

Diagonal Panel Functions for Table Pairs Plot

Description

Diagonal panel functions for pairs.table.

Usage

pairs_barplot(gp_bars = NULL,
  gp_vartext = gpar(fontsize = 17),
  gp_leveltext = gpar(),
  gp_axis = gpar(),
  just_leveltext = c("center", "bottom"),
  just_vartext = c("center", "top"),
  rot = 0, abbreviate = FALSE, check_overlap = TRUE, fill = "grey",
  var_offset = unit(1, "npc"), ...)
pairs_text(dimnames = TRUE, gp_vartext = gpar(fontsize = 17), 
  gp_leveltext = gpar(), gp_border = gpar(), ...) 
pairs_diagonal_text(varnames = TRUE, gp_vartext = gpar(fontsize = 17, fontface = "bold"),
  gp_leveltext = gpar(), gp_border = gpar(), pos = c("right","top"),
  distribute = c("equal","margin"), rot = 0, ...)
pairs_diagonal_mosaic(split_vertical = TRUE, margins = unit(0, "lines"),
  offset_labels = -0.4, offset_varnames = 0,
  gp = NULL, fill = "grey", labeling = labeling_values, alternate_labels = TRUE, ...)

Arguments

dimnames

vector of logicals indicating whether the factor levels should be displayed (only used for pairs_text).

varnames

vector of logicals indicating whether the variable names should be displayed (only used for pairs_text_diagonal).

gp_bars

object of class "gpar" used for bars (only used for pairs_barplot). If unspecified, the default is to set the fill component of this object to the fill argument.

gp_vartext

object of class "gpar" used for the factor names.

gp_leveltext

object of class "gpar" used for the factor levels.

gp_axis

object of class "gpar" used for the y axis.

gp_border

object of class "gpar" used for the border (only used for pairs_text).

gp

object of class "gpar" used for the tiles (only used for pairs_diagonal_mosaic). If unspecified, the default is to set the fill component of this object to the fill argument.

fill

color vector or palette function used for the fill colors of bars (for pairs_barplot) or tiles (for pairs_diagonal_mosaic).

labeling

labeling function, passed to mosaic()

alternate_labels

should labels alternate top/bottom?

just_leveltext, just_vartext

character string indicating the justification for variable names and levels.

pos

character string of length 2 controlling the horizontal and vertical position of the variable names (only used for pairs_text_diagonal).

rot

rotation angle for the variable levels.

distribute

character string indicating whether levels should be distributed equally or according to the margins (only used for pairs_text_diagonal).

abbreviate

integer or logical indicating the number of characters the labels should be abbreviated to. TRUE means 1 character, FALSE causes no abbreviation.

check_overlap

If TRUE, some levels will suppressed to avoid overlapping, if any.

split_vertical

vector of logicals of length kk, where kk is the number of margins of x (values are recycled as needed). A TRUE component indicates that the tile(s) of the corresponding dimension should be split vertically, FALSE means horizontal splits. Default is FALSE.

margins

either an object of class "unit" of length 4, or a numeric vector of length 4. The elements are recycled as needed. The four components specify the top, right, bottom, and left margin of the plot, respectively. When a numeric vector is supplied, the numbers are interpreted as "lines" units. In addition, the unit or numeric vector may have named arguments (‘⁠top⁠’, ‘⁠right⁠’, ‘⁠bottom⁠’, and ‘⁠left⁠’), in which case the non-named arguments specify the default values (recycled as needed), overloaded by the named arguments.

offset_labels, offset_varnames

numeric vector of length 4 indicating the offset of the labels (variable names) for each of the four sides of the plot.

var_offset

object of class "unit" specifying the offset of variable names from the bottom of the bar plots created by pairs_barplot. If numeric, the unit defaults to "npc".

...

other parameters passed to the underlying graphics functions.

Details

In the diagonal cells, the pairsplot visualizes statistics or information for each dimension (that is: the single factors) alone. pairs_text displays the factor's name, and optionally also the factor levels. pairs_barplot produces a bar plot of the corresponding factor, along with the factor's name.

Value

A function with one argument: the marginal table for the corresponding dimension.

Author(s)

David Meyer [email protected]

See Also

pairs.table, pairs_assoc, pairs_mosaic

Examples

data("UCBAdmissions")

pairs(UCBAdmissions) # pairs_barplot is default
pairs(UCBAdmissions, diag_panel = pairs_text)

pairs(UCBAdmissions, diag_panel = pairs_diagonal_text)
pairs(Titanic, diag_panel = pairs_diagonal_text)
pairs(Titanic, diag_panel = pairs_diagonal_text(distribute = "margin"))
pairs(Titanic,
      diag_panel = pairs_diagonal_text(distribute = "margin", rot = 45))

Off-diagonal Panel Functions for Table Pairs Plot

Description

Off-diagonal panel functions for pairs.table.

Usage

pairs_strucplot(panel = mosaic, 
  type = c("pairwise", "total", "conditional", "joint"),
  legend = FALSE, margins = c(0, 0, 0, 0), labeling = NULL, ...)
pairs_assoc(...)
pairs_mosaic(...)
pairs_sieve(...)

Arguments

panel

function to be used for the plots in each cell, such as pairs_assoc, pairs_mosaic, and pairs_sieve.

type

character string specifying the type of independence model visualized in the cells.

legend

logical specifying whether a legend should be displayed in the cells or not.

margins

margins inside each cell (see strucplot).

labeling

labeling function or labeling-generating function (see strucplot).

...

pairs_mosaic, pairs_assoc, and pairs_sieve: parameters passed to pairs_strucplot. pairs_strucplot: other parameters passed to panel function.

Details

These functions really just wrap assoc, sieve, and mosaic by basically inhibiting labeling and legend-drawing and setting the margins to 0.

Value

A function with arguments:

x

contingency table.

i, j

cell coordinates.

Author(s)

David Meyer [email protected]

References

Cohen, A. (1980), On the graphical display of the significant components in a two-way contingency table. Communications in Statistics—Theory and Methods, A9, 1025–1041.

Friendly, M. (1992), Graphical methods for categorical data. SAS User Group International Conference Proceedings, 17, 190–200. http://datavis.ca/papers/sugi/sugi17.pdf

See Also

pairs.table, pairs_text, pairs_barplot, assoc, mosaic

Examples

data("UCBAdmissions")
data("PreSex")

pairs(PreSex)
pairs(UCBAdmissions)
pairs(UCBAdmissions, upper_panel_args = list(shade = FALSE))
pairs(UCBAdmissions, lower_panel = pairs_mosaic(type = "conditional"))
pairs(UCBAdmissions, upper_panel = pairs_assoc)

Pairs Plot for Contingency Tables

Description

Produces a matrix of strucplot displays.

Usage

## S3 method for class 'table'
pairs(x, upper_panel = pairs_mosaic, upper_panel_args = list(),
  lower_panel = pairs_mosaic, lower_panel_args = list(),
  diag_panel = pairs_diagonal_mosaic, diag_panel_args = list(),
  main = NULL, sub = NULL, main_gp = gpar(fontsize = 20),
  sub_gp = gpar(fontsize = 15), space = 0.3,
  newpage = TRUE, pop = TRUE, return_grob = FALSE,
  margins = unit(1, "lines"), ...)

Arguments

x

a contingency table in array form, with optional category labels specified in the dimnames(x) attribute.

upper_panel

function for the upper triangle of the matrix, or corresponding generating function. If NULL, no panel is drawn.

upper_panel_args

list of arguments for the generating function, if specified.

lower_panel

function for the lower triangle of the matrix, or corresponding generating function. If NULL, no panel is drawn.

lower_panel_args

list of arguments for the panel-generating function, if specified.

diag_panel

function for the diagonal of the matrix, or corresponding generating function. If NULL, no panel is drawn.

diag_panel_args

list of arguments for the generating function, if specified.

main

either a logical, or a character string used for plotting the main title. If main is a logical and TRUE, the name of the object supplied as x is used.

sub

a character string used for plotting the subtitle. If sub is a logical and TRUE and main is unspecified, the name of the object supplied as x is used.

main_gp, sub_gp

object of class "gpar" containing the graphical parameters used for the main (sub) title, if specified.

space

double specifying the distance between the cells.

newpage

logical controlling whether a new grid page should be created.

pop

logical indicating whether all viewports should be popped after the plot has been drawn.

return_grob

logical. Should a snapshot of the display be returned as a grid grob?

margins

either an object of class "unit" of length 4, or a numeric vector of length 4. The elements are recycled as needed. The four components specify the top, right, bottom, and left margin of the plot, respectively. When a numeric vector is supplied, the numbers are interpreted as "lines" units. In addition, the unit or numeric vector may have named arguments (‘⁠top⁠’, ‘⁠right⁠’, ‘⁠bottom⁠’, and ‘⁠left⁠’), in which case the non-named arguments specify the default values (recycled as needed), overloaded by the named arguments.

...

For convenience, list of arguments for the panel-generating functions of upper and lower panels, if specified.

Details

This is a pairs method for objects inheriting from class "table" or "structable". It plots a matrix of pairwise mosaic plots.

Four independence types are distinguished: "pairwise", "total", "conditional" and "joint". The pairwise mosaic matrix shows bivariate marginal relations, collapsed over all other variables. The total independence mosaic matrix shows mosaic plots for mutual independence, i.e., for marginal and conditional independence among all pairs of variables. The conditional independence mosaic matrix shows mosaic plots for conditional independence for each pair of variables, given all other variables. The joint independence mosaic matrix shows mosaic plots for joint independence of all pairs of variables from the others.

This method uses panel functions called for each cell of the matrix which can be different for upper matrix, lower matrix, and diagonal cells. Correspondingly, for each panel parameter foo (= ‘⁠upper⁠’, ‘⁠lower⁠’, or ‘⁠diag⁠’), pairs.table takes two arguments: foo_panel and foo_panel_args, which can be used to specify the parameters as follows:

  1. Passing a suitable panel function to foo_panel which subsequently is called for each cell with the corresponding coordinates.

  2. Passing a corresponding generating function (of class "panel_generator") to foo_panel, along with parameters passed to foo_panel_args, that generates such a function.

Hence, the second approach is equivalent to the first if foo_panel(foo_panel_args) is passed to foo_panel.

Author(s)

David Meyer [email protected]

References

Cohen, A. (1980), On the graphical display of the significant components in a two-way contingency table. Communications in Statistics—Theory and Methods, A9, 1025–1041.

Friendly, M. (1992), Graphical methods for categorical data. SAS User Group International Conference Proceedings, 17, 190–200. http://datavis.ca/papers/sugi/sugi17.pdf

Meyer, D., Zeileis, A., and Hornik, K. (2006), The strucplot framework: Visualizing multi-way contingency tables with vcd. Journal of Statistical Software, 17(3), 1-48. doi:10.18637/jss.v017.i03 and available as vignette("strucplot").

See Also

pairs_mosaic, pairs_assoc, pairs_sieve, pairs_diagonal_text, pairs_diagonal_mosaic, pairs_text, pairs_barplot, assoc, sieve, mosaic

Examples

data("UCBAdmissions")
data("PreSex")
data(HairEyeColor)
hec = structable(Eye ~ Sex + Hair, data = HairEyeColor)

pairs(PreSex)
pairs(UCBAdmissions)
pairs(UCBAdmissions, upper_panel_args = list(shade = TRUE))
pairs(UCBAdmissions, lower_panel = pairs_mosaic(type = "conditional"))
pairs(UCBAdmissions, diag_panel = pairs_text)
pairs(UCBAdmissions, upper_panel = pairs_assoc, shade = TRUE)
pairs(hec, highlighting = 2, diag_panel_args = list(fill = grey.colors))
pairs(hec, highlighting = 2, diag_panel = pairs_diagonal_mosaic,
           diag_panel_args = list(fill = grey.colors, alternate_labels =TRUE))

Plotting (Log) Odds Ratios

Description

Produces a (conditional) line plot of extended (log) odds ratios.

Usage

## S3 method for class 'loddsratio'
plot(x, baseline = TRUE, gp_baseline = gpar(lty = 2),
     lines = TRUE, lwd_lines = 3,
     confidence = TRUE, conf_level = 0.95, lwd_confidence = 2,
     whiskers = 0, transpose = FALSE,
     col = NULL, cex = 0.8, pch = NULL,
     bars = NULL, gp_bars = gpar(fill = "lightgray", alpha = 0.5),
     bar_width = unit(0.05, "npc"),
             
     legend = TRUE, legend_pos = "topright", legend_inset = c(0, 0),
     legend_vgap = unit(0.5, "lines"),
     gp_legend_frame = gpar(lwd = 1, col = "black"),
     gp_legend_title = gpar(fontface = "bold"),
     gp_legend = gpar(), legend_lwd = 1, legend_size = 1,
             
     xlab = NULL, ylab = NULL, xlim = NULL, ylim = NULL,
     main = NULL, gp_main = gpar(fontsize = 12, fontface = "bold"),
     newpage = TRUE, pop = FALSE, return_grob = FALSE,
     add = FALSE, prefix = "", ...)
## S3 method for class 'loddsratio'
lines(x, legend = FALSE, confidence = FALSE, cex = 0, ...)

Arguments

x

an object of class loddsratio.

baseline

if TRUE, a dashed line is plotted at a value of 1 (in case of odds) or 0 (in case of log-odds).

gp_baseline

object of class "gpar" used for the baseline.

lines

if TRUE, the points are connected by lines (only sensible if the variable represented by the x-axis is ordinal).

lwd_lines

Width of the connecting lines (in char units).

confidence

logical; shall confindence intervals be plotted?

conf_level

confidence level used for confidence intervals.

lwd_confidence

Line width of the confidence interval bars (in char units).

whiskers

width of the confidence interval whiskers.

transpose

if TRUE, the plot is transposed.

col

character vector specifying the colors of the fitted lines, by default chosen with rainbow_hcl.

cex

size of the plot symbols (in lines).

pch

character or numeric vector of symbols used for plotting the (possibly conditioned) observed values, recycled as needed.

bars

logical; shall bars be plotted additionally to the points? Defaults to TRUE in case of only one conditioning variable.

gp_bars

object of class "gpar" used for the bars.

bar_width

Width of the bars, if drawn.

legend

logical; if TRUE (default), a legend is drawn.

legend_pos

numeric vector of length 2, specifying x and y coordinates of the legend, or a character string (e.g., "topleft", "center" etc.). Defaults to "topleft" if the fitted curve's slope is positive, and "topright" else.

legend_inset

numeric vector or length 2 specifying the inset from the legend's x and y coordinates in npc units.

legend_vgap

vertical space between the legend's line entries.

gp_legend_frame

object of class "gpar" used for the legend frame.

gp_legend_title

object of class "gpar" used for the legend title.

gp_legend

object of class "gpar" used for the legend defaults.

legend_lwd

line width used in the legend for the different groups.

legend_size

size used for the group symbols (in char units).

xlab

label for the x-axis. Defaults to "Strata" if transpose is FALSE.

ylab

label for the y-axis. Defaults to "Strata" if transpose is TRUE.

xlim

x-axis limits. Ignored if transpose is FALSE.

ylim

y-axis limits. Ignored if transpose is TRUE.

main

user-specified main title.

gp_main

object of class "gpar" used for the main title.

newpage

logical; if TRUE, the plot is drawn on a new page.

pop

logical; if TRUE, all newly generated viewports are popped after plotting.

return_grob

logical. Should a snapshot of the display be returned as a grid grob?

add

logical; should the plot added to an existing log odds ratio plot?

prefix

character string used as prefix for the viewport name.

...

other graphics parameters (see par).

Details

The function basically produces conditioned line plots of the (log) odds ratios structure provided in x.

The lines method can be used to overlay different plots (for example, observed and expected values).

cotabplot can be used for stratified analyses (see examples).

Value

if return_grob is TRUE, a grob object corresponding to the plot. NULL (invisibly) else.

Author(s)

David Meyer [email protected]

References

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

See Also

loddsratio

Examples

## 2 x 2 x k cases
data(CoalMiners, package = "vcd")
lor_CM <- loddsratio(CoalMiners)
plot(lor_CM)
lor_CM_df <- as.data.frame(lor_CM)

# fit linear models using WLS
age <- seq(20, 60, by = 5)
lmod <- lm(LOR ~ age, weights = 1 / ASE^2, data = lor_CM_df)
grid.lines(seq_along(age), fitted(lmod), gp = gpar(col = "blue", lwd = 2), default.units = "native")
qmod <- lm(LOR ~ poly(age, 2), weights = 1 / ASE^2, data = lor_CM_df)
grid.lines(seq_along(age), fitted(qmod), gp = gpar(col = "red", lwd = 2), default.units = "native")

## 2 x k x 2
lor_Emp <-loddsratio(Employment)
plot(lor_Emp)

## 4 way tables 
data(Punishment, package = "vcd")
mosaic(attitude ~ age + education + memory, data = Punishment,
highlighting_direction="left", rep = c(attitude = FALSE))

# visualize the log odds ratios, by education
plot(loddsratio(~ attitude + memory | education, data = Punishment))

# visualize the log odds ratios, by age
plot(loddsratio(~ attitude + memory | age, data = Punishment))

# visualize the log odds ratios, by age and education
plot(loddsratio(~ attitude + memory | age + education, data = Punishment))

# same, transposed
plot(loddsratio(~ attitude + memory | age + education, data = Punishment), transpose = TRUE)

# alternative visualization methods
image(loddsratio(Freq ~ ., data = Punishment))
tile(loddsratio(Freq ~ ., data = Punishment))

## cotabplots for more complex tables
cotabplot(Titanic, cond = c("Age","Sex"), panel = cotab_loddsratio)

cotabplot(Freq ~ opinion + grade + year | gender, data = JointSports, panel = cotab_loddsratio)
cotabplot(Freq ~ opinion + grade | year + gender, data = JointSports, panel = cotab_loddsratio)

Visualize Fitted Log-linear Models

Description

Visualize fitted "loglm" objects by mosaic or association plots.

Usage

## S3 method for class 'loglm'
plot(x, panel = mosaic, type = c("observed", "expected"),
  residuals_type = c("pearson", "deviance"), gp = shading_hcl, gp_args = list(),
  ...)

Arguments

x

a fitted "loglm" object, see loglm.

panel

a panel function for visualizing the observed values, residuals and expected values. Currently, mosaic and assoc in vcd.

type

a character string indicating whether the observed or the expected values of the table should be visualized.

residuals_type

a character string indicating the type of residuals to be computed.

gp

object of class "gpar", shading function or a corresponding generating function (see details and shadings). Ignored if shade = FALSE.

gp_args

list of arguments for the shading-generating function, if specified.

...

Other arguments passed to the panel function.

Details

The plot method for "loglm" objects by default visualizes the model using a mosaic plot (can be changed to an association plot by setting panel = assoc) with a shading based on the residuals of this model. The legend also reports the corresponding p value of the associated goodness-of-fit test. The mosaic and assoc methods are simple convenience interfaces to this plot method, setting the panel argument accordingly.

Value

The "structable" visualized is returned invisibly.

Author(s)

Achim Zeileis [email protected]

See Also

loglm, assoc, mosaic, strucplot

Examples

library(MASS)
## mosaic display for PreSex model
data("PreSex")
fm <- loglm(~ PremaritalSex * ExtramaritalSex * (Gender + MaritalStatus),
  data = aperm(PreSex, c(3, 2, 4, 1)))
fm
## visualize Pearson statistic
plot(fm, split_vertical = TRUE)
## visualize LR statistic
plot(fm, split_vertical = TRUE, residuals_type = "deviance")

## conditional independence in UCB admissions data
data("UCBAdmissions")
fm <- loglm(~ Dept * (Gender + Admit), data = aperm(UCBAdmissions))

## use mosaic display
plot(fm, labeling_args = list(abbreviate_labs = c(Admit = 3)))

## and association plot
plot(fm, panel = assoc)
assoc(fm)

Pre-marital Sex and Divorce

Description

Data from Thornes & Collard (1979), reported in Gilbert (1981), on pre- and extra-marital sex and divorce.

Usage

data("PreSex")

Format

A 4-dimensional array resulting from cross-tabulating 1036 observations on 4 variables. The variables and their levels are as follows:

No Name Levels
1 MaritalStatus Divorced, Married
2 ExtramaritalSex Yes, No
3 PremaritalSex Yes, No
4 Gender Women, Men

Source

Michael Friendly (2000), Visualizing Categorical Data: http://euclid.psych.yorku.ca/ftp/sas/vcd/catdata/marital.sas

References

G. N. Gilbert (1981), Modelling Society: An Introduction to Loglinear Analysis for Social Researchers. Allen and Unwin, London.

B. Thornes & J. Collard (1979), Who Divorces?. Routledge & Kegan, London.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("PreSex")

## Mosaic display for Gender and Premarital Sexual Experience
## (Gender Pre)
mosaic(margin.table(PreSex, c(3,4)), 
                main = "Gender and Premarital Sex")

## (Gender Pre)(Extra)
mosaic(margin.table(PreSex, c(2,3,4)), 
       expected = ~Gender * PremaritalSex + ExtramaritalSex ,
	   main = "PreMaritalSex*Gender +Sex")

## (Gender Pre Extra)(Marital)
mosaic(PreSex,
       expected = ~Gender*PremaritalSex*ExtramaritalSex + MaritalStatus,
       main = "PreMarital*ExtraMarital + MaritalStatus")

## (GPE)(PEM)
mosaic(PreSex, 
       expected = ~ Gender * PremaritalSex * ExtramaritalSex
                    + MaritalStatus * PremaritalSex * ExtramaritalSex,
       main = "G*P*E + P*E*M")

Corporal Punishment Data

Description

Data from a study of the Gallup Institute in Denmark in 1979 about the attitude of a random sample of 1,456 persons towards corporal punishment of children.

Usage

data("Punishment")

Format

A data frame with 36 observations and 5 variables.

Freq

frequency.

attitude

factor indicating attitude: (no, moderate) punishment of children.

memory

factor indicating whether the person had memories of corporal punishment as a child (yes, no).

education

factor indicating highest level of education (elementary, secondary, high).

age

factor indicating age group in years (15-24, 25-39, 40-).

Note

Anderson (1991) erroneously indicates the total sum of respondents to be 783.

Source

E. B. Andersen (1991), The Statistical Analysis of Categorical Data, pages 207–208.

References

E. B. Andersen (1991), The Statistical Analysis of Categorical Data. 2nd edition. Springer-Verlag, Berlin.

Examples

data("Punishment", package = "vcd")
pun <- xtabs(Freq ~ memory + attitude + age + education, data = Punishment)

## model: ~ (memory + attitude) * age * education
## use maximum sum-of-squares test/shading

cotabplot(~ memory + attitude | age + education, data = pun,
          panel = cotab_coindep, panel_args = list( 
  n = 5000, type = "assoc", test = "maxchisq", interpolate = 1:2))

Repeat Victimization Data

Description

Data from Reiss (1980) given by Fienberg (1980) about instances of repeat victimization for households in the U.S. National Crime Survey.

Usage

data("RepVict")

Format

A 2-dimensional array resulting from cross-tabulating victimization. The variables and their levels are as follows:

No Name Levels
1 First Victimization Rape, Assault, Robbery, Pickpocket, Personal Larceny,
Burglary, Household Larceny, Auto Theft
2 Second Victimization Rape, Assault, Robbery, Pickpocket, Personal Larceny,
Burglary, Household Larceny, Auto Theft

Source

Michael Friendly (2000), Visualizing Categorical Data, page 113.

References

S. E. Fienberg (1980), The Analysis of Cross-Classified Categorical Data, MIT Press, Cambridge, 2nd edition.

A. J. J. Reiss (1980), Victim proneness by type of crime in repeat victimization. In S. E. Fienberg & A. J. J. Reiss (eds.), Indicators of Crime and Criminal Justice. U.S. Government Printing Office, Washington, DC.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("RepVict")

mosaic(RepVict[-c(4,7),-c(4,7)], gp = shading_max,
       main = "Repeat Victimization Data")

Rochdale Data

Description

Information on 665 households of Rochdale, Lancashire, UK. The study was conducted to identify influence factors on economical activity of wives.

Usage

data("Rochdale")

Format

A 8-dimensional array resulting from cross-tabulating 665 observations on 8 variables. The variables and their levels are as follows:

No Name Levels
1 EconActive yes, no
2 Age <38, >38
3 HusbandEmployed yes, no
4 Child yes, no
5 Education yes, no
6 HusbandEducation yes, no
7 Asian yes, no
8 HouseholdWorking yes, no

Note

Many observations are missing: only 91 out of all 256 combinations contain information.

Source

Whittaker (1990).

References

H. Hofmann (2003). Constructing and reading mosaicplots. Computational Statistics & Data Analysis, 43, 4, 565–580.

J. Whittaker (1990), Graphical Models on Applied Multivariate Statistics, Wiley, New York.

Examples

data("Rochdale")
mosaic(Rochdale)

Rootograms

Description

Rootograms of observed and fitted values.

Usage

## Default S3 method:
rootogram(x, fitted, names = NULL, scale = c("sqrt", "raw"),
  type = c("hanging", "standing", "deviation"),
  shade = FALSE, legend = TRUE,
  legend_args = list(x = 0, y = 0.2, height = 0.6), df = NULL,
  rect_gp = NULL, rect_gp_args = list(),
  lines_gp = gpar(col = "red", lwd = 2),
  points_gp = gpar(col = "red"), pch = 19,
  xlab = NULL, ylab = NULL, ylim = NULL,
  main = NULL, sub = NULL,
  margins = unit(0, "lines"),
  title_margins = NULL, legend_width = NULL,
  main_gp = gpar(fontsize = 20),
  sub_gp = gpar(fontsize = 15),
  name = "rootogram", prefix = "",
  keep_aspect_ratio = FALSE,
  newpage = TRUE, pop = TRUE,
  return_grob = FALSE, ...)

Arguments

x

either a vector or a 1-way table of frequencies.

fitted

a vector of fitted frequencies.

names

a vector of names passed to grid_barplot, if set to NULL the names of x are used.

scale

a character string indicating whether the values should be plotted on the raw or square root scale.

type

a character string indicating if the bars for the observed frequencies should be hanging or standing or indicate the deviation between observed and fitted frequencies.

shade

logical specifying whether rect_gp should be set to colors corresponding to the pearson residuals, i.e., if a residual-based shading should be applied to the bars.

legend

either a legend-generating function, or a legend function (see details and legends), or a logical. If legend is NULL or TRUE and gp is a function, legend defaults to legend_resbased.

legend_args

list of arguments for the legend-generating function, if specified.

df

degrees of freedom passed to the shading functions used for inference.

rect_gp

a "gpar" object controlling the grid graphical parameters of the rectangles, shading function or a corresponding generating function (see shadings). If unspecified and no shading is applied, defaults to light grey fill color for the bars.

rect_gp_args

list of arguments for the shading-generating function, if specified for rect_gp.

lines_gp

a "gpar" object controlling the grid graphical parameters of the lines.

points_gp

a "gpar" object controlling the grid graphical parameters of the points.

pch

plotting character for the points.

xlab

a label for the x axis.

ylab

a label for the y axis.

ylim

limits for the y axis.

main

either a logical, or a character string used for plotting the main title. If main is a logical and TRUE, the name of the object supplied as x is used.

sub

a character string used for plotting the subtitle. If sub is a logical and TRUE and main is unspecified, the name of the object supplied as x is used.

margins

either an object of class "unit" of length 4, or a numeric vector of length 4. The elements are recycled as needed. The four components specify the top, right, bottom, and left margin of the plot, respectively. When a numeric vector is supplied, the numbers are interpreted as "lines" units. In addition, the unit or numeric vector may have named arguments (‘⁠top⁠’, ‘⁠right⁠’, ‘⁠bottom⁠’, and ‘⁠left⁠’), in which case the non-named arguments specify the default values (recycled as needed), overloaded by the named arguments.

title_margins

either an object of class "unit" of length 2, or a numeric vector of length 2. The elements are recycled as needed. The two components specify the top and bottom title margin of the plot, respectively. The default for each specified title are 2 lines (and 0 else), except when a legend is plotted and keep_aspect_ratio is TRUE: in this case, the default values of both margins are set as to align the heights of legend and actual plot. When a numeric vector is supplied, the numbers are interpreted as "lines" units. In addition, the unit or numeric vector may have named arguments (‘⁠top⁠’ and ‘⁠bottom⁠’), in which case the non-named argument specify the default value (recycled as needed), overloaded by the named arguments.

legend_width

An object of class "unit" of length 1 specifying the width of the legend (if any). Default: 5 lines.

main_gp, sub_gp

object of class "gpar" containing the graphical parameters used for the main (sub) title, if specified.

name

name of the plotting viewport.

keep_aspect_ratio

logical indicating whether the aspect ratio should be fixed or not.

prefix

optional character string used as a prefix for the generated viewport and grob names.

newpage

logical. Should grid.newpage be called before plotting?

pop

logical. Should the viewport created be popped?

return_grob

logical. Should a snapshot of the display be returned as a grid grob?

...

further arguments passed to grid_barplot.

Details

The observed frequencies are displayed as bars and the fitted frequencies as a line. By default a sqrt scale is used to make the smaller frequencies more visible.

Author(s)

Achim Zeileis [email protected], David Meyer [email protected]

References

J. W. Tukey (1977), Exploratory Data Analysis. Addison Wesley, Reading, MA.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

See Also

grid_barplot

Examples

## Simulated data examples:
dummy <- rnbinom(200, size = 1.5, prob = 0.8)
observed <- table(dummy)
fitted1 <- dnbinom(as.numeric(names(observed)),
                   size = 1.5, prob = 0.8) * sum(observed)
fitted2 <- dnbinom(as.numeric(names(observed)),
                   size = 2, prob = 0.6) * sum(observed)
rootogram(observed, fitted1)
rootogram(observed, fitted2)

## Real data examples:
data("HorseKicks")
HK.fit <- goodfit(HorseKicks)
summary(HK.fit)
plot(HK.fit)
## or equivalently
rootogram(HK.fit)

data("Federalist")
F.fit <- goodfit(Federalist, type = "nbinomial")
summary(F.fit)
plot(F.fit)

## (Pearson) residual-based shading
data("Federalist")
Fed_fit0 <- goodfit(Federalist, type = "poisson")
plot(Fed_fit0, shade = TRUE)

Families in Saxony

Description

Data from Geissler, cited in Sokal & Rohlf (1969) and Lindsey (1995) on gender distributions in families in Saxony in the 19th century.

Usage

data("Saxony")

Format

A 1-way table giving the number of male children in 6115 families of size 12. The variable and its levels are

No Name Levels
1 nMales 0, 1, ..., 12

Source

M. Friendly (2000), Visualizing Categorical Data, pages 40–42.

References

J. K. Lindsey (1995), Analysis of Frequency and Count Data. Oxford University Press, Oxford, UK.

R. R. Sokal & F. J. Rohlf (1969), Biometry. The Principles and Practice of Statistics. W. H. Freeman, San Francisco, CA.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("Saxony")
gf <- goodfit(Saxony, type = "binomial")
summary(gf)
plot(gf)

Sex is Fun

Description

Data from Hout et al. (1987) given by Agresti (1990) summarizing the responses of married couples to the questionnaire item: Sex is fun for me and my partner: (a) never or occasionally, (b) fairly often, (c) very often, (d) almost always.

Usage

data("SexualFun")

Format

A 2-dimensional array resulting from cross-tabulating the ratings of 91 married couples. The variables and their levels are as follows:

No Name Levels
1 Husband Never Fun, Fairly Often, Very Often, Always Fun
2 Wife Never Fun, Fairly Often, Very Often, Always Fun

Source

M. Friendly (2000), Visualizing Categorical Data, page 91.

References

A. Agresti (1990), Categorical Data Analysis. Wiley-Interscience, New York.

M. Hout, O. D. Duncan, M. E. Sobel (1987), Association and heterogeneity: Structural models of similarities and differences, Sociological Methodology, 17, 145-184.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("SexualFun")

## Kappa statistics
Kappa(SexualFun)

## Agreement Chart
agreementplot(t(SexualFun), weights = 1)
## Partial Agreement Chart and B-Statistics
agreementplot(t(SexualFun),
              xlab = "Husband's Rating",
              ylab = "Wife's Rating",
              main = "Husband's and Wife's Sexual Fun")

Shading-generating Functions for Residual-based Shadings

Description

Shading-generating functions for computing residual-based shadings for mosaic and association plots.

Usage

shading_hcl(observed, residuals = NULL, expected = NULL, df = NULL,
  h = NULL, c = NULL, l = NULL, interpolate = c(2, 4), lty = 1,
  eps = NULL, line_col = "black", p.value = NULL, level = 0.95, ...)

shading_hsv(observed, residuals = NULL, expected = NULL, df = NULL,
  h = c(2/3, 0), s = c(1, 0), v = c(1, 0.5),
  interpolate = c(2, 4), lty = 1, eps = NULL, line_col = "black",
  p.value = NULL, level = 0.95, ...)

shading_max(observed = NULL, residuals = NULL, expected = NULL, df = NULL,
  h = NULL, c = NULL, l = NULL, lty = 1, eps = NULL, line_col = "black",
  level = c(0.9, 0.99), n = 1000, ...)

shading_Friendly(observed = NULL, residuals = NULL, expected = NULL, df = NULL,
  h = c(2/3, 0), lty = 1:2, interpolate = c(2, 4),
  eps = 0.01, line_col = "black", ...)

shading_Friendly2(observed = NULL, residuals = NULL,
  expected = NULL, df = NULL, lty = 1:2, interpolate = c(2, 4), eps =
  0.01, line_col = "black", ...)

shading_sieve(observed = NULL, residuals = NULL, expected = NULL, df = NULL,
  h = c(260, 0), lty = 1:2, interpolate = c(2, 4),
  eps = 0.01, line_col = "black", ...)

shading_binary(observed = NULL, residuals = NULL, expected = NULL, df = NULL,
  col = NULL)

shading_Marimekko(x, fill = NULL, byrow = FALSE)

shading_diagonal(x, fill = NULL)

hcl2hex(h = 0, c = 35, l = 85, fixup = TRUE)

Arguments

observed

contingency table of observed values

residuals

contingency table of residuals

expected

contingency table of expected values

df

degrees of freedom of the associated independence model.

h

hue value in the HCL or HSV color description, has to be in [0, 360] for HCL and in [0, 1] for HSV colors. The default is to use blue and red for positive and negative residuals respectively. In the HCL specification it is c(260, 0) by default and for HSV c(2/3, 0).

c

chroma value in the HCL color description. This controls the maximum chroma for significant and non-significant results respectively and defaults to c(100, 20).

l

luminance value in the HCL color description. Defaults to c(90, 50) for small and large residuals respectively.

s

saturation value in the HSV color description. Defaults to c(1, 0) for large and small residuals respectively.

v

saturation value in the HSV color description. Defaults to c(1, 0.5) for significant and non-significant results respectively.

interpolate

a specification for mapping the absolute size of the residuals to a value in [0, 1]. This can be either a function or a numeric vector. In the latter case, a step function with steps of equal size going from 0 to 1 is used.

lty

a vector of two line types for positive and negative residuals respectively. Recycled if necessary.

eps

numeric tolerance value below which absolute residuals are considered to be zero, which is used for coding the border color and line type. If set to NULL (default), all borders have the default color specified by line\_col. If set to a numeric value, all border colors corresponding to residuals with a larger absolute value are set to the full positive or negative color, respectively; borders corresponding to smaller residuals are are drawn with line\_col and lty[1]

. This is used principally in shading\_Friendly.

line_col

default border color (for shading_sieve: default sieve color).

p.value

the pp value associated with the independence model. By default, this is computed from a Chi-squared distribution with df degrees of freedom. p.value can be either a scalar or a function(observed, residuals, expected, df) that computes the pp value from the data. If set to NA no inference is performed.

level

confidence level of the test used. If p.value is smaller than 1 - level, bright colors are used, otherwise dark colors are employed. For shading_max a vector of levels can be supplied. The corresponding critical values are then used as interpolate cut-offs.

n

number of permutations used in the call to coindep_test.

col

a vector of two colors for positive and negative residuals respectively.

fixup

logical. Should the color be corrected to a valid RGB value before correction?

x

object of class table used to determine the dimension.

fill

Either a character vector of color codes, or a palette function that generates such a vector. Defaults to rainbow_hcl

byrow

logical; shall tiles be filled by row or by column?

...

Other arguments passed to hcl2hex or hsv, respectively.

Details

These shading-generating functions can be passed to strucplot to generate residual-based shadings for contingency tables. strucplot calls these functions with the arguments observed, residuals, expected, df which give the observed values, residuals, expected values and associated degrees of freedom for a particular contingency table and associated independence model.

The shadings shading_hcl and shading_hsv do the same thing conceptually, but use HCL or HSV colors respectively. The former is usually preferred because they are perceptually based. Both shadings visualize the sign of the residuals of an independence model using two hues (by default: blue and red). The absolute size of the residuals is visualized by the colorfulness and the amount of grey, by default in three categories: very colorful for large residuals (> 4), less colorful for medium sized residuals (< 4 and > 2), grey/white for small residuals (< 2). More categories or a continuous scale can be specified by setting interpolate. Furthermore, the result of a significance test can be visualized by the amount of grey in the colors. If significant, a colorful palette is used, if not, the amount of color is reduced. See Zeileis, Meyer, and Hornik (2007) and diverge_hcl for more details.

The shading shading_max is applicable in 2-way contingency tables and uses a similar strategy as shading_hcl. But instead of using the cut-offs 2 and 4, it employs the critical values for the maximum statistic (by default at 90% and 99%). Consequently, color in the plot signals a significant result at 90% or 99% significance level, respectively. The test is carried out by calling coindep_test.

The shading shading_Friendly is very similar to shading_hsv, but additionally codes the sign of the residuals by different line types. See Friendly (1994) for more details. shading_Friendly2 and shading_sieve are similar, but use HCL colors.

The shading shading_binary just visualizes the sign of the residuals by using two different colors (default: blue HCL(260, 50, 70) and red HCL(0, 50, 70)).

shading_Marimekko is a simple generating function for producing, in conjunction with mosaic, so-called Marimekko-charts, which paint the tiles of each columns of a mosaic display in the same color to better display departures from independence.

shading_diagonal generates a color shading for basically square matrices (or arrays having the first two dimensons of same length) visualizing the diagonal cells, and the off-diagonal cells 1, 2, ... steps removed.

The color implementations employed are hsv from base R and polarLUV from the colorspace package, respectively. To transform the HCL coordinates to a hexadecimal color string (as returned by hsv), the function hex is employed. A convenience wrapper hcl2hex is provided.

Value

A shading function which takes only a single argument, interpreted as a vector/table of residuals, and returns a "gpar" object with the corresponding vector(s)/table(s) of graphical parameter(s).

Author(s)

Achim Zeileis [email protected]

References

Friendly M. (1994), Mosaic Displays for Multi-Way Contingency Tables. Journal of the American Statistical Association, 89, 190–200.

Meyer D., Zeileis A., and Hornik K. (2006), The Strucplot Framework: Visualizing Multi-Way Contingency Tables with vcd. Journal of Statistical Software, 17(3), 1–48. doi:10.18637/jss.v017.i03. See also vignette("strucplot", package = "vcd").

Zeileis A., Meyer D., Hornik K. (2007), Residual-Based Shadings for Visualizing (Conditional) Independence. Journal of Computational and Graphical Statistics, 16, 507–525.

Zeileis A., Hornik K. and Murrell P. (2008), Escaping RGBland: Selecting Colors for Statistical Graphics. Computational Statistics & Data Analysis, 53, 3259–3270. Preprint available from https://www.zeileis.org/papers/Zeileis+Hornik+Murrell-2009.pdf.

See Also

hex, polarLUV, hsv, mosaic, assoc, strucplot, diverge_hcl

Examples

## load Arthritis data
data("Arthritis")
art <- xtabs(~Treatment + Improved, data = Arthritis)

## plain mosaic display without shading
mosaic(art)

## with shading for independence model
mosaic(art, shade = TRUE)
## which uses the HCL shading
mosaic(art, gp = shading_hcl)
## the residuals are too small to have color,
## hence the cut-offs can be modified
mosaic(art, gp = shading_hcl, gp_args = list(interpolate = c(1, 1.8)))
## the same with the Friendly palette 
## (without significance testing)
mosaic(art, gp = shading_Friendly, gp_args = list(interpolate = c(1, 1.8)))

## assess independence using the maximum statistic
## cut-offs are now critical values for the test statistic
mosaic(art, gp = shading_max)

## association plot with shading as in base R
assoc(art, gp = shading_binary(col = c(1, 2)))

## Marimekko Chart
hec <- margin.table(HairEyeColor, 1:2)
mosaic(hec, gp = shading_Marimekko(hec))
mosaic(HairEyeColor, gp = shading_Marimekko(HairEyeColor))

## Diagonal cells shading
ac <- xtabs(VisualAcuity)
mosaic(ac, gp = shading_diagonal(ac))

Extended Sieve Plots

Description

(Extended) sieve displays for n-way contingency tables: plots rectangles with areas proportional to the expected cell frequencies and filled with a number of squares equal to the observed frequencies. Thus, the densities visualize the deviations of the observed from the expected values.

Usage

## Default S3 method:
sieve(x, condvars = NULL, gp = NULL, shade = NULL,
  legend = FALSE, split_vertical = NULL, direction = NULL, spacing = NULL,
  spacing_args = list(), sievetype = c("observed","expected"),
  gp_tile = gpar(), scale = 1, main = NULL, sub = NULL, ...)
## S3 method for class 'formula'
sieve(formula, data, ..., main = NULL, sub = NULL, subset = NULL)

Arguments

x

a contingency table in array form, with optional category labels specified in the dimnames(x) attribute.

condvars

vector of integers or character strings indicating conditioning variables, if any. The table will be permuted to order them first.

formula

a formula specifying the variables used to create a contingency table from data. For convenience, conditioning formulas can be specified; the conditioning variables will then be used first for splitting. Formulas for sieve displays (unlike those for doubledecker plots) have no response variable.

data

either a data frame, or an object of class "table" or "ftable".

subset

an optional vector specifying a subset of observations to be used.

shade

logical specifying whether gp should be used or not (see gp). If TRUE and expected is unspecified, a default model is fitted: if condvars is specified, a corresponding conditional independence model, and else the total independence model. If shade is NULL (default), gp is used if specified.

sievetype

logical indicating whether rectangles should be filled according to observed or expected frequencies.

gp

object of class "gpar", shading function or a corresponding generating function (see details of strucplot and shadings). Components of "gpar" objects are recycled as needed along the last splitting dimension. The default is a modified version of shading_Friendly: if sievetype is "observed", cells with positive residuals are painted with a red sieve, and cells with negative residuals with a blue one. If sievetype is "expected", the sieves' color is gray. Ignored if shade = FALSE.

gp_tile

object of class "gpar", controlling the appearance of all static elements of the cells (e.g., border and fill color).

scale

scaling factor for the sieve.

legend

either a legend-generating function, a legend function (see details of strucplot and legends), or a logical value. If legend is NULL or TRUE and gp is a function, legend defaults to legend_resbased.

split_vertical

vector of logicals of length kk, where kk is the number of margins of x (default: FALSE). Values are recycled as needed. A TRUE component indicates that the tile(s) of the corresponding dimension should be split vertically, FALSE means horizontal splits. Ignored if direction is not NULL.

direction

character vector of length kk, where kk is the number of margins of x (values are recycled as needed). For each component, a value of "h" indicates that the tile(s) of the corresponding dimension should be split horizontally, whereas "v" indicates vertical split(s).

spacing

spacing object, spacing function, or corresponding generating function (see strucplot for more information). The default is no spacing at all if x has two dimensions, and spacing_increase for more dimensions.

spacing_args

list of arguments for the generating function, if specified (see strucplot for more information).

main, sub

either a logical, or a character string used for plotting the main (sub) title. If logical and TRUE, the name of the data object is used.

...

Other arguments passed to strucplot

Details

sieve is a generic function which currently has a default method and a formula interface. Both are high-level interfaces to the strucplot function, and produce (extended) sieve displays. Most of the functionality is described there, such as specification of the independence model, labeling, legend, spacing, shading, and other graphical parameters.

The layout is very flexible: the specification of shading, labeling, spacing, and legend is modularized (see strucplot for details).

Value

The "structable" visualized is returned invisibly.

Note

To be faithful to the original definition by Riedwyl & Schüpbach, the default is to have no spacing between the tiles for two-way tables.

Author(s)

David Meyer [email protected]

References

H. Riedwyl & M. Schüpbach (1994), Parquet diagram to plot contingency tables. In F. Faulbaum (ed.), Softstat '93: Advances in Statistical Software, 293–299. Gustav Fischer, New York.

M. Friendly (2000), Visualizing Categorical Data, SAS Institute, Cary, NC.

Meyer, D., Zeileis, A., and Hornik, K. (2006), The strucplot framework: Visualizing multi-way contingency tables with vcd. Journal of Statistical Software, 17(3), 1-48. doi:10.18637/jss.v017.i03 and available as vignette("strucplot").

See Also

assoc, strucplot, mosaic, structable, doubledecker

Examples

data("HairEyeColor")

## aggregate over 'sex':
(haireye <- margin.table(HairEyeColor, c(2,1)))

## plot expected values:
sieve(haireye, sievetype = "expected", shade = TRUE)

## plot observed table:
sieve(haireye, shade = TRUE)

## plot complete diagram:
sieve(HairEyeColor, shade = TRUE)

## example with observed values in the cells:
sieve(haireye, shade = TRUE, labeling = labeling_values,
               gp_text = gpar(fontface = 2))

## example with expected values in the cells:
sieve(haireye, shade = TRUE, labeling = labeling_values,
               value_type = "expected", gp_text = gpar(fontface = 2))

## an example for the formula interface:
data("VisualAcuity")
sieve(Freq ~ right + left,  data = VisualAcuity)

Space Shuttle O-ring Failures

Description

Data from Dalal et al. (1989) about O-ring failures in the NASA space shuttle program. The damage index comes from a discussion of the data by Tufte (1997).

Usage

data("SpaceShuttle")

Format

A data frame with 24 observations and 6 variables.

FlightNumber

Number of space shuttle flight.

Temperature

temperature during start (in degrees F).

Pressure

pressure.

Fail

did any O-ring failures occur? (no, yes).

nFailures

how many (of six) 0-rings failed?.

Damage

damage index.

Source

Michael Friendly (2000), Visualizing Categorical Data: http://euclid.psych.yorku.ca/ftp/sas/vcd/catdata/orings.sas

References

S. Dalal, E. B. Fowlkes, B. Hoadly (1989), Risk analysis of the space shuttle: Pre-Challenger prediction of failure, Journal of the American Statistical Association, 84, 945–957.

E. R. Tufte (1997), Visual Explanations: Images and Quantities, Evidence and Narrative. Graphics Press, Cheshire, CT.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("SpaceShuttle")
plot(nFailures/6 ~ Temperature, data = SpaceShuttle,
     xlim = c(30, 81), ylim = c(0,1),
     main = "NASA Space Shuttle O-Ring Failures",
     ylab = "Estimated failure probability",
     pch = 19, col = 4)
fm <- glm(cbind(nFailures, 6 - nFailures) ~ Temperature,
          data = SpaceShuttle,
          family = binomial)
lines(30 : 81,
      predict(fm, data.frame(Temperature = 30 : 81), type = "re"),
      lwd = 2)
abline(v = 31, lty = 3)

Spacing-generating Functions

Description

These functions generate spacing functions to be used with strucplot to obtain customized spaces between the elements of a strucplot.

Usage

spacing_equal(sp = unit(0.3, "lines"))
spacing_dimequal(sp)
spacing_increase(start = unit(0.3, "lines"), rate = 1.5)
spacing_conditional(sp = unit(0.3, "lines"), start = unit(2, "lines"), rate = 1.8)
spacing_highlighting(start = unit(0.2, "lines"), rate = 1.5)

Arguments

start

object of class "unit" indicating the start value for increasing spacings.

rate

increase rate for spacings.

sp

object of class "unit" specifying a fixed spacing.

Details

These generating functions return a function used by strucplot to generate appropriate spaces between tiles of a strucplot, using the dimnames information of the visualized table.

spacing_equal allows to specify one fixed space for all dimensions.

spacing_dimequal allows to specify a fixed space for each dimension.

spacing_increase creates increasing spaces for all dimensions, based on a starting value and an increase rate.

spacing_conditional combines spacing_equal and spacing_increase to create fixed spaces for conditioned dimensions, and increasing spaces for conditioning dimensions.

spacing_highlighting is essentially spacing_conditional but with the space of the last dimension set to 0. With a corresponding color scheme, this gives the impression of the last class being ‘highlighted’ in the penultimate class (as, e.g., in doubledecker plots).

Value

A spacing function with arguments:

d

"dim" attribute of a contingency table.

condvars

index vector of conditioning dimensions (currently only used by spacing_conditional).

This function computes a list of objects of class "unit". Each list element contains the spacing information for the corresponding dimension of the table. The length of the "unit" objects is k1k-1, kk number of levels of the corresponding factor.

Author(s)

David Meyer [email protected]

References

Meyer, D., Zeileis, A., and Hornik, K. (2006), The strucplot framework: Visualizing multi-way contingency tables with vcd. Journal of Statistical Software, 17(3), 1-48. doi:10.18637/jss.v017.i03 and available as vignette("strucplot").

See Also

strucplot, doubledecker

Examples

data("Titanic")
strucplot(Titanic, spacing = spacing_increase(start = 0.5, rate = 1.5))
strucplot(Titanic, spacing = spacing_equal(1))
strucplot(Titanic, spacing = spacing_dimequal(1:4 / 4))
strucplot(Titanic, spacing = spacing_highlighting,
                   gp = gpar(fill = c("light gray","dark gray")))
data("PreSex")
strucplot(aperm(PreSex, c(1,4,2,3)), spacing = spacing_conditional,
          condvars = 2)

Spine Plots and Spinograms

Description

Spine plots are a special cases of mosaic plots, and can be seen as a generalization of stacked (or highlighted) bar plots. Analogously, spinograms are an extension of histograms.

Usage

spine(x, ...)
## Default S3 method:
spine(x, y = NULL,
  breaks = NULL, ylab_tol = 0.05, off = NULL,
  main = "", xlab = NULL, ylab = NULL, ylim = c(0, 1), margins = c(5.1, 4.1, 4.1, 3.1),
  gp = gpar(), name = "spineplot", newpage = TRUE, pop = TRUE,
  ...)
## S3 method for class 'formula'
spine(formula, data = list(),
  breaks = NULL, ylab_tol = 0.05, off = NULL,
  main = "", xlab = NULL, ylab = NULL, ylim = c(0, 1), margins = c(5.1, 4.1, 4.1, 3.1),
  gp = gpar(), name = "spineplot", newpage = TRUE, pop = TRUE,
  ...)

Arguments

x

an object, the default method expects either a single variable (interpreted to be the explanatory variable) or a 2-way table. See details.

y

a "factor" interpreted to be the dependent variable

formula

a "formula" of type y ~ x with a single dependent "factor" and a single explanatory variable.

data

an optional data frame.

breaks

if the explanatory variable is numeric, this controls how it is discretized. breaks is passed to hist and can be a list of arguments.

ylab_tol

convenience tolerance parameter for y-axis annotation. If the distance between two labels drops under this threshold, they are plotted equidistantly.

off

vertical offset between the bars (in per cent). It is fixed to 0 for spinograms and defaults to 2 for spine plots.

main, xlab, ylab

character strings for annotation

ylim

limits for the y axis

margins

margins when calling plotViewport

gp

a "gpar" object controlling the grid graphical parameters of the rectangles. It should specify in particular a vector of fill colors of the same length as levels(y). The default is to call gray.colors.

name

name of the plotting viewport.

newpage

logical. Should grid.newpage be called before plotting?

pop

logical. Should the viewport created be popped?

...

additional arguments passed to plotViewport.

Details

spine creates either a spinogram or a spine plot. It can be called via spine(x, y) or spine(y ~ x) where y is interpreted to be the dependent variable (and has to be categorical) and x the explanatory variable. x can be either categorical (then a spine plot is created) or numerical (then a spinogram is plotted). Additionally, spine can also be called with only a single argument which then has to be a 2-way table, interpreted to correspond to table(x, y).

Spine plots are a generalization of stacked bar plots where not the heights but the widths of the bars corresponds to the relative frequencies of x. The heights of the bars then correspond to the conditional relative frequencies of y in every x group. This is a special case of a mosaic plot with specific spacing and shading.

Analogously, spinograms extend stacked histograms. As for the histogram, x is first discretized (using hist) and then for the discretized data a spine plot is created.

Value

The table visualized is returned invisibly.

Author(s)

Achim Zeileis [email protected]

References

Hummel, J. (1996), Linked bar charts: Analysing categorical data graphically. Computational Statistics, 11, 23–33.

Hofmann, H., Theus, M. (2005), Interactive graphics for visualizing conditional distributions, Unpublished Manuscript.

See Also

cd_plot, mosaic, hist

Examples

## Arthritis data (dependence on a categorical variable)
data("Arthritis")
(spine(Improved ~ Treatment, data = Arthritis))

## Arthritis data (dependence on a numerical variable)
(spine(Improved ~ Age, data = Arthritis, breaks = 5))
(spine(Improved ~ Age, data = Arthritis, breaks = quantile(Arthritis$Age)))
(spine(Improved ~ Age, data = Arthritis, breaks = "Scott"))

## Space shuttle data (dependence on a numerical variable)
data("SpaceShuttle")
(spine(Fail ~ Temperature, data = SpaceShuttle, breaks = 3))

Core-generating Function for Association Plots

Description

Core-generating function for strucplot returning a function producing association plots.

Usage

struc_assoc(compress = TRUE, xlim = NULL, ylim = NULL,
  yspace = unit(0.5, "lines"), xscale = 0.9, gp_axis = gpar(lty = 3))

Arguments

compress

logical; if FALSE, the space between the rows (columns) are chosen such that the total heights (widths) of the rows (column) are all equal. If TRUE, the space between the rows and columns is fixed and hence the plot is more “compressed”.

xlim

either a 2×k2 \times k matrix of doubles, kk the number of total columns of the plot, or a recycled vector from which such a matrix will be constructed. The columns of xlim correspond to the columns of the association plot, the rows describe the column ranges (minimums in the first row, maximums in the second row). If xlim is NULL, the ranges are determined from the residuals according to compress (if TRUE: widest range from each column, if FALSE: from the whole association plot matrix).

ylim

either a 2×k2 \times k matrix of doubles, kk the number of total rows of the plot, or a recycled vector from which such a matrix will be constructed. The columns of ylim correspond to the rows of the association plot, the rows describe the column ranges (minimums in the first row, maximums in the second row). If ylim is NULL, the ranges are determined from the residuals according to compress (if TRUE: widest range from each row, if FALSE: from the whole association plot matrix).

xscale

scale factor resizing the tile's width, thus adding additional space between the tiles.

yspace

object of class "unit" specifying additional space separating the rows.

gp_axis

object of class "gpar" specifying the visual aspects of the tiles' baseline.

Details

This function is usually called by strucplot (typically when called by assoc) and returns a function used by strucplot to produce association plots.

Value

A function with arguments:

residuals

table of residuals.

observed

not used by struc_assoc.

expected

table of expected frequencies.

spacing

object of class "unit" specifying the space between the tiles.

gp

list of gpar objects used for the drawing the tiles.

split_vertical

vector of logicals indicating, for each dimension of the table, the split direction.

Author(s)

David Meyer [email protected]

References

Cohen, A. (1980), On the graphical display of the significant components in a two-way contingency table. Communications in Statistics—Theory and Methods, A9, 1025–1041.

Friendly, M. (1992), Graphical methods for categorical data. SAS User Group International Conference Proceedings, 17, 190–200. http://datavis.ca/papers/sugi/sugi17.pdf

Meyer, D., Zeileis, A., and Hornik, K. (2006), The strucplot framework: Visualizing multi-way contingency tables with vcd. Journal of Statistical Software, 17(3), 1-48. doi:10.18637/jss.v017.i03 and available as vignette("strucplot").

See Also

assoc, strucplot, structable

Examples

## UCB Admissions
data("UCBAdmissions")
ucb <- aperm(UCBAdmissions)

## association plot for conditional independence
strucplot(ucb, expected = ~ Dept * (Admit + Gender),
  core = struc_assoc(ylim = c(-4, 4)), labeling_args = list(abbreviate_labs = c(Admit = 3)))

Core-generating Function for Mosaic Plots

Description

Core-generating function for strucplot returning a function producing mosaic plots.

Usage

struc_mosaic(zero_size = 0.5, zero_split = FALSE, zero_shade = TRUE,
             zero_gp = gpar(col = 0), panel = NULL)

Arguments

zero_size

size of the bullets used for zero-entries in the contingency table (if 0, no bullets are drawn).

zero_split

logical controlling whether zero cells should be further split. If FALSE and zero_shade is FALSE, only one bullet is drawn (centered) for unsplit zero cells. If FALSE and zero_shade is TRUE, a bullet for each zero cell is drawn to allow, e.g., residual-based shadings to be effective also for zero cells.

zero_shade

logical controlling whether zero bullets should be shaded.

zero_gp

object of class "gpar" used for zero bullets in case they are not shaded.

panel

Optional function with arguments: residuals, observed, expected, index, gp, and name called by the struc_mosaic workhorse for each tile that is drawn in the mosaic. index is an integer vector with the tile's coordinates in the contingency table, gp a gpar object for the tile, and name a label to be assigned to the drawn grid object.

Details

This function is usually called by strucplot (typically when called by mosaic) and returns a function used by strucplot to produce mosaic plots.

Value

A function with arguments:

residuals

table of residuals.

observed

table of observed values.

expected

not used by struc_mosaic.

spacing

object of class "unit" specifying the space between the tiles.

gp

list of gpar objects used for the drawing the tiles.

split_vertical

vector of logicals indicating, for each dimension of the table, the split direction.

Author(s)

David Meyer [email protected]

References

Cohen, A. (1980), On the graphical display of the significant components in a two-way contingency table. Communications in Statistics—Theory and Methods, A9, 1025–1041.

Friendly, M. (1992), Graphical methods for categorical data. SAS User Group International Conference Proceedings, 17, 190–200. http://datavis.ca/papers/sugi/sugi17.pdf

Meyer, D., Zeileis, A., and Hornik, K. (2006), The strucplot framework: Visualizing multi-way contingency tables with vcd. Journal of Statistical Software, 17(3), 1-48. doi:10.18637/jss.v017.i03 and available as vignette("strucplot").

See Also

mosaic, strucplot, structable

Examples

## Titanic data
data("Titanic")
## mosaic plot with large zeros
strucplot(Titanic, core = struc_mosaic(zero_size = 1))

Core-generating Function for Sieve Plots

Description

Core-generating function for strucplot returning a function producing sieve plots.

Usage

struc_sieve(sievetype = c("observed","expected"), gp_tile = gpar(),
scale = 1)

Arguments

sievetype

logical indicating whether rectangles should be filled according to observed or expected frequencies.

gp_tile

object of class "gpar", controlling the appearance of all static elements of the cells (e.g., border and fill color).

scale

Scaling factor for the sieve.

Details

This function is usually called by strucplot (typically when called by sieve) and returns a function used by strucplot to produce sieve plots.

Value

A function with arguments:

residuals

table of residuals.

observed

table of observed values.

expected

not used by struc_sieve.

spacing

object of class "unit" specifying the space between the tiles.

gp

list of gpar objects used for the drawing the tiles.

split_vertical

vector of logicals indicating, for each dimension of the table, the split direction.

Author(s)

David Meyer [email protected]

References

Riedwyl, H., and Schüpbach, M. (1994), Parquet diagram to plot contingency tables. In F. Faulbaum (ed.), Softstat '93: Advances in Statistical Software, 293–299. Gustav Fischer, New York.

Friendly, M. (2000), Visualizing Categorical Data, SAS Institute, Cary, NC.

Meyer, D., Zeileis, A., and Hornik, K. (2006), The strucplot framework: Visualizing multi-way contingency tables with vcd. Journal of Statistical Software, 17(3), 1-48. doi:10.18637/jss.v017.i03 and available as vignette("strucplot").

See Also

sieve, strucplot, structable

Examples

## Titanic data
data("Titanic")
strucplot(Titanic, core = struc_sieve)

Structured Displays of Contingency Tables

Description

This modular function visualizes certain aspects of high-dimensional contingency tables in a hierarchical way.

Usage

strucplot(x, residuals = NULL, expected = NULL,
  condvars = NULL, shade = NULL, type = c("observed", "expected"),
  residuals_type = NULL, df = NULL, split_vertical = NULL, 
  spacing = spacing_equal, spacing_args = list(),
  gp = NULL, gp_args = list(),
  labeling = labeling_border, labeling_args = list(),
  core = struc_mosaic, core_args = list(),
  legend = NULL, legend_args = list(),
  main = NULL, sub = NULL, margins = unit(3, "lines"),
  title_margins = NULL, legend_width = NULL,
  main_gp = gpar(fontsize = 20), sub_gp = gpar(fontsize = 15),
  newpage = TRUE, pop = TRUE, return_grob = FALSE,
  keep_aspect_ratio = NULL, prefix = "", ...)

Arguments

x

a contingency table in array form, with optional category labels specified in the dimnames attribute.

residuals

optionally, an array of residuals of the same dimension as x (see details).

expected

optionally, an array of expected values of the same dimension as x, or alternatively the corresponding independence model specification as used by loglin or loglm (see details).

df

degrees of freedom passed to the shading functions used for inference. Will be calculated (and overwritten if specified) if both expected and residuals are NULL, or if expected is given a formula.

condvars

number of conditioning variables, if any; those are expected to be ordered first in the table. This information is used for computing the expected values, and is also passed to the spacing functions (see spacings).

shade

logical specifying whether gp should be used or not (see gp). If TRUE and expected is unspecified, a default model is fitted: if condvars is specified, a corresponding conditional independence model, and else the total independence model.

residuals_type

a character string indicating the type of residuals to be computed when none are supplied. If residuals is NULL, residuals_type must be one of "pearson" (default; giving components of Pearson's chi-squared), "deviance" (giving components of the likelihood ratio chi-squared), or "FT" for the Freeman-Tukey residuals. The value of this argument can be abbreviated. If residuals are specified, the value of residuals_type is just passed “as is” to the legend function.

type

a character string indicating whether the observed or the expected values of the table should be visualized.

split_vertical

vector of logicals of length kk, where kk is the number of margins of x (values are recycled as needed). A TRUE component indicates that the tile(s) of the corresponding dimension should be split vertically, FALSE means horizontal splits. Default is FALSE.

spacing

spacing object, spacing function, or a corresponding generating function (see details and spacings).

spacing_args

list of arguments for the spacing-generating function, if specified.

gp

object of class "gpar", shading function or a corresponding generating function (see details and shadings). Components of "gpar" objects are recycled as needed along the last splitting dimension. Ignored if shade = FALSE.

gp_args

list of arguments for the shading-generating function, if specified.

labeling

either a logical, or a labeling function, or a corresponding generating function (see details and labelings. If FALSE or NULL, no labeling is produced.

labeling_args

list of arguments for the labeling-generating function, if specified.

core

either a core function, or a corresponding generating function (see details). Currently, generating functions for mosaic plots (struc_mosaic), association plots (struc_assoc), and sieve plots (struc_sieve) are provided.

core_args

list of arguments for the core-generating function, if specified.

legend

either a legend-generating function, or a legend function (see details and legends), or a logical. If legend is NULL or TRUE and gp is a function, legend defaults to legend_resbased.

legend_args

list of arguments for the legend-generating function, if specified.

main

either a logical, or a character string used for plotting the main title. If main is a logical and TRUE, the name of the object supplied as x is used.

sub

a character string used for plotting the subtitle. If sub is a logical and TRUE and main is unspecified, the name of the object supplied as x is used.

margins

either an object of class "unit" of length 4, or a numeric vector of length 4. The elements are recycled as needed. The four components specify the top, right, bottom, and left margin of the plot, respectively. When a numeric vector is supplied, the numbers are interpreted as "lines" units. In addition, the unit or numeric vector may have named arguments (‘⁠top⁠’, ‘⁠right⁠’, ‘⁠bottom⁠’, and ‘⁠left⁠’), in which case the non-named arguments specify the default values (recycled as needed), overloaded by the named arguments.

title_margins

either an object of class "unit" of length 2, or a numeric vector of length 2. The elements are recycled as needed. The two components specify the top and bottom title margin of the plot, respectively. The default for each specified title are 2 lines (and 0 else), except when a legend is plotted and keep_aspect_ratio is TRUE: in this case, the default values of both margins are set as to align the heights of legend and actual plot. When a numeric vector is supplied, the numbers are interpreted as "lines" units. In addition, the unit or numeric vector may have named arguments (‘⁠top⁠’ and ‘⁠bottom⁠’), in which case the non-named argument specify the default value (recycled as needed), overloaded by the named arguments.

legend_width

An object of class "unit" of length 1 specifying the width of the legend (if any). Default: 5 lines.

pop

logical indicating whether the generated viewport tree should be removed at the end of the drawing or not.

main_gp, sub_gp

object of class "gpar" containing the graphical parameters used for the main (sub) title, if specified.

newpage

logical indicating whether a new page should be created for the plot or not.

return_grob

logical. Should a snapshot of the display be returned as a grid grob?

keep_aspect_ratio

logical indicating whether the aspect ratio should be fixed or not. If unspecified, the default is TRUE for two-dimensional tables and FALSE otherwise.

prefix

optional character string used as a prefix for the generated viewport and grob names.

...

For convenience, list of arguments passed to the labeling-generating function used.

Details

This function—usually called by higher-level functions such as assoc and mosaic—generates conditioning plots of contingency tables. First, it sets up a set of viewports for main- and subtitles, legend, and the actual plot region. Then, residuals are computed as needed from observed and expected frequencies, where the expected frequencies are optionally computed for a specified independence model. Finally, the specified functions for spacing, gp, main plot, legend, and labeling are called to produce the plot. The function invisibly returns the "structable" object visualized.

Most elements of the plot, such as the core function, the spacing between the tiles, the shading of the tiles, the labeling, and the legend, are modularized in graphical appearance control (“grapcon”) functions and specified as parameters. For each element foo (= spacing, labeling, core, or legend), strucplot takes two arguments: foo and foo_args, which can be used to specify the parameters in the following alternative ways:

  1. Passing a suitable function to foo which subsequently will be called from strucplot to compute shadings, labelings, etc.

  2. Passing a corresponding generating function to foo, along with parameters passed to foo_args, that generates such a function. Generating functions must inherit from classes "grapcon_generator" and "foo".

  3. Except for the shading functions (shading_bar), passing foo(foo_args) to the foo argument.

  4. For shadings and spacings, passing the final parameter object itself; see the corresponding help pages for more details on the data structures.

If legends are drawn, a ‘cinemascope’-like layout is used for the plot to preserve the 1:1 aspect ratio.

If type = "expected", the expected values are passed to the observed argument of the core function, and the observed values to the expected argument.

Although the gp argument is typically used for shading, it can be used for arbitrary modifications of the tiles' graphics parameters (e.g., for highlighting particular cells, etc.).

Value

Invisibly, an object of class "structable" corresponding to the plot. If return_grob is TRUE, additionally, the plot as a grob object is returned in a grob attribute.

Note

The created viewports, as well as the tiles and bullets, are named and thus can conveniently be modified after a plot has been drawn (and pop = FALSE).

Author(s)

David Meyer [email protected]

References

Meyer, D., Zeileis, A., and Hornik, K. (2006), The strucplot framework: Visualizing multi-way contingency tables with vcd. Journal of Statistical Software, 17(3), 1-48. doi:10.18637/jss.v017.i03 and available as vignette("strucplot").

See Also

assoc, mosaic, sieve, struc_assoc, struc_sieve, struc_mosaic, structable, doubledecker, labelings, shadings, legends, spacings

Examples

data("Titanic")

strucplot(Titanic)
strucplot(Titanic, core = struc_assoc)
strucplot(Titanic, spacing = spacing_increase,
                   spacing_args = list(start = 0.5, rate = 1.5))
strucplot(Titanic, spacing = spacing_increase(start = 0.5, rate = 1.5))

## modify a tile's color
strucplot(Titanic, pop = FALSE)
grid.edit("rect:Class=1st,Sex=Male,Age=Adult,Survived=Yes",
          gp = gpar(fill = "red"))

Structured Contingency Tables

Description

This function produces a ‘flat’ representation of a high-dimensional contingency table constructed by recursive splits (similar to the construction of mosaic displays).

Usage

## S3 method for class 'formula'
structable(formula, data,
direction = NULL, split_vertical = NULL, ..., subset, na.action)
## Default S3 method:
structable(..., direction = NULL, split_vertical = FALSE)

Arguments

formula

a formula object with possibly both left and right hand sides specifying the column and row variables of the flat table.

data

a data frame, list or environment containing the variables to be cross-tabulated, or an object inheriting from class table.

subset

an optional vector specifying a subset of observations to be used. Ignored if data is a contingency table.

na.action

a function which indicates what should happen when the data contain NAs. Ignored if data is a contingency table

...

R objects which can be interpreted as factors (including character strings), or a list (or data frame) whose components can be so interpreted, or a contingency table object of class "table" or "ftable".

split_vertical

logical vector indicating, for each dimension, whether it should be split vertically or not (default: FALSE). Values are recycled as needed. If the argument is of length 1, the value is alternated for all dimensions. Ignored if direction is provided.

direction

character vector alternatively specifying the splitting direction ("h" for horizontal and "v" for vertical splits). Values are recycled as needed. If the argument is of length 1, the value is alternated for all dimensions.

Details

This function produces textual representations of mosaic displays, and thus ‘flat’ contingency tables. The formula interface is quite similar to the one of ftable, but also accepts the mosaic-like formula interface (empty left-hand side). Note that even if the ftable interface is used, the split_vertical or direction argument is needed to specify the order of the horizontal and vertical splits. If pretabulated data with a Freq column is used, than the left-hand side should be left empty—the Freq column will be handled correctly.

"structable" objects can be subset using the [ and [[ operators, using either level indices or names (see examples). The corresponding replacement functions are available as well. In addition, appropriate aperm, cbind, rbind, length, dim, and is.na methods do exist.

Value

An object of class "structable", inheriting from class "ftable", with the splitting information ("split_vertical") as additional attribute.

Author(s)

David Meyer [email protected]

References

Meyer, D., Zeileis, A., and Hornik, K. (2006), The strucplot framework: Visualizing multi-way contingency tables with vcd. Journal of Statistical Software, 17(3), 1-48. doi:10.18637/jss.v017.i03 and available as vignette("strucplot").

See Also

strucplot, mosaic, ftable

Examples

structable(Titanic)
structable(Titanic, split_vertical = c(TRUE, TRUE, FALSE, FALSE))
structable(Titanic, direction = c("h","h","v","v"))
structable(Sex + Class ~ Survived + Age, data = Titanic)

## subsetting of structable objects
(hec <- structable(aperm(HairEyeColor)))

## The "[" operator treats structables as a block-matrix and selects parts of the matrix:
hec[1]
hec[2]
hec[1,c(2,4)]
hec["Male",c("Blue","Green")]

## replacement funcion:
tmp <- hec
(tmp[1,2:3] <- tmp[2,c(1,4)])

## In contrast, the "[[" operator treats structables as two-dimensional
## lists. Indexing conditions on specified levels and thus reduces the dimensionality:

## seek subtables conditioning on levels of the first dimension:
hec[[1]]
hec[[2]]

## Seek subtable from the first two dimensions, given the level "Male"
## of the first variable, and "Brown" from the second
## (the following two commands are equivalent):
hec[["Male"]][["Brown"]]
hec[[c("Male","Brown")]]

## Seeking subtables by conditioning on row and/or column variables:
hec[["Male","Hazel"]]
hec[[c("Male","Brown"),]]
hec[[c("Male","Brown"),"Hazel"]]

## a few other operations
t(hec)
dim(hec)
dimnames(hec)
as.matrix(hec)
length(hec)
cbind(hec[,1],hec[,3])

as.vector(hec) ## computed on the _multiway_ table
as.vector(unclass(hec))

Suicide Rates in Germany

Description

Data from Heuer (1979) on suicide rates in West Germany classified by age, sex, and method of suicide.

Usage

data("Suicide")

Format

A data frame with 306 observations and 6 variables.

Freq

frequency of suicides.

sex

factor indicating sex (male, female).

method

factor indicating method used.

age

age (rounded).

age.group

factor. Age classified into 5 groups.

method2

factor indicating method used (same as method but some levels are merged).

Source

Michael Friendly (2000), Visualizing Categorical Data: http://euclid.psych.yorku.ca/ftp/sas/vcd/catdata/suicide.sas

References

J. Heuer (1979), Selbstmord bei Kindern und Jugendlichen. Ernst Klett Verlag, Stuttgart.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("Suicide")
structable(~ sex + method2 + age.group, data = Suicide)

Summary of a 2-way Table

Description

Prints a 2-way contingency table along with percentages, marginal, and conditional distributions.

Usage

table2d_summary(object, margins = TRUE, percentages = FALSE,
  conditionals = c("none", "row", "column"), chisq.test = TRUE, ...)

Arguments

object

a r×cr \times c-contingency table

margins

if TRUE, marginal distributions are computed.

percentages

if TRUE, relative frequencies are computed.

conditionals

if not "none", the conditional distributions, given the row/column factor, are computed.

chisq.test

if TRUE, a chi-squared test of independence is carried out.

...

currently not used.

Value

Returns invisibly a r×c×kr \times c \times k table, kk depending on the amount of choices (at most 3).

Author(s)

David Meyer [email protected]

See Also

mar_table, prop.table, independence_table

Examples

data("UCBAdmissions")
table2d_summary(margin.table(UCBAdmissions, 1:2))

Ternary Diagram

Description

Visualizes compositional, 3-dimensional data in an equilateral triangle.

Usage

ternaryplot(x, scale = 1, dimnames = NULL,
  dimnames_position = c("corner","edge","none"),
  dimnames_color = "black", dimnames_rot = c(-60, 60, 0),
  id = NULL, id_color = "black",
  id_just = c("center", "center"),
  coordinates = FALSE, grid = TRUE, grid_color = "gray",
  labels = c("inside", "outside", "none"),
  labels_color = "darkgray", labels_rot = c(120, -120, 0),
  border = "black", bg = "white",
  pch = 19, cex = 1, prop_size = FALSE, col = "red",
  main = "ternary plot", newpage = TRUE, pop = TRUE,
  return_grob = FALSE, ...)

Arguments

x

a matrix with three columns.

scale

row sums scale to be used.

dimnames

dimension labels (defaults to the column names of x).

dimnames_position, dimnames_color

position and color of dimension labels.

dimnames_rot

Numeric vector of length 3, specifying the angle of the dimension labels.

id

optional labels to be plotted below the plot symbols. coordinates and id are mutual exclusive.

id_color

color of these labels.

id_just

character vector of length 1 or 2 indicating the justification of these labels.

coordinates

if TRUE, the coordinates of the points are plotted below them. coordinates and id are mutual exclusive.

grid

if TRUE, a grid is plotted. May optionally be a string indicating the line type (default: "dotted").

grid_color

grid color.

labels, labels_color

position and color of the grid labels.

labels_rot

Numeric vector of length 3, specifying the angle of the grid labels.

border

color of the triangle border.

bg

triangle background.

pch

plotting character. Defaults to filled dots.

cex

a numerical value giving the amount by which plotting text and symbols should be scaled relative to the default. Ignored for the symbol size if prop_size is not FALSE.

prop_size

if TRUE, the symbol size is plotted proportional to the row sum of the three variables, i.e., represents the weight of the observation.

col

plotting color.

main

main title.

newpage

if TRUE, the plot will appear on a new graphics page.

pop

logical; if TRUE, all newly generated viewports are popped after plotting.

return_grob

logical. Should a snapshot of the display be returned as a grid grob?

...

additional graphics parameters (see par)

Details

A points' coordinates are found by computing the gravity center of mass points using the data entries as weights. Thus, the coordinates of a point P(a,b,c)P(a,b,c), a+b+c=1a + b + c = 1, are: P(b+c/2,c3/2)P(b + c/2, c \sqrt{3}/2).

Author(s)

David Meyer [email protected]

References

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("Arthritis")

## Build table by crossing Treatment and Sex
tab <- as.table(xtabs(~ I(Sex:Treatment) + Improved, data = Arthritis))

## Mark groups
col <- c("red", "red", "blue", "blue")
pch <- c(1, 19, 1, 19)

## plot
ternaryplot(
            tab,
            col = col,
            pch = pch,
            prop_size = TRUE,
            bg = "lightgray",
            grid_color = "white",
            labels_color = "white",
            main = "Arthritis Treatment Data"
           )
## legend
grid_legend(0.8, 0.7, pch, col, rownames(tab), title = "GROUP")

## Titanic
data("Lifeboats")
attach(Lifeboats)
ternaryplot(
  Lifeboats[,4:6],
  pch = ifelse(side == "Port", 1, 19),
  col = ifelse(side == "Port", "red", "blue"),
  id  = ifelse(men / total > 0.1, as.character(boat), NA),
  prop_size = 2,
  dimnames_position = "edge",
  main = "Lifeboats on Titanic"
)
grid_legend(0.8, 0.9, c(1, 19),
  c("red", "blue"), c("Port", "Starboard"),
  title = "SIDE")


## Hitters
data("Hitters")
attach(Hitters)
colors <- c("black","red","green","blue","red","black","blue")
pch <- substr(levels(Positions), 1, 1)
ternaryplot(
  Hitters[,2:4],
  pch = as.character(Positions),
  col = colors[as.numeric(Positions)],
  main = "Baseball Hitters Data"
)
grid_legend(0.8, 0.9, pch, colors, levels(Positions),
  title = "POSITION(S)")

Tile Plot

Description

Plots a tile display.

Usage

## Default S3 method:
tile(x,
         tile_type = c("area", "squaredarea", "height", "width"),
         halign = c("left", "center", "right"),
         valign = c("bottom", "center", "top"),
         split_vertical = NULL,
         shade = FALSE,
         spacing = spacing_equal(unit(1, "lines")),
         set_labels = NULL,
         margins = unit(3, "lines"),
         keep_aspect_ratio = FALSE,
         legend = NULL,
         legend_width = NULL,
         squared_tiles = TRUE,
         main = NULL, sub = NULL, ...)
## S3 method for class 'formula'
tile(formula, data,
  ..., main = NULL, sub = NULL, subset = NULL, na.action = NULL)

Arguments

x

a contingency table, or an object coercible to one.

formula

a formula specifying the variables used to create a contingency table from data

.

data

either a data frame, or an object of class "table" or "ftable".

subset

an optional vector specifying a subset of observations to be used.

na.action

a function which indicates what should happen when the data contain NAs. Ignored if data is a contingency table.

tile_type

character string indicating how the tiles should reflect the table frequencies (see details).

halign, valign

character string specifying the horizontal and vertical alignment of the tiles.

split_vertical

vector of logicals of length kk, where kk is the number of margins of x (values are recycled as needed). A TRUE component indicates that the tile(s) of the corresponding dimension should be split vertically, FALSE means horizontal splits. Default is FALSE.

spacing

spacing object, spacing function, or corresponding generating function (see strucplot for more information).

set_labels

An optional character vector with named components replacing the so-specified variable names. The component names must exactly match the variable names to be replaced.

shade

logical specifying whether shading should be enabled or not (see strucplot).

margins

either an object of class "unit" of length 4, or a numeric vector of length 4. The elements are recycled as needed. The four components specify the top, right, bottom, and left margin of the plot, respectively. When a numeric vector is supplied, the numbers are interpreted as "lines" units. In addition, the unit or numeric vector may have named arguments (‘⁠top⁠’, ‘⁠right⁠’, ‘⁠bottom⁠’, and ‘⁠left⁠’), in which case the non-named arguments specify the default values (recycled as needed), overloaded by the named arguments.

legend

either a legend-generating function, or a legend function (see details and legends), or a logical. If legend is NULL or TRUE and gp is a function or missing, legend defaults to legend_resbased.

legend_width

An object of class "unit" of length 1 specifying the width of the legend (if any). Default: 5 lines.

keep_aspect_ratio

logical indicating whether the aspect ratio should be fixed or not. The default is FALSE to enable the creation of squared tiles.

squared_tiles

logical indicating whether white space should be added as needed to rows or columns to obtain squared tiles in case of an unequal number of row and column labels.

main, sub

either a logical, or a character string used for plotting the main (sub) title. If logical and TRUE, the name of the data object is used.

...

Other arguments passed to strucplot

Details

A tile plot is a matrix of tiles. For each tile, either the "width", "height", "area", or squared area is proportional to the corresponding entry. The first three options allow column-wise, row-wise and overall comparisons, respectively. The last variant allows to compare the tiles both column-wise and row-wise, considering either the width or the height, respectively.

In contrast to other high-level strucplot functions, tile also accepts a table with duplicated levels (see examples). In this case, artificial dimnames will be created, and the actual ones are drawn using set_labels.

Note that multiway-tables are first “flattened” using structable.

Value

The "structable" visualized is returned invisibly.

Author(s)

David Meyer [email protected]

See Also

assoc, strucplot, mosaic, structable,

Examples

data("Titanic")

## default plot
tile(Titanic)
tile(Titanic, type = "expected")
tile(Titanic, shade = TRUE)

## some variations
tile(Titanic, tile_type = "squaredarea")
tile(Titanic, tile_type = "width", squared_tiles = FALSE)
tile(Titanic, tile_type = "height", squared_tiles = FALSE)
tile(Titanic, tile_type = "area", halign = "center", valign = "center")

## repeat levels
tile(Titanic[,,,c(1,2,1,2)])

Truck Accidents Data

Description

Data from a study in England in two periods from November 1969 to October 1971 and November 1971 to October 1973. A new compulsory safety measure for trucks was introduced in October 1971. Therefore, the question is whether the safety measure had an effect on the number of accidents and on the point of collision on the truck.

Usage

data("Trucks")

Format

A data frame with 24 observations on 5 variables.

Freq

frequency of accidents involving trucks.

period

factor indicating time period (before, after) 1971-11-01.

collision

factor indicating whether the collision was in the back or forward (including the front and the sides) of the truck (back, forward).

parked

factor indicating whether the truck was parked (yes, no).

light

factor indicating light conditions: day light (daylight), night on an illuminated road (night, illuminate), night on a dark road (night, dark).

Source

E. B. Andersen (1991), The Statistical Analysis of Categorical Data, Table 6.8.

References

E. B. Andersen (1991), The Statistical Analysis of Categorical Data. 2nd edition. Springer-Verlag, Berlin.

Examples

library(MASS)
data("Trucks")
tab <- xtabs(Freq ~ period + collision + light + parked, data = Trucks)
loglm(~ (collision + period) * parked * light, data = tab)
doubledecker(collision ~ parked + light + period, data = tab)
cotabplot(tab, panel = cotab_coindep)

UK Soccer Scores

Description

Data from Lee (1997), on the goals scored by Home and Away teams in the Premier Football League, 1995/6 season.

Usage

data("UKSoccer")

Format

A 2-dimensional array resulting from cross-tabulating the number of goals scored in 380 games. The variables and their levels are as follows:

No Name Levels
1 Home 0, 1, ..., 4
2 Away 0, 1, ..., 4

Source

M. Friendly (2000), Visualizing Categorical Data, page 27.

References

A. J. Lee (1997), Modelling scores in the Premier League: Is Manchester United really the best?, Chance, 10(1), 15–19.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

See Also

Bundesliga

Examples

data("UKSoccer")
mosaic(UKSoccer, gp = shading_max, main = "UK Soccer Scores")

Visual Acuity in Left and Right Eyes

Description

Data from Kendall & Stuart (1961) on unaided vision among 3,242 men and 7,477 women, all aged 30-39 and employed in the U.K. Royal Ordnance factories 1943-1946.

Usage

data("VisualAcuity")

Format

A data frame with 32 observations and 4 variables.

Freq

frequency of visual acuity measurements.

right

visual acuity on right eye.

left

visual acuity on left eye.

gender

factor indicating gender of patient.

Source

M. Friendly (2000), Visualizing Categorical Data: http://euclid.psych.yorku.ca/ftp/sas/vcd/catdata/vision.sas

References

M. G. Kendall & A. Stuart (1961), The Advanced Theory of Statistics, Vol. 2. Griffin, London.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("VisualAcuity")
structable(~ gender + left + right, data = VisualAcuity)
sieve(Freq ~ left + right | gender, data = VisualAcuity, shade = TRUE)
cotabplot(Freq ~ left + right | gender, data = VisualAcuity,
          panel = cotab_agreementplot)

Von Bortkiewicz Horse Kicks Data

Description

Data from von Bortkiewicz (1898), given by Andrews & Herzberg (1985), on number of deaths by horse or mule kicks in 14 corps of the Prussian army.

Usage

data("VonBort")

Format

A data frame with 280 observations and 4 variables.

deaths

number of deaths.

year

year of the deaths.

corps

factor indicating the corps.

fisher

factor indicating whether the corresponding corps was considered by Fisher (1925) or not.

Source

Michael Friendly (2000), Visualizing Categorical Data: http://euclid.psych.yorku.ca/ftp/sas/vcd/catdata/vonbort.sas

References

D. F. Andrews & A. M. Herzberg (1985), Data: A Collection of Problems from Many Fields for the Student and Research Worker. Springer-Verlag, New York, NY.

R. A. Fisher (1925), Statistical Methods for Research Workers. Oliver & Boyd, London.

L. von Bortkiewicz (1898), Das Gesetz der kleinen Zahlen. Teubner, Leipzig.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

See Also

HorseKicks for a popular subsample.

Examples

data("VonBort")
## HorseKicks data
xtabs(~ deaths, data = VonBort, subset = fisher == "yes")

Weldon's Dice Data

Description

Data from Pearson (1900) about the frequency of 5s and 6s in throws of 12 dice. Weldon tossed the dice 26,306 times and reported his results in a letter to Francis Galton on 1894-02-02.

Usage

data("WeldonDice")

Format

A 1-way table giving the frequency of a 5 or a 6 in 26,306 throws of 12 dice where 10 indicates ‘10 or more’ 5s or 6s. The variable and its levels are

No Name Levels
1 n56 0, 1, ..., 10

Source

M. Friendly (2000), Visualizing Categorical Data, pages 20–21.

References

K. Pearson (1900), On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen by random sampling, Philosophical Magazine, 50 (5th series), 157–175.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("WeldonDice")
gf <- goodfit(WeldonDice, type = "binomial")
summary(gf)
plot(gf)

Women in Queues

Description

Data from Jinkinson & Slater (1981) and Hoaglin & Tukey (1985) reporting the frequency distribution of females in 100 queues of length 10 in a London Underground station.

Usage

data("WomenQueue")

Format

A 1-way table giving the number of women in 100 queues of length 10. The variable and its levels are

No Name Levels
1 nWomen 0, 1, ..., 10

Source

M. Friendly (2000), Visualizing Categorical Data, pages 19–20.

References

D. C. Hoaglin & J. W. Tukey (1985), Checking the shape of discrete distributions. In D. C. Hoaglin, F. Mosteller, J. W. Tukey (eds.), Exploring Data Tables, Trends and Shapes, chapter 9. John Wiley & Sons, New York.

R. A. Jinkinson & M. Slater (1981), Critical discussion of a graphical method for identifying discrete distributions, The Statistician, 30, 239–248.

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Examples

data("WomenQueue")
gf <- goodfit(WomenQueue, type = "binomial")
summary(gf)
plot(gf)

Woolf Test

Description

Test for homogeneity on 2×2×k2 \times 2 \times k tables over strata (i.e., whether the log odds ratios are the same in all strata).

Usage

woolf_test(x)

Arguments

x

A 2×2×k2 \times 2 \times k table.

Value

A list of class "htest" containing the following components:

statistic

the chi-squared test statistic.

parameter

degrees of freedom of the approximate chi-squared distribution of the test statistic.

p.value

pp-value for the test.

method

a character string indicating the type of test performed.

data.name

a character string giving the name(s) of the data.

observed

the observed counts.

expected

the expected counts under the null hypothesis.

References

Woolf, B. 1955. On estimating the relation between blood group and disease. Ann. Human Genet. (London) 19, 251-253.

See Also

mantelhaen.test

Examples

data("CoalMiners")
woolf_test(CoalMiners)