Package 'cata'

Title: Analysis of Check-All-that-Apply (CATA) Data
Description: Package contains functions for analyzing check-all-that-apply (CATA) data from consumer and sensory tests. Cochran's Q test, McNemar's test, and Penalty-Lift analysis are provided; for details, see Meyners, Castura & Carr (2013) <doi:10.1016/j.foodqual.2013.06.010>. Cluster analysis can be performed using b-cluster analysis, then evaluated using various measures; for details, see Castura, Meyners, Varela & Næs (2022) <doi:10.1016/j.foodqual.2022.104564>. Methods are adapted to cluster consumers based on their product-related hedonic responses; for details, see Castura, Meyners, Pohjanheimo, Varela & Næs (2023) <doi:10.1111/joss.12860>.
Authors: J.C. Castura [aut, cre, ctb]
Maintainer: J.C. Castura <[email protected]>
License: GPL (>= 2)
Version: 0.1.0.7
Built: 2024-12-08 07:13:38 UTC
Source: CRAN

Help Index

Adjusted Rand index

Description

Calculate the adjusted Rand index between two sets of cluster memberships.

Usage

ARI(x, y, signif = FALSE, n = 1000)

Arguments

x

vector of cluster memberships (integers)
y

vector of cluster memberships (integers)
signif

conduct significance test; default is FALSE
n

number of replicates in Monte Carlo significance test

Value

ari adjusted Rand index

nari normalized adjusted Rand index

sim.mean average value of null distribution (should be closed to zero)

sim.var variance of null distribution

pvalue P value of observed ARI (or NARI) value

References

Hubert, L., & Arabie, P. (1985). Comparing partitions. Journal of Classification, 2, 193–218. doi:10.1007/BF01908075.

Qannari, E.M., Courcoux, P., & Faye, P. (2014). Significance test of the adjusted Rand index. Application to the free sorting task. Food Quality and Preference, 32, 93-97. doi:10.1016/j.foodqual.2013.05.005.

Examples

x <- sample(1:3, 20, replace = TRUE)
y <- sample(1:3, 20, replace = TRUE)

ARI(x, y, signif = FALSE)

Convert 3d array of CATA data to 4d array of CATA differences

Description

Converts a three-dimensional array (I assessors, J products, M attributes) to a four-dimensional array of product comparisons (I assessors, J(J-1)/2 product comparisons, two outcomes (of type b or c), M attributes)

Usage

barray(X, values = "bc", type.in = "binary", type.out = "binary")

Arguments

X

three-dimensional array (I assessors, J products, M attributes) where values are 0 (not checked) or 1 (checked)
values

"bc" (default) returns two outcomes: b and c; otherwise "abcd" returns four outcomes: a, b, c, d.
type.in

type of data submitted; default (binary) may be set to ordinal or scale.
type.out

currently only binary is implemented

Value

A four-dimensional array of product comparisons having I assessors, J(J-1)/2 product comparisons, outcomes (see values parameter), M attributes

References

Castura, J.C., Meyners, M., Varela, P., & Næs, T. (2022). Clustering consumers based on product discrimination in check-all-that-apply (CATA) data. Food Quality and Preference, 104564. doi:10.1016/j.foodqual.2022.104564.

Examples

data(bread)

# Get the 4d array of CATA differences for the first 8 consumers
b <- barray(bread$cata[1:8,,])

Wrapper function for b-cluster analysis

Description

By default, bcluster calls a function to perform b-cluster analysis by a non-hierarchical iterative ascent algorithm, then inspects results if there are multiple runs.

Usage

bcluster(X, inspect = TRUE, inspect.plot = TRUE, algorithm = "n", 
measure = "b", G = NULL, M = NULL, max.iter = 500, X.input = "data", 
tol = exp(-32), runs = 1, seed = 2021)

Arguments

X

three-way array with I assessors, J products, M attributes where CATA data have values 0 (not checked) and 1 (checked)
inspect

default (TRUE) calls the inspect function to evaluate all solutions (when runs>1)
inspect.plot

default (TRUE) plots results from the inspect function
algorithm

default is n for non-hierarchical; h for hierarchical
measure

default is b for the b-measure; Q for Cochran's Q test
G

number of clusters (required for non-hierarchical algorithm)
M

initial cluster memberships
max.iter

maximum number of iteration allowed (default 500)
X.input

available only for non-hierarchical algorithm; its value is either "data" (default) or "bc" if X is obtained from the function barray
tol

non-hierarchical algorithm stops if variance over 5 iterations is less than tol (default: exp(-32))
runs

number of runs (defaults to 1)
seed

for reproducibility (default is 2021)

Value

list with elements:

  • runs : b-cluster analysis results from bcluster.n or bcluster.h (in a list if runs>1)

  • inspect : result from inspect (the plot from this function is rendered if inspect.plot is TRUE)

References

Castura, J.C., Meyners, M., Varela, P., & Næs, T. (2022). Clustering consumers based on product discrimination in check-all-that-apply (CATA) data. Food Quality and Preference, 104564. doi:10.1016/j.foodqual.2022.104564.

Examples

data(bread)

# b-cluster analysis on the first 8 consumers and the first 5 attributes
(b1 <- bcluster(bread$cata[1:8,,1:5], G=2, seed = 123))
# Since the seed is the same, the result will be identical to
# (b2 <- bcluster.n(bread$cata[1:8,,1:5], G=2, seed = 123))
b3 <- bcluster(bread$cata[1:8,,1:5], G=2, runs = 5, seed = 123)

b-cluster analysis by hierarchical agglomerative strategy

Description

Perform b-clustering using the hierarchical agglomerative clustering strategy.

Usage

bcluster.h(X, measure = "b", runs = 1, seed = 2021)

Arguments

X

three-way array; the I, J, M array has I assessors, J products, M attributes where CATA data have values 0 (not checked) and 1 (checked)
measure

currently only b (the b-measure) is implemented
runs

number of runs (defaults to 1; use a higher number of runs for a real application)
seed

for reproducibility (default is 2021)

Value

An object of class hclust from hierarchical b-cluster analysis results (a list of such objects if runs>1), where each hclust object has the structure described in hclust as well as the item retainedB (a vector indicating the retained sensory differentiation at each iteration (merger)).

References

Castura, J.C., Meyners, M., Varela, P., & Næs, T. (2022). Clustering consumers based on product discrimination in check-all-that-apply (CATA) data. Food Quality and Preference, 104564. doi:10.1016/j.foodqual.2022.104564.

Examples

data(bread)

# hierarchical b-cluster analysis on first 8 consumers and first 5 attributes
b <- bcluster.h(bread$cata[1:8,,1:5])

plot(as.dendrogram(b), 
  main = "Hierarchical b-cluster analysis", 
  sub = "8 bread consumers on 5 attributes")

b-cluster analysis by non-hierarchical iterative ascent clustering strategy

Description

Non-hierarchical b-cluster analysis transfers assessors iteratively to reach a local maximum in sensory differentiation retained.

Usage

bcluster.n(X, G, M = NULL, measure = "b", max.iter = 500, runs = 1,
X.input = "data", tol = exp(-32), seed = 2021)

Arguments

X

CATA data organized in a three-way array (assessors, products, attributes)
G

number of clusters (required for non-hierarchical algorithm)
M

initial cluster memberships (default: NULL), but can be a vector (one run) or a matrix (consumers in rows; runs in columns)
measure

b (default) for the b-measure is implemented
max.iter

maximum number of iteration allowed (default 500)
runs

number of runs (defaults to 1)
X.input

either "data" (default) or "bc" if X is obtained from the function barray
tol

algorithm stops if variance over 5 iterations is less than tol (default: exp(-32))
seed

for reproducibility (default is 2021)

Value

An object of class bclust.n (or a list of such objects if runs>1), where each such object has the following components:

  • cluster : vector of the final cluster memberships

  • totalB : value of the total sensory differentiation in data set

  • retainedB : value of sensory differentiation retained in b-cluster analysis solution

  • progression : vector of sensory differentiation retained in each iteration

  • iter : number of iterations completed

  • finished : boolean indicates whether the algorithm converged before max.iter

References

Castura, J.C., Meyners, M., Varela, P., & Næs, T. (2022). Clustering consumers based on product discrimination in check-all-that-apply (CATA) data. Food Quality and Preference, 104564. doi:10.1016/j.foodqual.2022.104564.

Examples

data(bread)

# b-cluster analysis on the first 8 consumers and the first 5 attributes
(b <- bcluster.n(bread$cata[1:8, , 1:5], G=2))

Cochran's Q test

Description

Calculate Cochran's Q test statistic. The null hypothesis that is assumed is that product proportions are all equal. The alternative hypothesis is that product proportions are not all equal.

Usage

cochranQ(X, na.rm = TRUE, quiet = FALSE, digits = getOption("digits"))

Arguments

X

matrix of I assessors (rows) and J products (columns) where values are 0 (not checked) or 1 (checked)
na.rm

should NA values be removed?
quiet

if FALSE (default) then it prints information related to the test; if TRUE it returns only the test statistic (Q)
digits

significant digits (to display)

Value

Q test statistic

References

Cochran, W. G. (1950). The comparison of percentages in matched samples. Biometrika, 37, 256-266.

Meyners, M., Castura, J.C., & Carr, B.T. (2013). Existing and new approaches for the analysis of CATA data. Food Quality and Preference, 30, 309-319, doi:10.1016/j.foodqual.2013.06.010

See Also

mcnemarQ

Examples

data(bread)

# Cochran's Q test on the first 25 consumers on the first attribute ("Fresh")
cochranQ(bread$cata[1:25,,1])

Apply top-k box coding to scale data

Description

Apply top-k box coding to scale data. Using defaults give top-2 box (T2B) coding.

Usage

code.topk(X, zero.below = 8, one.above = 7)

Arguments

X

input matrix
zero.below

default is 8; values below this numeric threshold will be coded 0; use NULL if there is no such threshold
one.above

default is 7; values above this numeric threshold will be coded 1; use NULL if there is no such threshold

Value

matrix X with top-k coding applied

References

Castura, J.C., Meyners, M., Pohjanheimo, T., Varela, P., & Næs, T. (2023). An approach for clustering consumers by their top-box and top-choice responses. Journal of Sensory Studies, e12860. doi:10.1111/joss.12860

Examples

# Generate some data
set.seed(123)
X <- matrix(sample(1:9, 100, replace = TRUE), nrow = 5)

# apply top-2 box (T2B) coding
code.topk(X, zero.below = 8, one.above = 7)

Consumer CATA data set: bread

Description

Raw results from CATA and Liking evaluations of six bread products samples by 161 consumers.

Format

A list with 4 items:

  • $cata : check-all-that-apply (CATA) data (array, 161 consumers x 6 breads x 31 sensory attributes)

  • $liking : 9-point hedonic scale data (matrix, 161 consumers x 6 breads)

  • $ideal.cata : check-all-that-apply (CATA) data for ideal bread (matrix, 161 consumers x 31 sensory attributes)

  • $liking : 9-point hedonic scale data for ideal bread(vector, 161 consumers)

CATA data is coded 1 if the attribute is checked; otherwise it is coded 0

References

Meyners, M., Castura, J.C., & Carr, B.T. (2013). Existing and new approaches for the analysis of CATA data. Food Quality and Preference, 30, 309-319, doi:10.1016/j.foodqual.2013.06.010

Examples

data(bread)
head(bread$cata)

Evaluate Quality of Cluster Analysis Solution

Description

Evaluate the quality of cluster analysis solutions using measures related to within-cluster product discrimination, between-cluster non-redundancy, overall diversity (coverage), average RV, sensory differentiation retained, and within-cluster homogeneity.

Usage

evaluateClusterQuality(X, M, alpha = .05, M.order = NULL, 
quiet = FALSE, digits = getOption("digits"), ...)

Arguments

X

three-way array; the I, J, M array has I assessors, J products, M attributes where CATA data have values 0 (not checked) and 1 (checked)
M

cluster memberships
alpha

significance level to be used for two-tailed tests
M.order

can be used to change the cluster numbers (e.g. to label cluster 1 as cluster 2 and vice versa); defaults to NULL
quiet

if FALSE (default) then it prints information quality measures; if TRUE then returns results without printing
digits

significant digits (to display)
...

other parameters for print.default (if quiet = TRUE).

Value

A list containing cluster analysis quality measures:

  • $solution :

    • Pct.b = percentage of the total sensory differentiation retained in the solution

    • min(NR) = smallest observed between-cluster non-redundancy

    • Div_G = overall diversity (coverage)

    • H_G = overall homogeneity (weighted average of within-cluster homogeneity indices)

    • avRV = average RV coefficient for all between-cluster comparisons

  • $clusters :

    • ng = number of cluster members

    • bg = sensory differentiation retained in cluster

    • xbarg = average citation rate in cluster

    • Hg = homogeneity index within cluster (see homogeneity)

    • Dg = within-cluster product discrimination

  • $nonredundancy.clusterpairs :

    • square data frame showing non-redundancy for each pair of clusters (low values indicate high redundancy)

  • $rv.clusterpairs :

    • square data frame with RV coefficient for each pair of clusters (high values indicate higher similarity in product configurations)

References

Castura, J.C., Meyners, M., Varela, P., & Næs, T. (2022). Clustering consumers based on product discrimination in check-all-that-apply (CATA) data. Food Quality and Preference, 104564. doi:10.1016/j.foodqual.2022.104564.

See Also

homogeneity

Examples

data(bread)
evaluateClusterQuality(bread$cata[1:8,,1:5], M = rep(1:2, each = 4))

Calculate the b-measure

Description

Function to calculate the b-measure, which quantifies the sensory differentiation retained.

Usage

getb(X.b, X.c, oneI = FALSE, oneM = FALSE)

Arguments

X.b

three-way (I, J(J-1)/2, M) array with I assessors, J(J-1)/2 product comparisons, M CATA attributes, where values are counts of type b from the function barray)
X.c

array of same dimension as X.b, where values are counts of type b from the function barray)
oneI

indicates whether calculation is for one assessor (default: FALSE)
oneM

indicates whether calculation is for one attribute (default: FALSE)

Value

b-measure

References

Castura, J.C., Meyners, M., Varela, P., & Næs, T. (2022). Clustering consumers based on product discrimination in check-all-that-apply (CATA) data. Food Quality and Preference, 104564. doi:10.1016/j.foodqual.2022.104564.

Examples

data(bread)

bread.bc <- barray(bread$cata[1:8,,1:5])
getb(bread.bc[,,1,], bread.bc[,,2,])

Calculate within-cluster homogeneity

Description

Within a group of N consumers, the Homogeneity index lies between 1/N (no homogeneity) to 1 (perfect homogeneity).

Usage

homogeneity(X, oneI = FALSE, oneM = FALSE)

Arguments

X

three-way array; the I, J, M array has I assessors, J products, M attributes where CATA data have values 0 (not checked) and 1 (checked)
oneI

indicates whether calculation is for one assessor (default: FALSE)
oneM

indicates whether calculation is for one attribute (default: FALSE)

Value

homogeneity index

References

Llobell, F., Cariou, V., Vigneau, E., Labenne, A., & Qannari, E. M. (2019). A new approach for the analysis of data and the clustering of subjects in a CATA experiment. Food Quality and Preference, 72, 31-39, doi:10.1016/j.foodqual.2018.09.006

Examples

data(bread)

# homogeneity index for the first 7 consumers on the first 6 attributes
homogeneity(bread$cata[1:7,,1:6])

Inspect/summarize many b-cluster analysis runs

Description

Inspect many runs of b-cluster analysis. Calculate sensory differentiation retained and recurrence rate.

Usage

inspect(X, G = 2, bestB = NULL, bestM = NULL, inspect.plot = TRUE)

Arguments

X

list of multiple runs of b-cluster analysis results from bcluster.n or bcluster.h
G

number of clusters (required for non-hierarchical algorithm)
bestB

total sensory differentiation retained in the best solution. If not provided, then bestB is determined from best solution in the runs provided (in X).
bestM

cluster memberships for best solution. If not provided, then the best solution is determined from the runs provided (in X).
inspect.plot

default (TRUE) plots results from the inspect function

Value

A data frame with unique solutions in rows and the following columns:

  • B : Sensory differentiation retained

  • PctB : Percentage of the total sensory differentiation retained

  • B.prop : Proportion of sensory differentiation retained compared to best solution

  • Raw.agree : raw agreement with best solution

  • Count : number of runs for which this solution was observed

  • Index : list index (i.e., run number) of first solution solution in X corresponding to this row

References

Castura, J.C., Meyners, M., Varela, P., & Næs, T. (2022). Clustering consumers based on product discrimination in check-all-that-apply (CATA) data. Food Quality and Preference, 104564. doi:10.1016/j.foodqual.2022.104564.

Examples

data(bread)

res <- bcluster.n(bread$cata[1:8, , 1:5], G = 3, runs = 3)
(ires <- inspect(res))
# get index of solution retaining the most sensory differentiation (in these runs)
indx <- ires$Index[1]
# cluster memberships for solution of this solution
res[[indx]]$cluster

McNemar's test

Description

Pairwise tests are conducted using the two-tailed binomial test. These tests can be conducted after Cochran's Q test.

Usage

mcnemarQ(X, na.rm = TRUE, quiet = FALSE, digits = getOption("digits"))

Arguments

X

matrix of I assessors (rows) and J products (columns) where values are 0 (not checked) or 1 (checked)
na.rm

should NA values be removed?
quiet

if FALSE (default) then it prints information related to the test; if TRUE it returns only the test statistic (Q)
digits

significant digits (to display)

Value

Test results for all McNemar pairwise tests conducted via the binomial test

References

Cochran, W. G. (1950). The comparison of percentages in matched samples. Biometrika, 37, 256-266.

McNemar, Q. (1947). Note on the sampling error of the difference between correlated proportions or percentages. Psychometrika, 12(2), 153-157.

Meyners, M., Castura, J.C., & Carr, B.T. (2013). Existing and new approaches for the analysis of CATA data. Food Quality and Preference, 30, 309-319, doi:10.1016/j.foodqual.2013.06.010

See Also

cochranQ

Examples

data(bread)

# McNemar's exact pairwise test for all product pairs
# on the first 25 consumers and the first attribute ("Fresh")
mcnemarQ(bread$cata[1:25,,1])

Penalty-Lift Analysis

Description

Penalty-Lift analysis for CATA variables, which is the difference between the average hedonic response when CATA attribute is checked vs. the average hedonic response when CATA attribute is not checked.

Usage

pLift(X, Y)

Arguments

X

either a matrix of CATA data with I consumers (rows) and J products (columns) or an array of CATA data with I consumers, J products, and M attributes.
Y

matrix of hedonic data with I consumers (rows) and J products (columns)

Value

Penalty lift for the attribute if X is a matrix; otherwise, penalty-lift for each attribute if X is a 3d array. If an attributes is only checked or not check then NA is returned.

References

Meyners, M., Castura, J.C., & Carr, B.T. (2013). Existing and new approaches for the analysis of CATA data. Food Quality and Preference, 30, 309-319, doi:10.1016/j.foodqual.2013.06.010

Examples

data(bread)

# penalty lift, based only on the first 12 consumers

# for the first attribute ("Fresh")
pLift(bread$cata[1:12,,1], bread$liking[1:12, ]) 

# for the first 3  attributes
pLift(bread$cata[1:12,,1:3], bread$liking[1:12, ])

Calculate RV Coefficient

Description

Calculate RV coefficient

Usage

rv.coef(X, Y, method = 1)

Arguments

X

input matrix (same dimensions as Y)
Y

input matrix (same dimensions as X)
method

1 (default) and 2 give identical RV coefficients

Value

RV coefficient

References

Robert, P., & Escoufier, Y. (1976). A unifying tool for linear multivariate statistical methods: the RV-coefficient. Journal of the Royal Statistical Society: Series C (Applied Statistics), 25, 257-265.

Examples

# Generate some data
set.seed(123)
X <- matrix(rnorm(8), nrow = 4)
Y <- matrix(rnorm(8), nrow = 4)

# get the RV coefficient
rv.coef(X, Y)

Salton's cosine measure

Description

Calculate Salton's cosine measure

Usage

salton(X, Y)

Arguments

X

input matrix (same dimensions as Y)
Y

input matrix (same dimensions as X)

Value

Salton's cosine measure

References

Salton, G., & McGill, M.J. (1983). Introduction to Modern Information Retrieval. Toronto: McGraw-Hill.

Examples

# Generate some data
set.seed(123)
X <- matrix(rnorm(8), nrow = 4)
Y <- matrix(rnorm(8), nrow = 4)

# get Salton's cosine measure
salton(X, Y)

Plot variation in retained sensory differentiation

Description

Plot variation in retained sensory differentiation of cluster memberships obtained from b-cluster analysis. This plot can be used to help the decision of how many clusters to retain.

Usage

selectionPlot(x, pctB = NULL, x.input = "deltaB", indx = NULL, 
ylab = "change in B (K to G)", xlab = NULL)

Arguments

x

input vector which is either deltaB (default; change in sensory differentiation retained) or B (sensory differentiation retained) if x.input is "B"
pctB

vector of percentage of the total sensory differentiation retained
x.input

indicates what x is; either "deltaB" (default) or B.
indx

numeric value indicating which point(s) to emphasize
ylab

label shown on y axis and at selection point
xlab

label for points along x axis

References

Castura, J.C., Meyners, M., Varela, P., & Næs, T. (2022). Clustering consumers based on product discrimination in check-all-that-apply (CATA) data. Food Quality and Preference, 104564. doi:10.1016/j.foodqual.2022.104564.

Examples

set.seed(123)
G2 <- bcluster.n(bread$cata[1:8, , 1:5], G = 2, runs = 3)
G3 <- bcluster.n(bread$cata[1:8, , 1:5], G = 3, runs = 3)
G4 <- bcluster.n(bread$cata[1:8, , 1:5], G = 4, runs = 3)

best.indx <- c(which.max(unlist(lapply(G2, function(x) x$retainedB))),
               which.max(unlist(lapply(G3, function(x) x$retainedB))),
               which.max(unlist(lapply(G4, function(x) x$retainedB))))
               
G1.bc <- barray(bread$cata[1:8, , 1:5])
G1.B <- getb(G1.bc[,,1,], G1.bc[,,2,])
BpctB <- data.frame(retainedB = c(G1.B, 
                                  G2[[best.indx[1]]]$retainedB, 
                                  G3[[best.indx[2]]]$retainedB,
                                  G4[[best.indx[3]]]$retainedB))
BpctB$pctB <- 100*BpctB$retainedB / G2[[1]]$totalB
BpctB$deltaB <- 
           c(100*(1-BpctB$retainedB[-nrow(BpctB)] / BpctB$retainedB[-1]), NA)
BpctB <- BpctB[-nrow(BpctB),]

opar <- par(no.readonly=TRUE)
par(mar = rep(5,4))
selectionPlot(BpctB$deltaB, BpctB$pctB, indx = 2)
par(opar)

Converts 3d array of CATA data to a tall 2d matrix format

Description

Converts a three-dimensional array (I assessors, J products, M attributes) to a two-dimensional matrix with (I assessors, J products) rows and (M attributes) columns, optionally preceded by two columns of row headers.

Usage

toMatrix(X, header.rows = TRUE, oneI = FALSE, oneM = FALSE)

Arguments

X

three-dimensional array (I assessors, J products, M attributes) where values are 0 (not checked) or 1 (checked)
header.rows

TRUE (default) includes row headers; set to FALSE to exclude these headers
oneI

indicates whether calculation is for one assessor (default: FALSE)
oneM

indicates whether calculation is for one attribute (default: FALSE)

Value

A matrix with I assessors * J products in rows and M attributes in columns (preceded by 2 columns) of headers if header.rows = TRUE

Examples

data(bread)

# convert CATA results from the first 8 consumers and the first 4 attributes
# to a tall matrix
toMatrix(bread$cata[1:8,,1:4])

Apply top-c choices coding to a vector of scale data from a respondent

Description

Apply top-c choices coding to a vector of scale data from a respondent

Usage

topc(x, c = 2, coding = "B")

Arguments

x

input matrix
c

number of top choices considered to be 'success'; other choices are considered to be 'failure' and are coded 0
coding

"B" (default) codes all successes as 1; "N" codes all successes with their numeric coding

Value

matrix X with top-k coding applied

References

Castura, J.C., Meyners, M., Pohjanheimo, T., Varela, P., & Næs, T. (2023). An approach for clustering consumers by their top-box and top-choice responses. Journal of Sensory Studies, e12860. doi:10.1111/joss.12860

Examples

# Generate some data
set.seed(123)
X <- matrix(sample(1:9, 100, replace = TRUE), nrow = 5)

# apply top-2 choice (T2C) coding
apply(X, 1, topc)

Converts 3d array of CATA data to a wide 2d matrix format

Description

Converts a three-dimensional array (I assessors, J products, M attributes) to a two-dimensional matrix (J products, (I assessors, M attributes))

Usage

toWideMatrix(X)

Arguments

X

three-dimensional array (I assessors, J products, M attributes) where values are 0 (not checked) or 1 (checked)

Value

A matrix with J products in rows and I assessors * M attributes in columns

Examples

data(bread)

# convert CATA results from the first 8 consumers and the first 4 attributes
# to a wide matrix
toWideMatrix(bread$cata[1:8,,1:4])