Type:	Package
Title:	Analysis of Check-All-that-Apply (CATA) Data
Version:	0.1.0.27
Date:	2025-02-24
Author:	J.C. Castura [aut, cre, ctb]
Maintainer:	J.C. Castura <jcastura@compusense.com>
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>. Permutation tests based on the L1-norm methods are provided; for details, see Chaya, Castura & Greenacre (2025) <doi:10.48550/arXiv.2502.15945>.
URL:	https://CRAN.R-project.org/package=cata
Depends:	R (≥ 4.4.0)
Imports:	stats, utils, graphics
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
LazyData:	TRUE
Encoding:	UTF-8
RoxygenNote:	7.3.2
NeedsCompilation:	no
Packaged:	2025-02-25 04:42:20 UTC; jcastura
Repository:	CRAN
Date/Publication:	2025-02-25 08:20:02 UTC

Adjusted Rand index

Description

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

Usage

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

Arguments

Value

list of the following:

• 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

• p.value P value of observed ARI (or NARI) value

Author(s)

J.C. Castura

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)

Consumer CATA data set: bread

Description

Consumer data from 161 assessors (consumers) who evaluated 6 products (breads) using a check-all-that-apply (CATA) question and the 9-point hedonic scale.

Format

List with items:

• $cata: CATA data array (161 consumers \times 6 breads \times 31 sensory attributes)

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

• $ideal.cata: CATA data matrix for ideal bread evaluations (161 consumers \times 31 sensory attributes)

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

Responses to CATA questions are each coded 1 if the assessor checks the attribute for the product; 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)
  # view CATA frequency table
  apply(bread$cata, 2:3, sum)

Consumer CATA data set: squashes

Description

Check-all-that-apply (CATA) data set from 100 assessors (consumers) who evaluated 11 products (blackcurrant squashes) using 34 terms.

Format

Array of data coded 1 if the assessor checked the term for the attribute and 0 otherwise.

• Dimension 1 : 100 assessors

• Dimension 2 : 11 products

• Dimension 3 : 34 terms

A response is coded 1 if the attribute is checked; otherwise it is coded 0.

References

Ng, M., Chaya, C., & Hort, J. (2013). Beyond liking: Comparing the measurement of emotional response using EsSense Profile and consumer defined check-all-that-apply methodologies. Food Quality and Preference, 28, 193-205, doi:10.1016/j.foodqual.2012.08.012

Examples

  data(squashes)
  # view CATA frequency table
  apply(squashes, 2:3, sum)

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

Value

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

Author(s)

J.C. Castura

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

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)

Author(s)

J.C. Castura

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

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)).

Author(s)

J.C. Castura

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

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

Author(s)

J.C. Castura

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

Conduct Cochran's Q test assuming equal columns proportions for matched binary responses versus the alternative hypothesis of unequal column proportions.

Usage

cochranQ(X, quiet = FALSE, digits = getOption("digits"))

Arguments

Details

Method returns test statistic, degrees of freedom, and p value from Cochran's Q test.

Value

Cochran's Q test results (statistic, degrees of freedom, p-value)

Author(s)

J.C. Castura

References

Cochran, W.G. (1950). The comparison of percentages in matched samples. Biometrika, 37, 256-266, doi:10.2307/2332378

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 50 consumers on the first attribute ("Fresh")
cochranQ(bread$cata[1:50, , 1], digits=3)

# Same, returning only test statistics for the first 4 attributes
t(res <- apply(bread$cata[1:50, , 1:4], 3, cochranQ, quiet=TRUE, digits=3))

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

Value

matrix X with top-k coding applied

Author(s)

J.C. Castura

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)

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

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)

Author(s)

J.C. Castura

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

Value

b-measure

Author(s)

J.C. Castura

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

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

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

Author(s)

J.C. Castura

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

MAD distances between objects

Description

Computes and returns inter-object median of absolute deviations (MADs) based differences.

Usage

mad.dist(X)

Arguments

Value

object of class dist giving inter-object MAD distances

Author(s)

J.C. Castura

References

Chaya, C., Castura, J.C., & Greenacre, M.J. (2025). One citation, one vote! A new approach for analyzing check-all-that-apply (CATA) data in sensometrics, using L1 norm methods. doi:10.48550/arXiv.2502.15945

Examples

data(bread)
CATA.freq <- apply(bread$cata, 2:3, sum)
# median-center columns (attributes)
CATA.swept <- sweep(CATA.freq, 2, apply(CATA.freq, 2, median))
# cluster analysis of products using complete linkage
dist.Products <- mad.dist(CATA.swept)
plot(as.dendrogram(hclust(dist.Products, method = "complete")), main = "Product clusters")
# cluster analysis of attributes using complete linkage
dist.Att <- mad.dist(t(CATA.swept))
plot(as.dendrogram(hclust(dist.Att, method = "complete")), main = "Attribute clusters")

Permutation tests for CATA data

Description

Permutation tests for check-all-that-apply (CATA) data following the 'one citation, one vote' principle. Returns CATA frequency and percentage tables per condition and permutation test results specified.

Usage

madperm(X, B = 99, seed = .Random.seed, tests = 1:5, alpha = 0.05, control.fdr = FALSE, 
verbose = FALSE)

Arguments

Value

list, one per condition:

• CATA.table : table of CATA citation percentages (P \times T)

• CATA.freq : CATA frequency table (P \times T)

• Permutation test results specified by the tests parameter

  1. Global.Results : list of multivariate (global) results

  2. Univariate.Results : list of T univariate results

  3. Elementwise.Results : list of PT elementwise results

  4. Multivariate.Paired.Results : list of P(P-1)/2 multivariate paired results

  5. Univariate.Paired.Results : list of P(P-1)T/2 univariate paired results

also, if verbose is TRUE:

• Null.Dist list of null distributions for tests specified

• Call : madperm function call

Author(s)

J.C. Castura

References

Chaya, C., Castura, J.C., & Greenacre, M.J. (2025). One citation, one vote! A new approach for analyzing check-all-that-apply (CATA) data in sensometrics, using L1 norm methods. doi:10.48550/arXiv.2502.15945

Examples

data(bread)
# add product names
X <- bread$cata[1:100,,1:5]
dimnames(X)[[2]] <- paste0("P", dimnames(X)[[2]])
# permutation tests for the first 100 consumers and 5 attributes
# will be run with default parameter values for illustrative purposes only
res <- madperm(X, B = 99, seed = 123)
print(res) # inspect results

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, quiet = FALSE, digits = getOption("digits"))

Arguments

Value

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

Author(s)

J.C. Castura

References

Cochran, W.G. (1950). The comparison of percentages in matched samples. Biometrika, 37, 256-266. doi:10.2307/2332378

McNemar, Q. (1947). Note on the sampling error of the difference between correlated proportions or percentages. Psychometrika, 12(2), 153-157. doi:10.1007/BF02295996

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 50 consumers and the first attribute ("Fresh")
mcnemarQ(bread$cata[1:50, , 1])

# Same, returning only results for the first 4 attributes
(res <- apply(bread$cata[1:50, , 1:4], 3, mcnemarQ, quiet=TRUE, simplify=FALSE))

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, digits = getOption("digits"), verbose = FALSE)

Arguments

Value

Penalty lift per attribute, with counts and averages if verbose is TRUE.

Author(s)

J.C. Castura

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, ], digits = 3) 

# for the first 3  attributes with counts and averages
plift(bread$cata[1:12,,1:3], bread$liking[1:12, ], digits = 3, verbose = TRUE) 

Calculate RV Coefficient

Description

Calculate RV coefficient

Usage

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

Arguments

Value

RV coefficient

Author(s)

J.C. Castura

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. doi:10.2307/2347233

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

Value

Salton's cosine measure

Author(s)

J.C. Castura

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

Author(s)

J.C. Castura

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

Value

A matrix with I assessors \times 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])

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

Value

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

Author(s)

J.C. Castura

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])

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

Value

matrix X with top-k coding applied

Author(s)

J.C. Castura

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)