Package 'earth'

Description

Contrasts function for factors in the earth response. For internal use by earth.

Usage

contr.earth.response(x, base, contrasts)

Arguments

Value

Returns a diagonal matrix. An example for a 3 level factor with levels A, B, and C:

      A B C
    A 1 0 0
    B 0 1 0
    C 0 0 1

Note

Earth uses this function internally. You shouldn't need it. It is made publicly available only because it seems that is necessary for model.matrix.

See Also

contrasts

Description

Build a regression model using the techniques in Friedman's papers "Multivariate Adaptive Regression Splines" and "Fast MARS".

See the package vignette “Notes on the earth package”.

Usage

## S3 method for class 'formula'
earth(formula = stop("no 'formula' argument"), data = NULL,
   weights = NULL, wp = NULL, subset = NULL,
   na.action = na.fail,
   pmethod = c("backward", "none", "exhaustive", "forward", "seqrep", "cv"),
   keepxy = FALSE, trace = 0, glm = NULL, degree = 1, nprune = NULL,
   nfold=0, ncross=1, stratify=TRUE,
   varmod.method = "none", varmod.exponent = 1,
   varmod.conv = 1, varmod.clamp = .1, varmod.minspan = -3,
   Scale.y = NULL, ...)

## Default S3 method:
earth(x = stop("no 'x' argument"), y = stop("no 'y' argument"),
    weights = NULL, wp = NULL, subset = NULL,
    na.action = na.fail,
    pmethod = c("backward", "none", "exhaustive", "forward", "seqrep", "cv"),
    keepxy = FALSE, trace = 0, glm = NULL, degree = 1, nprune = NULL,
    nfold=0, ncross=1, stratify=TRUE,
    varmod.method = "none", varmod.exponent = 1,
    varmod.conv = 1, varmod.clamp = .1, varmod.minspan = -3,
    Scale.y = NULL, ...)

## S3 method for class 'fit'
earth(x = stop("no 'x' argument"), y = stop("no 'y' argument"),
    weights = NULL, wp = NULL, subset = NULL,
    na.action = na.fail, offset = NULL,
    pmethod = c("backward", "none", "exhaustive", "forward", "seqrep", "cv"),
    keepxy = FALSE, trace = 0, glm = NULL, degree = 1,
    penalty = if(degree > 1) 3 else 2,
    nk = min(200, max(20, 2 * ncol(x))) + 1,
    thresh = 0.001, minspan = 0, endspan = 0,
    newvar.penalty = 0, fast.k = 20, fast.beta = 1,
    linpreds = FALSE, allowed = NULL,
    nprune = NULL, Object = NULL,
    Scale.y = NULL, Adjust.endspan = 2, Auto.linpreds = TRUE,
    Force.weights = FALSE, Use.beta.cache = TRUE, Force.xtx.prune = FALSE,
    Get.leverages = NROW(x) < 1e5, Exhaustive.tol = 1e-10, ...)

Arguments

To start off, look at the arguments formula, data, x, y, nk, degree, and trace.
If the response is binary or a factor, consider using the glm argument.
For cross validation, use the nfold argument.
For prediction intervals, use the varmod.method argument.

Most users will find that the above arguments are all they need, plus in some cases keepxy and nprune. Unless you are a knowledgeable user, it's best not subvert the standard algorithm by toying with tuning parameters such as thresh, penalty, and endspan.

Value

An S3 model of class "earth". See earth.object for a complete description.

Author(s)

Stephen Milborrow, derived from mda::mars by Trevor Hastie and Robert Tibshirani.

The approach used for GLMs was motivated by work done by Jane Elith and John Leathwick (a representative paper is given below).

The evimp function uses ideas from Max Kuhn's caret package https://CRAN.R-project.org/package=caret.

Parts of Thomas Lumley's leaps package have been incorporated into earth, so earth can directly access Alan Miller's Fortran functions without going through hidden functions in the leaps package.

References

The Wikipedia article is recommended for an elementary introduction. The primary references are the Friedman papers, but readers may find the MARS section in Hastie, Tibshirani, and Friedman a more accessible introduction. Faraway takes a hands-on approach, using the ozone data to compare mda::mars with other techniques. (If you use Faraway's examples with earth instead of mars, use $bx instead of $x, and check out the book's errata.) Friedman and Silverman is recommended background reading for the MARS paper. Earth's pruning pass uses code from the leaps package which is based on techniques in Miller.

Faraway (2005) Extending the Linear Model with R https://www.maths.bath.ac.uk/~jjf23

Friedman (1991) Multivariate Adaptive Regression Splines (with discussion) Annals of Statistics 19/1, 1–141 http://projecteuclid.org/euclid.aos/1176347963
doi:10.1214/aos/1176347963

Friedman (1993) Fast MARS Stanford University Department of Statistics, Technical Report 110 https://statistics.stanford.edu/research/fast-mars

Friedman and Silverman (1989) Flexible Parsimonious Smoothing and Additive Modeling Technometrics, Vol. 31, No. 1.

Hastie, Tibshirani, and Friedman (2009) The Elements of Statistical Learning (2nd ed.) https://hastie.su.domains/pub.htm

Leathwick, J.R., Rowe, D., Richardson, J., Elith, J., & Hastie, T. (2005) Using multivariate adaptive regression splines to predict the distributions of New Zealand's freshwater diadromous fish Freshwater Biology, 50, 2034-2052 https://hastie.su.domains/pub.htm

Miller, Alan (1990, 2nd ed. 2002) Subset Selection in Regression https://wp.csiro.au/alanmiller/index.html

Wikipedia article on MARS https://en.wikipedia.org/wiki/Multivariate_adaptive_regression_splines

See Also

Start with summary.earth, plot.earth, evimp, and plotmo.

Please see the main package vignette “Notes on the earth package”. The vignette can also be downloaded from http://www.milbo.org/doc/earth-notes.pdf.

The vignette “Variance models in earth” is also included with the package. It describes how to generate prediction intervals for earth models.

Examples

earth.mod <- earth(Volume ~ ., data = trees)
plotmo(earth.mod)
summary(earth.mod, digits = 2, style = "pmax")

Description

The object returned by the earth function.

This is an S3 model of class "earth". It is a list with the components listed below.

Term refers to a term created during the forward pass (each line of the output from format.earth is a term). Term number 1 is always the intercept.

Value

     (Intercept)  h(Girth-12.9)  h(12.9-Girth)  h(Girth-12.9)*h(...
[1,]           1            0.0            4.6                    0
[2,]           1            0.0            4.3                    0
[3,]           1            0.0            4.1                    0
...

                        Girth Height
(Intercept)                 0      0  # intercept
h(12.9-Girth)              -1      0  # 2nd term uses Girth
h(Girth-12.9)               1      0  # 3rd term uses Girth
h(Girth-12.9)*h(Height-76)  1      1  # 4th term uses Girth and Height
...

                           Girth Height
(Intercept)                    0      0  # intercept, no cuts
h(12.9-Girth)               12.9      0  # 2nd term has cut at 12.9
h(Girth-12.9)               12.9      0  # 3rd term has cut at 12.9
h(Girth-12.9)*h(Height-76)  12.9     76  # 4th term has two cuts
...

     [,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,]    1    0    0    0    0    0    0   # intercept-only model
[2,]    1    2    0    0    0    0    0   # best 2 term model uses terms 1,2
[3,]    1    2    4    0    0    0    0   # best 3 term model uses terms 1,2,4
[4,]    1    2    6    9    0    0    0   # and so on
...

    survived ~ age + pclass + sqrt(age) - sex

                age  pclass  sqrt(age)
    survived      0       0          0  # the response will be dropped
    age           1       0          0
    pclass        0       1          0
    sqrt(age)     0       0          1  # sqrt(age) will be merged with age
    sex           0       0          0  # sex is unused and will be dropped

            age pclass2nd pclass3rd sqrt(age)
    age       1         0         0         1  # age and sqrt(age) use "age"
    pclass    0         1         1         0  # pclass2nd and pclass3rd use "pclass"

           y  mean
fold1  0.909 0.909
fold2  0.869 0.869
fold3  0.952 0.952
fold4  0.157 0.157
fold5  0.961 0.961
mean   0.769 0.769

         y1   y2    y3   mean
fold1 0.915 0.951 0.944 0.937
fold2 0.962 0.970 0.970 0.968
fold3 0.914 0.940 0.942 0.932
fold4 0.907 0.929 0.925 0.920
fold5 0.947 0.987 0.979 0.971
mean  0.929 0.955 0.952 0.946

See Also

earth

Description

Titanic data with incomplete cases, passenger names, and other details removed.

Format

A data frame with 1046 observations on 6 variables.

Source

This dataset is included in the earth package because it is a convenient vehicle for illustrating earth's GLM and factor handling.

The dataset was compiled by Frank Harrell and Robert Dawson: https://hbiostat.org/data/repo/titanic.html
See also:
https://biostat.app.vumc.org/wiki/pub/Main/DataSets/titanic3info.txt.

For this version of the Titanic data, passenger details and incomplete cases were deleted and the name changed to etitanic to minimize confusion with other versions ("e" because it is part of the earth package).

Note that survived is an integer (it should arguably be a logical).

In this data the crew are conspicuous by their absence.

Contents of etitanic:

         pclass survived    sex    age sibsp parch
    1       1st        1 female 29.000     0     0
    2       1st        1   male  0.917     1     2
    3       1st        0 female  2.000     1     2
    4       1st        0   male 30.000     1     2
    5       1st        0 female 25.000     1     2
    ...
    1309    3rd        0   male 29.000     0     0
    

How etitanic was built:

    load("titanic3") # from Harrell's web site
    # discard name, ticket, fare, cabin, embarked, body, home.dest
    etitanic <- titanic3[,c(1,2,4,5,6,7)]
    etitanic <- etitanic[!is.na(etitanic$age),]
    save(etitanic, file="etitanic.rda")
    

References

Further details and analyses of the Titanic data may be found in:

F. Harrell (2001) Regression Modeling Strategies with Applications to Linear Models, Logistic Regression, and Survival Analysis https://biostat.app.vumc.org/wiki/bin/view/Main/RmS

See Also

earth

Description

Estimate variable importances in an earth object

Usage

evimp(object, trim=TRUE, sqrt.=TRUE)

Arguments

Value

This function returns a matrix showing the relative importances of the variables in the model. There is a row for each variable. The row name is the variable name, but with -unused appended if the variable does not appear in the final model.

The columns of the matrix are (not all of these are printed by print.evimp):

• col: Column index of the variable in the x argument to earth.

• used: 1 if the variable is used in the final model, else 0. Equivalently, 0 if the row name has an -unused suffix.

• nsubsets: Variable importance using the "number of subsets" criterion. Is the number of subsets that include the variable (see "Three Criteria" in the chapter on evimp in the earth vignette “Notes on the earth package”).

• gcv: Variable importance using the GCV criterion (see "Three Criteria").

• gcv.match: 1, except is 0 where the rank using the gcv criterion differs from that using the nsubsets criterion. In other words, there is a 0 for values that increase as you go down the gcv column.

• rss: Variable importance using the RSS criterion (see "Three Criteria").

• rss.match: Like gcv.match but for the rss.

The rows are sorted on the nsubsets criterion. This means that values in the nsubsets column decrease as you go down the column (more accurately, they are non-increasing). The values in the gcv and rss columns are also non-increasing, except where the gcv or rss rank differs from the nsubsets ranking.

Note

There is a chapter on evimp in the earth package vignette “Notes on the earth package”.

Acknowledgment

Thanks to Max Kuhn for the original evimp code and for helpful discussions.

See Also

earth, plot.evimp

Examples

data(ozone1)
earth.mod <- earth(O3 ~ ., data=ozone1, degree=2)
ev <- evimp(earth.mod, trim=FALSE)
plot(ev)
print(ev)

Description

Expand binomial-pair data from “short” to “long” form.

The short form specifies the response with two columns giving the numbers of successes and failures. Example short form:

    survived died dose    sex
           3    0   10   male
           2    1   10 female
           1    2   20   male
           1    2   20 female

The long form specifies the response as single column of TRUEs and FALSEs. For example, the long form of the above data (spaces and comments added):

    survived dose    sex
        TRUE   10   male     # row 1 of short data: 0 died, 3 survived
        TRUE   10   male
        TRUE   10   male

       FALSE   10 female     # row 2 of short data: 1 died, 2 survived
        TRUE   10 female
        TRUE   10 female

       FALSE   20   male     # row 3 of short data: 2 died, 1 survived
       FALSE   20   male
        TRUE   20   male

       FALSE   20 female     # row 4 of short data: 2 died, 1 survived
       FALSE   20 female
        TRUE   20 female

In this example the total number of survived and died for each row in the short data is the same, but in general that need not be true.

Usage

## S3 method for class 'formula'
expand.bpairs(formula = stop("no 'formula' argument"), data = NULL, sort = FALSE, ...)

## Default S3 method:
expand.bpairs(data = stop("no 'data' argument"), y = NULL, sort = FALSE, ...)

Arguments

Value

A dataframe of the data in the long form, with expanded binomial pairs. The first column of the data will be the response column (a column of TRUEs and FALSEs).

Additionally, the returned value has two attached attributes:

bpairs.index A vector of row indices into the returned data. Can be used to reconstruct the short data from the long data (although this package does not yet provide a function to do so).

ynames Column names of the original response (a two-element character vector).

Examples

survived <- c(3,2,1,1) # short data for demo (too short to build a real model)
died     <- c(0,1,2,2)
dose <- c(10,10,20,20)
sex  <- factor(c("male", "female", "male", "female"))

short.data <- data.frame(survived, died, dose, sex)

expand.bpairs(survived + died ~ ., short.data) # returns long form of the data

# expand.bpairs(data=short.data, y=cbind(survived, died)) # equivalent
# expand.bpairs(short.data, c(1,2))                       # equivalent
# expand.bpairs(short.data, c("survived", "died"))        # equivalent

# For example models, see the earth vignette
# section "Short versus long binomial data".

Description

Return a string representing an earth expression (summary.earth calls this function internally to display the terms of the earth model).

Usage

## S3 method for class 'earth'
format(x = stop("no 'x' argument"),
       style = "h", decomp = "anova", digits = getOption("digits"),
       use.names = TRUE, colon.char = ":", ...)

Arguments

Value

A character representation of the earth model.

If there are multiple responses, format.earth will return multiple strings.

If there are embedded GLM model(s), the strings for the GLM model(s) come after the strings for the standard earth model(s).

Note

The FAQ section in the package vignette gives precise details of the "anova" ordering.

Using format.earth, perhaps after hand editing the returned string, you can create an alternative to predict.earth. For example:

as.func <- function(object, digits = 8, use.names = FALSE, ...)
  eval(parse(text=paste(
    "function(x){\n",
    "if(is.vector(x))\n",
    "  x <- matrix(x, nrow = 1, ncol = length(x))\n",
    "with(as.data.frame(x),\n",
    format(object, digits = digits, use.names = use.names, style = "pmax", ...),
    ")\n",
    "}\n", sep = "")))

earth.mod <- earth(Volume ~ ., data = trees)
my.func <- as.func(earth.mod, use.names = FALSE)
my.func(c(10,80))             # returns 16.84
predict(earth.mod, c(10,80))  # returns 16.84

Note that with pmax the R expression generated by format.earth can handle multiple cases. Thus the expression is consistent with the way predict functions usually work in R — we can give predict multiple cases (i.e., multiple rows in the input matrix) and it will return a vector of predicted values.

The earth package also provides a function format.lm. It has arguments as follows
format.lm(x, digits=getOption("digits"), use.names=TRUE, colon.char=":")
(Strictly speaking, format.lm doesn't belong in the earth package.) Example:

lm.mod <- lm(Volume ~ Height*Girth, data = trees)
cat(format(lm.mod, colon.char="*"))

# yields:
#    69.4
#    -  1.30 * Height
#    -  5.86 * Girth
#    + 0.135 * Height*Girth

See Also

summary.earth, pmax,

Examples

earth.mod <- earth(Volume ~ ., data = trees)
cat(format(earth.mod))

# yields:
#    29.0
#    -  3.42 * h(14.2-Girth)
#    +  6.23 * h(Girth-14.2)
#    + 0.581 * h(Height-75)

cat(format(earth.mod, style="pmax"))

# yields:
#    29.0
#    -  3.42 * pmax(0,   14.2 -  Girth)
#    +  6.23 * pmax(0,  Girth -  14.2)
#    + 0.581 * pmax(0, Height -  75)

cat(format(earth.mod, style="C"))

# yields (note zero based indexing):
#    29.0
#    -  3.42 * max(0, 14.2 - x[0])
#    +  6.23 * max(0, x[0] - 14.2)
#    + 0.581 * max(0, x[1] - 75)

cat(format(earth.mod, style="bf"))

# yields:
#    29.0
#    -  3.42 * bf1
#    +  6.23 * bf2
#    + 0.581 * bf3
#
#     bf1  h(14.2-Girth)
#     bf2  h(Girth-14.2)
#     bf3  h(Height-75)

Description

Convert a mars object from the mda package to an earth object

Usage

mars.to.earth(object, trace=TRUE)

Arguments

Value

The value is the same format as that returned by earth but with skeletal versions of rss.per.subset, gcv.per.subset, and prune.terms.

You can fully initialize these components by calling update.earth after mars.to.earth, but if you do this selected.terms may change. However with pmethod="backward" a change is unlikely — selected.terms would change only if GCVs are so close that numerical errors have an effect.

Note

Differences between mars and earth objects

Perhaps the most notable difference between mars and earth objects is that mars returns the MARS basis matrix in a field called "x" whereas earth returns "bx" with only the selected terms. Also, earth returns "dirs" rather than "factors", and in earth this matrix can have entries of value 2 for linear predictors.

For details of other differences between mars and earth objects, see the comments in the source code of mars.to.earth.

Weights

The w argument is silently ignored by mars.

mars normalizes wp to (euclidean) length 1; earth normalizes wp to length equal to the number of responses, i.e., the number of columns in y. This change was made so an all ones wp (or in fact any all constant wp) is equivalent to using no wp.

If the original call to mars used the wp argument, mars.to.earth will run update.earth to force consistency. This could modify the model, so a warning is issued.

See Also

earth, mars

Examples

if(require(mda)) {
    mars.mod <- mars(trees[,-3], trees[,3])
    earth.mod <- mars.to.earth(mars.mod)
    # the standard earth functions can now be used
    # note the reconstructed call in the summary
    summary(earth.mod, digits = 2)
}

Description

Get the basis matrix of an earth model.

Usage

## S3 method for class 'earth'
model.matrix(object = stop("no 'object' argument"),
    x = NULL, subset = NULL, which.terms = NULL,
    trace = 0,
    ...,
    Env = parent.frame(),
    Callers.name = "model.matrix.earth")

Arguments

Value

A basis matrix bx of the same form returned by earth. The format of bx is described in earth.object.

If x, subset, and which.terms are all NULL (the default), this function returns the model's bx. In this case, it is perhaps easier to simply use object$bx.

The matrix bx can be used as the input matrix to lm or glm, as shown below in the example. In fact, that is what earth does internally after the pruning pass — it calls lm.fit, and additionally glm if earth's glm argument is used.

See Also

earth

Examples

# Example 1

data(trees)
earth.mod <- earth(Volume ~ ., data = trees) # standard earth model
summary(earth.mod, decomp = "none")  # "none" to print terms in same order as lm.mod below
bx <- model.matrix(earth.mod)        # earth model's basis mat (equivalent to bx <- earth.mod$bx)
lm.mod <- lm(trees$Volume ~ bx[,-1]) # -1 to drop intercept
summary(lm.mod)                      # yields same coeffs as above summary
                                     # displayed t values are not meaningful

# Example 2

earth.mod <- earth(Volume~., data=trees) # standard earth model
summary(earth.mod, decomp = "none")  # "none" to print terms in same order as lm.mod below
bx <- model.matrix(earth.mod)        # earth model's basis mat (equivalent to bx <- earth.mod$bx)
bx <- bx[, -1]                       # drop intercept column
bx <- as.data.frame(bx)              # lm requires a data frame
bx$Volume <- trees$Volume            # add Volume to data
lm.mod <- lm(Volume~., data=bx)      # standard linear regression on earth's basis mat
summary(lm.mod)                      # yields same coeffs as above summary
                                     # displayed t values are not meaningful

Description

Ozone readings in Los Angeles, with incomplete cases removed.

Format

A data frame with 330 observations on 10 variables.

Source

This dataset was copied from library(faraway) and the name changed to ozone1 to prevent a name clash. The data were originally made available by Leo Breiman who was a consultant on a project where the data were generated. Example analyses using these data may be found in Faraway and in Hastie and Tibshirani.

    > ozone1
        O3   vh wind humidity temp  ibh dpg ibt vis doy
    1    3 5710    4       28   40 2693 -25  87 250  33
    2    5 5700    3       37   45  590 -24 128 100  34
    3    5 5760    3       51   54 1450  25 139  60  35
    ...
    330  1 5550    4       85   39 5000   8  44 100 390

References

Faraway (2005) Extending the Linear Model with R https://www.maths.bath.ac.uk/~jjf23

Hastie and Tibshirani (1990) Generalized Additive Models https://hastie.su.domains/pub.htm

See Also

earth

airquality a different set of ozone data

Description

Plot an earth object. By default the plot shows model selection, cumulative distribution of the residuals, residuals versus fitted values, and the residual QQ plot.

This function calls plotres internally. The first arguments are identical to plotres.

Usage

## S3 method for class 'earth'
plot(x = stop("no 'x' argument"),

  # the following are identical to plotres arguments

  which = 1:4, info = FALSE, versus = 1, standardize = FALSE, delever = FALSE,
  level = 0, id.n = 3, labels.id = NULL, smooth.col = 2, grid.col = 0,
  jitter = 0, do.par = NULL, caption = NULL,
  trace = 0, npoints = 3000, center = TRUE, type = NULL, nresponse = NA,

  # the following are earth specific

  col.cv = "lightblue", col.grsq = 1, col.rsq = 2, col.infold.rsq = 0,
  col.mean.infold.rsq = 0, col.mean.oof.rsq = "palevioletred",
  col.npreds = if(is.null(object$cv.oof.rsq.tab)) 1 else 0, col.oof.labs = 0,
  col.oof.rsq = "mistyrose2", col.oof.vline = col.mean.oof.rsq,
  col.pch.cv.rsq = 0, col.pch.max.oof.rsq = 0, col.vline = col.grsq,
  col.vseg = 0, lty.grsq = 1, lty.npreds = 2, lty.rsq = 5, lty.vline = "12",
  legend.pos = NULL, ...)

earth_plotmodsel( # for internal use by plotres
  x, col.rsq = 2, col.grsq = 1, col.infold.rsq = 0,
  col.mean.infold.rsq = 0, col.mean.oof.rsq = "palevioletred",
  col.npreds = NULL, col.oof.labs = 0, col.oof.rsq = "mistyrose2",
  col.oof.vline = col.mean.oof.rsq, col.pch.cv.rsq = 0,
  col.pch.max.oof.rsq = 0, col.vline = col.grsq, col.vseg = 0,
  lty.grsq = 1, lty.npreds = 2, lty.rsq = 5, lty.vline = "12",
  legend.pos=NULL, add = FALSE, jitter = 0,
  max.nterms = length(object$rss.per.subset),
  max.npreds=max(1,get.nused.preds.per.subset(object$dirs,object$prune.terms)),
  ...)

Arguments

Note

For details on interpreting the graphs, please see the earth package vignettes “Notes on the earth package” and “Variance models in earth”.

Note that cross-validation data will not be displayed unless both nfold and keepxy were used in the original call to earth.

To remove the Number of used predictors from the Model Selection graph (to reduce clutter), use col.npreds=0.

earth_plotmodsel is provided for use by plotres.

Acknowledgment

This function incorporates the function spread.labs from the orphaned package TeachingDemos written by Greg Snow.

See Also

earth, plot.earth.models, plotd, plotmo

Examples

data(ozone1)
earth.mod <- earth(O3 ~ ., data = ozone1, degree = 2)
plot(earth.mod)

Description

Compare earth models by plotting them.

Usage

## S3 method for class 'earth.models'
plot(x = stop("no 'x' argument"), which = c(1:2),
    caption = "", jitter = 0,
    col.grsq = discrete.plot.cols(length(objects)), lty.grsq = 1,
    col.rsq = 0, lty.rsq = 5,
    col.vline = col.grsq, lty.vline = "12",
    col.npreds = 0,  lty.npreds  = 2,
    legend.text = NULL, do.par = NULL, trace = 0,
    ...)

Arguments

Note

This function ignores GLM and cross-validation components of the earth model, if any.

See Also

earth, plot.earth, plot.earth.models, plotd, plotmo

Examples

data(ozone1)
a1 <- earth(O3 ~ .,          data = ozone1, degree = 2)
a2 <- earth(O3 ~ .-wind,     data = ozone1, degree = 2)
a3 <- earth(O3 ~ .-humidity, data = ozone1, degree = 2)
plot.earth.models(list(a1,a2,a3), ylim=c(.65,.85))

Description

Plot an evimp object.

Usage

## S3 method for class 'evimp'
plot(x = stop("no 'x' argument"),
    cex.var = 1,
    type.nsubsets = "l", col.nsubsets = "black", lty.nsubsets = 1,
    type.gcv = "l", col.gcv = 2, lty.gcv = 1,
    type.rss = "l", col.rss = "gray60", lty.rss = 1,
    cex.legend = 1, x.legend = nrow(x), y.legend = x[1,"nsubsets"],
    rh.col = 1, do.par = TRUE, ...)

Arguments

See Also

earth, evimp, plot.earth.models, plotmo

Examples

data(ozone1)
earth.mod <- earth(O3 ~ ., data=ozone1, degree=2)
ev <- evimp(earth.mod)
plot(ev)
print(ev)

Description

Plot a variance model (a varmod object).

Typically you call this function for a variance model embedded in an earth model.

Usage

## S3 method for class 'varmod'
plot(x = stop("no 'x' argument"), which = 1:4,
  do.par = NULL, info=FALSE,
  cex = NULL, caption = NULL,
  line.col = 2, min.sd.col = line.col,
  trace = 0, ...)

Arguments

Note

The horizontal red dotted line in the first two plots shows the value of min.sd. See earth's varmod.clamp argument.

See Also

varmod

Examples

data(ozone1)

set.seed(1) # optional, for cross validation reproducibility

# note: should really use ncross=30 below but for a quick demo we don't

earth.mod <- earth(O3~temp, data=ozone1, nfold=10, ncross=3, varmod.method="lm")

plot(earth.mod$varmod) # plot the embedded variance model (this calls plot.varmod)

Description

Plot the distribution of the predicted values for each class. Can be used for earth models, but also for models built by lm, glm, lda, etc.

Usage

plotd(object, hist = FALSE, type = NULL, nresponse = NULL, dichot = FALSE,
      trace = FALSE, xlim = NULL, ylim = NULL, jitter = FALSE, main=NULL,
      xlab = "Predicted Value", ylab = if(hist) "Count" else "Density",
      lty = 1, col = c("gray70", 1, "lightblue", "brown", "pink", 2, 3, 4),
      fill = if(hist) col[1] else 0,
      breaks = "Sturges", labels = FALSE,
      kernel = "gaussian", adjust = 1, zero.line = FALSE,
      legend = TRUE, legend.names = NULL, legend.pos = NULL,
      cex.legend = .8, legend.bg = "white", legend.extra = FALSE,
      vline.col = 0, vline.thresh = .5, vline.lty = 1, vline.lwd = 1,
      err.thresh = vline.thresh, err.col = 0, err.border = 0, err.lwd = 1,
      xaxt = "s", yaxt = "s", xaxis.cex = 1, sd.thresh = 0.01, ...)

Arguments

To start off, look at the arguments object, hist, type.
For predict methods with multiple column responses, see the nresponse argument.
For factor responses with more than two levels, see the dichot argument.

data(etitanic)
earth.mod <- earth(survived ~ ., data=etitanic)
plotd(earth.mod, vline.col=1, err.col=c(2,3,4))
      

Note

This function calls predict with the data originally used to build the model, and with the type specified above. It then separates the predicted values into classes, where the class for each predicted value is determined by the class of the observed response. Finally, it calls density (or hist if hist=TRUE) for each class-specific set of values, and plots the results.

This function estimates distributions with the density and hist functions, and also calls plot.density and plot.histogram. For an overview see Venables and Ripley MASS section 5.6.

Partitioning the response into classes

Considerable effort is made to partition the predicted response into classes in a sensible way. This is not always possible for multiple column responses and the nresponse argument should be used where necessary. The partitioning details depend on the types and numbers of columns in the observed and predicted responses. These in turn depend on the model object and the type argument.

Use the trace argument to see how plotd partitions the response for your model.

Degenerate densities

A message such as
Warning: standard deviation of "male" density is 0, density is degenerate?
means that the density for that class will not be plotted (the legend will say "not plotted").

Set sd.thresh=0 to get rid of this check, but be aware that histograms (and sometimes x axis labels) for degenerate densities will be misleading.

Using plotd for various models

This function is included in the earth package but can also be used with other models.

Example with glm:

      library(earth); data(etitanic)
      glm.model <- glm(sex ~ ., data=etitanic, family=binomial)
      plotd(glm.model)
  

Example with lm:

      library(earth); data(etitanic)
      lm.model <- lm(as.numeric(sex) ~ ., data=etitanic)
      plotd(lm.model)
  

Using plotd with lda or qda

The plotd function has special handling for lda (and qda) objects. For such objects, the type argument can take one of the following values:

"response" (default) linear discriminant
"ld" same as "response"
"class" predicted classes
"posterior" posterior probabilities

Example:

    library(MASS); library(earth); data(etitanic)
    lda.model <- lda(sex ~ ., data=etitanic)
    plotd(lda.model) # linear discriminant by default
    plotd(lda.model, type="class", hist=TRUE, labels=TRUE)
    

This handling of type is handled internally by plotd and type is not passed to predict.lda (type is used merely to select fields in the list returned by predict.lda). The type names can be abbreviated down to a single character.

For objects created with lda.matrix (as opposed to lda.formula), plotd blindly assumes that the grouping argument was the second argument.

plotd does not yet support objects created with lda.data.frame.

For lda responses with more than two factor levels, use the nresponse argument to select a column in the predicted response. Thus with the default type=NULL, (which gets automatically converted by plotd to type="response"), use nresponse=1 to select just the first linear discriminant. The default nresponse=NULL selects all columns, which is typically not what you want for lda models. Example:

    library(MASS); library(earth);
    set.seed(1)      # optional, for reproducibility
    example(lda)     # creates a model called "z"
    plot(z, dimen=1) # invokes plot.lda from the MASS package
    plotd(z, nresponse=1, hist=1) # equivalent using plotd
                                 # nresponse=1 selects first linear discr.
    

The dichot=TRUE argument is also useful for lda responses with more than two factor levels.

TODO

Handle degenerate densities in a more useful way.
Add freq argument for hist.

See Also

density, plot.density
hist, plot.histogram
earth, plot.earth

Examples

if (require(earth)) {
    old.par <- par(no.readonly=TRUE);
    par(mfrow=c(2,2), mar=c(4, 3, 1.7, 0.5), mgp=c(1.6, 0.6, 0), cex = 0.8)
    data(etitanic)
    mod <- earth(survived ~ ., data=etitanic, degree=2, glm=list(family=binomial))

    plotd(mod)

    plotd(mod, hist=TRUE, legend.pos=c(.25,220))

    plotd(mod, hist=TRUE, type="class", labels=TRUE, xlab="", xaxis.cex=.8)

    par(old.par)
}

Description

Predict with an earth model.

Usage

## S3 method for class 'earth'
predict(object = stop("no 'object' argument"), newdata = NULL,
        type = c("link", "response", "earth", "class", "terms"),
        interval = "none", level = .95,
        thresh = .5, trace = FALSE, ...)

Arguments

Value

The predicted values (a matrix for multiple response models).

If type="terms", a matrix with each column showing the contribution of a predictor.

If interval="pint" or "cint", a matrix with three columns:
fit: the predicted values
lwr: the lower confidence or prediction limit
upr: the upper confidence or prediction limit

If interval="se", the standard errors.

Note

Predicting with standard earth models

Use the default type="link", or possibly type="class".

Actually, the "link", "response", and "earth" choices all return the same value unless the glm argument was used in the original call to earth.

Predicting with earth-GLM models

This section applies to earth models with a GLM component, i.e., when the glm argument was used in the original call to earth.

The "link" and "response" options: see predict.glm for a description of these. In brief: for logistic models use type="response" to get probabilities, and type="link" to get log-odds.

Use option "earth" to get the linear fit (this gives the prediction you would get if your original call to earth had no glm argument).

Predicting with "class"

Use option "class" to get the predicted class. With option "class", this function first makes predictions with type="response" and then assigns the predicted values to classes as follows:

(i) When the response is a logical, predict TRUE if the predicted probability is greater than thresh (default 0.5).

(ii) When the response is a numeric, predict TRUE if the predicted value is greater than thresh. Actually, this is identical to the above case, although thresh here may legitimately be a value outside the 0...1 range.

(iii) When the response is a two level factor, predict the second level if its probability is more than thresh. In other words, with the default thresh=0.5 predict the most probable level.

(iv) When the response is a three or more level factor, predict the most probable level (and thresh is ignored).

Predicting with "terms"

The "terms" option returns a "link" response suitable for termplot. Only the additive terms and the first response (for multi-response models) are returned. Also, "terms" always returns the earth terms, and ignores the GLM component of the model, if any.

See Also

earth, predict

Examples

data(trees)
earth.mod <- earth(Volume ~ ., data = trees)
predict(earth.mod) # same as earth.mod$fitted.values
predict(earth.mod, data.frame(Girth=10, Height=80)) # yields 17.6
predict(earth.mod, c(10,80))                        # equivalent

Description

You probably won't need to call this function directly. It is called by predict.earth when that function's interval argument is used.

Usage

## S3 method for class 'varmod'
predict(
    object  = stop("no 'object' argument"),
    newdata = NULL,
    type    = c("pint", "cint", "se", "abs.residual"),
    level   = .95,
    trace   = FALSE,
    ...)

Arguments

Note

predict.varmod is called by predict.earth when its interval argument is used.

See Also

predict.earth varmod

Examples

data(ozone1)

set.seed(1) # optional, for cross validation reproducibility

# note: should really use ncross=30 below but for a quick demo we don't

earth.mod <- earth(O3~temp, data=ozone1, nfold=10, ncross=3, varmod.method="lm")

# call predict.earth, which calls predict.varmod

predict(earth.mod, newdata=ozone1[200:203,], interval="pint", level=.95)

Description

Residuals of an earth model.

Usage

## S3 method for class 'earth'
residuals(object = stop("no 'object' argument"),
          type = NULL, warn = TRUE, ...)

Arguments

Value

The residual values (will be a matrix for multiple response models).

See Also

earth
residuals
resid identical to residuals

Examples

data(etitanic)
earth.mod <- earth(pclass ~ ., data=etitanic, glm=list(family=binomial))
head(resid(earth.mod, warn=FALSE))      # earth residuals, a column for each response
head(resid(earth.mod, type="response")) # GLM response resids, a column for each response

Description

Summary method for earth objects.

Usage

## S3 method for class 'earth'
summary(object = stop("no 'object' argument"),
        details = FALSE,  style = c("h", "pmax", "max", "C", "bf"),
        decomp = "anova", digits = getOption("digits"), fixed.point=TRUE,
        newdata = NULL, ...)

## S3 method for class 'summary.earth'
print(x = stop("no 'x' argument"),
        details = x$details,
        decomp = x$decomp, digits = x$digits, fixed.point = x$fixed.point,
        newdata = x$newdata, ...)

Arguments

        (Intercept)    15.029
        h(temp-58)      0.313
        h(234-ibt)     -0.046
        ...

        (Intercept)   1.5e+01
        h(temp-58)    3.1e-01
        h(234-ibt)   -4.6e-02
        ...

Value

The value is the same as that returned by earth but with the following extra components.

Note

The printed Estimated importance uses evimp with the nsubsets criterion. The most important predictor is printed first, and so on.

See Also

earth, evimp, format.earth

Examples

earth.mod <- earth(Volume~ ., data = trees)
summary(earth.mod, digits = 2)

Description

Update an earth model.

Usage

## S3 method for class 'earth'
update(object = stop("no 'object' argument"),
       formula. = NULL, ponly = FALSE, ..., evaluate = TRUE)

Arguments

Details

If only the following arguments are used, a forward pass is unnecessary, and update.earth will perform only the pruning pass. This is usually much faster for large models.

     object
     glm
     trace
     nprune
     pmethod
     Eval.model.subsets
     Print.pruning.pass
     Force.xtx.prune
     Use.beta.cache
     Endspan.penalty
     Get.leverages

This automatic determination to do a forward pass can be overridden with the ponly argument. If ponly=TRUE the forward pass will be skipped and only the pruning pass will be executed. This is useful for doing a pruning pass with new data. (Use earth's data argument to specify the new data.) Typically in this scenario you would also specify penalty=-1. This is because with sufficient new data, independent of the original training data, the RSS not the GCV should be used for evaluating model subsets (The GCV approximates what the RSS would be on new data — but here we actually have new data, so why bother approximating. This "use new data for pruning" approach is useful in situations where you don't trust the GCV approximation for your data.) By making penalty=-1, earth will calculate the RSS, not the GCV. See also the description of penalty on the earth help page.

Another (somewhat esoteric) use of ponly=TRUE is to do subset selection with a different penalty from that used to build the original model.

With trace=1, update.earth will tell you if earth's forward pass was skipped.

If you used keepxy=TRUE in your original call to earth, then update.earth will use the saved values of x, y, etc., unless you specify otherwise by arguments to update.earth. It can be helpful to set trace=1 to see which x and y is used by update.earth.

Value

The value is the same as that returned by earth. If object is the only parameter then no changes are made — the returned value will be the same as the original object.

See Also

earth

Examples

data(ozone1)

(earth.mod <- earth(O3 ~ ., data = ozone1, degree = 2))

update(earth.mod, formula = O3 ~ . - temp) # requires forward pass and pruning

update(earth.mod, nprune = 8)              # requires only pruning

update(earth.mod, penalty=1, ponly=TRUE)   # pruning pass only with a new penalty

Description

A variance model estimates the variance of predicted values. It can be used to estimate prediction intervals. See the interval argument of predict.earth.

A variance model is built by earth if earth's varmod.method argument is specified. Results are stored in the $varmod field of the earth model. See the vignette “Variance models in earth” for details.

You probably won't need to directly call print.varmod or summary.varmod. They get called internally by summary.earth.

Usage

## S3 method for class 'varmod'
summary(
    object  = stop("no 'object' argument"),
    level   = .95,
    style   = "standard",
    digits  = 2,
    newdata = NULL,
    ...)

Arguments

Note

A "varmod" object has the following fields:

• call The call used internally in the parent model to build the varmod object.

• parent The parent earth model.

• method Copy of the varmod.method argument to the parent model.

• package NULL, unless method="gam", in which case either "gam" or "mgcv".

• exponent Copy of the varmod.exponent argument to the parent model.

• lambda Currently always 1, meaning use absolute residuals.

• rmethod Currently always "hc2", meaning correct the residuals with 1/(1-h_ii).

• converged Did the residual submodel IRLS converge?

• iters Number of residual model IRLS iterations (1 to 50).

• residmod The residual submodel. So for example, if varmod.method="lm", this will be an lm object.

• min.sd The predicted residual standard deviation is clamped so it will always be at least this value. This prevents prediction of negative or absurdly small variances. See earth's varmod.clamp argument. Clamping takes place in predict.varmod, which is called by predict.earth when estimating prediction intervals.

• model.var An n x 1 matrix. The model.var for an observation is the estimated model variance for that observation over all datasets, and is estimated with repeated cross validation. It is the variance of the mean out-of-fold prediction for that observation over ncross repetitions.

• abs.resids An n x 1 matrix. The absolute residuals used to build the residual model.

• parent.x An n x p matrix. Parent earth model x.

• parent.y An n x 1 matrix. Parent earth model y.

• iter.rsq Weighted R-Squared of residual submodel residmod, after IRLS iteration.

• iter.stderr Standard errors of the coefficients of the residual submodel residmod, after IRLS iteration.

See Also

plot.varmod, predict.varmod

Examples

data(ozone1)

set.seed(1) # optional, for cross validation reproducibility

# note: should really use ncross=30 below but for a quick demo we don't

earth.mod <- earth(O3~temp, data=ozone1, nfold=10, ncross=3, varmod.method="lm")

print(summary(earth.mod)) # note additional info on the variance model

old.mfrow <- par(mfrow=c(2,2), mar=c(3, 3, 3, 1), mgp=c(1.5, 0.5, 0))

plotmo(earth.mod, do.par=FALSE, response.col=1, level=.90, main="earth model: O3~temp")

plot(earth.mod, which=3, level=.90) # residual plot: note 90% pred and darker conf intervals

par(par=old.mfrow)