Title:	Flexible Clustering of Ordinal and Mixed-with-Ordinal Data
Version:	1.0.0
Description:	Extends the capabilities for flexible partitioning and model-based clustering available in the packages 'flexclust' and 'flexmix' to handle ordinal and mixed-with-ordinal data types via new distance, centroid and driver functions that make various assumptions regarding ordinality. Using them within the flex-scheme allows for easy comparisons across methods.
Imports:	flexclust (≥ 1.5.0), methods, mvtnorm, flexmix
Suggests:	rmarkdown, knitr
License:	GPL-2
Encoding:	UTF-8
URL:	https://zettlchen.github.io/flexord/
BugReports:	https://github.com/dernst/flexord/issues
RoxygenNote:	7.3.2
VignetteBuilder:	rmarkdown, knitr
Depends:	R (≥ 4.3)
NeedsCompilation:	no
Packaged:	2025-03-26 12:02:37 UTC; zettlchen
Author:	Lena Ortega Menjivar [aut, cre], Dominik Ernst [aut], Theresa Scharl [ctb], Bettina Gruen [ctb], Ivan Kondofersky [ctb]
Maintainer:	Lena Ortega Menjivar <lena.ortega-menjivar@boku.ac.at>
Repository:	CRAN
Date/Publication:	2025-03-27 17:50:02 UTC

FlexMix Driver for Regularized Beta-Binomial Mixtures

Description

This model driver can be used to cluster data using the beta-binomial distribution.

Usage

FLXMCregbetabinom(
  formula = . ~ .,
  size = NULL,
  alpha = 0,
  eps = sqrt(.Machine$double.eps)
)

Arguments

Details

Using a regularization parameter alpha greater than zero can be viewed as adding alpha observations equal to the population mean to each component. This can be used to avoid degenerate solutions (i.e., probabilites of 0 or 1). It also has the effect that clusters become more similar to each other the larger alpha is chosen. For small values this effect is, however, mostly negligible.

Value

An object of class "FLXC".

References

Ernst, D, Ortega Menjivar, L, Scharl, T, Grün, B (2025). Ordinal Clustering with the flex-Scheme. Austrian Journal of Statistics. Submitted manuscript.

Kondofersky, I (2008). Modellbasiertes Clustern mit der Beta-Binomialverteilung. Bachelor's thesis, Ludwig-Maximilians-Universität München.

Examples

library("flexmix")
library("flexord")
library("flexclust")

# Sample data
k <- 4     # nr of clusters
size <- 4  # nr of trials
N <- 100   # obs. per cluster

set.seed(0xdeaf)

# random probabilities per component
probs <- lapply(seq_len(k), \(ki) runif(10, 0.01, 0.99))

# sample data
dat <- lapply(probs, \(p) {
    lapply(p, \(p_i) {
        rbinom(N, size, p_i)
    }) |> do.call(cbind, args=_)
}) |> do.call(rbind, args=_)

true_clusters <- rep(1:4, rep(N, k))

# Sample data is drawn from a binomial distribution but we fit
# beta-binomial which is a slight mis-specification but the
# beta-binomial can be seen as a generalized binomial.
m <- flexmix(dat~1, model=FLXMCregbetabinom(size=size, alpha=0),
             cluster = true_clusters)

# Cluster without regularization
m1 <- stepFlexmix(dat~1, model=FLXMCregbetabinom(size=size, alpha=0), k=k)

# Cluster with regularization
m2 <- flexmix(dat~1, model=FLXMCregbetabinom(size=size, alpha=1), k=k,
              cluster = posterior(m1))

# Both models are mostly able to reconstruct the true clusters (ARI ~ 0.95)
# (it's a very easy clustering problem)
# Small values for the regularization don't seem to affect the ARI (much)
randIndex(clusters(m1), true_clusters)
randIndex(clusters(m2), true_clusters)

FlexMix Driver for Regularized Binomial Mixtures

Description

This model driver can be used to cluster data using the binomial distribution.

Usage

FLXMCregbinom(formula = . ~ ., size = NULL, hasNA = FALSE, alpha = 0, eps = 0)

Arguments

Details

Using a regularization parameter alpha greater than zero can be viewed as adding alpha observations equal to the population mean to each component. This can be used to avoid degenerate solutions (i.e., probabilites of 0 or 1). It also has the effect that clusters become more similar to each other the larger alpha is chosen. For small values this effect is, however, mostly negligible.

Parameter estimation is achieved using the MAP estimator for each component and variable using a Beta prior.

Value

An object of class "FLXC".

References

• Ernst, D, Ortega Menjivar, L, Scharl, T, Grün, B (2025). Ordinal Clustering with the flex-Scheme. Austrian Journal of Statistics. Submitted manuscript.

Examples

library("flexmix")
library("flexord")
library("flexclust")

# Sample data
k <- 4     # nr of clusters
size <- 4  # nr of trials
N <- 100   # obs. per cluster

set.seed(0xdeaf)

# random probabilities per component
probs <- lapply(seq_len(k), \(ki) runif(10, 0.01, 0.99))

# sample data
dat <- lapply(probs, \(p) {
    lapply(p, \(p_i) {
        rbinom(N, size, p_i)
    }) |> do.call(cbind, args=_)
}) |> do.call(rbind, args=_)

true_clusters <- rep(1:4, rep(N, k))

# Cluster without regularization
m1 <- stepFlexmix(dat~1, model=FLXMCregbinom(size=size, alpha=0), k=k)

# Cluster with regularization
m2 <- stepFlexmix(dat~1, model=FLXMCregbinom(size=size, alpha=1), k=k)

# Both models are mostly able to reconstruct the true clusters (ARI ~ 0.96)
# (it's a very easy clustering problem)
# Small values for the regularization don't seem to affect the ARI (much)
randIndex(clusters(m1), true_clusters)
randIndex(clusters(m2), true_clusters)

FlexMix Driver for Regularized Multinomial Mixtures

Description

This model driver can be used to cluster data using a multinomial distribution.

Usage

FLXMCregmultinom(formula = . ~ ., r = NULL, alpha = 0)

Arguments

Details

Using a regularization parameter alpha greater than zero acts as adding alpha observations conforming to the population mean to each component. This can be used to avoid degenerate solutions. It also has the effect that clusters become more similar to each other the larger alpha is chosen. For small values it is mostly negligible however.

For regularization we compute the MAP estimates for the multinomial distribution using the Dirichlet distribution as prior, which is the conjugate prior. The parameters of this prior are selected to correspond to the marginal distribution of the variable across all observations.

Value

An object of class "FLXC".

References

• Galindo Garre, F, Vermunt, JK (2006). Avoiding Boundary Estimates in Latent Class Analysis by Bayesian Posterior Mode Estimation Behaviormetrika, 33, 43-59. - Ernst, D, Ortega Menjivar, L, Scharl, T, Grün, B (2025). Ordinal Clustering with the flex-Scheme. Austrian Journal of Statistics. Submitted manuscript.

Examples

library("flexmix")
library("flexord")
library("flexclust")


set.seed(0xdeaf)

# Sample data
k <- 4     # nr of clusters
nvar <- 10  # nr of variables
r <- sample(2:7, size=nvar, replace=TRUE)  # nr of categories
N <- 100   # obs. per cluster


# random probabilities per component
probs <- lapply(seq_len(k), \(ki) runif(nvar, 0.01, 0.99))

# sample data by drawing from a binomial distribution with size = r - 1
# values are expect values to lie inside 1:r hence we add +1.
dat <- lapply(probs, \(p) {
    mapply(\(p_i, r_i) {
        rbinom(N, r_i, p_i) + 1
    }, p, r-1, SIMPLIFY=FALSE) |> do.call(cbind, args=_)
}) |> do.call(rbind, args=_)

true_clusters <- rep(1:4, rep(N, k))

# Cluster without regularization
m1 <- stepFlexmix(dat~1, model=FLXMCregmultinom(r=r, alpha=0), k=k)

# Cluster with regularization
m2 <- stepFlexmix(dat~1, model=FLXMCregmultinom(r=r, alpha=1), k=k)

# Both models are mostly able to reconstruct the true clusters (ARI ~ 0.95)
# (it's a very easy clustering problem)
# Small values for the regularization don't seem to affect the ARI (much)
randIndex(clusters(m1), true_clusters)
randIndex(clusters(m2), true_clusters)

FlexMix Driver for Regularized Multivariate Normal Mixtures

Description

This model driver implements the regularization method as introduced by Fraley and Raftery (2007) for univariate normal mixtures. Default parameters for the regularization according to that paper may be obtained using FLXMCregnorm_defaults(). We extend this to the multivariate case assuming independence between variables within components, i.e., we only implement the special case where the covariance matrix is diagonal. For more general applications of normal mixtures see package mclust.

Usage

FLXMCregnorm(formula = . ~ ., params)

Arguments

Details

For the regularization the conjugate prior distributions for the normal distribution are used, which are:

• Normal prior with parameter mu_p and sigma^2/kappa_p for the mean.

• Inverse Gamma prior with parameters nu_p/2 and zeta_p^2/2 for the variance.

Value

An object of class "FLXC".

References

• Ernst, D, Ortega Menjivar, L, Scharl, T, Grün, B (2025). Ordinal Clustering with the flex-Scheme. Austrian Journal of Statistics. Submitted manuscript.

• Fraley, C, Raftery, AE (2007) Bayesian Regularization for Normal Mixture Estimation and Model-Based Clustering. Journal of Classification, 24(2), 155-181

See Also

FLXMCregnorm_defaults

Examples

library("flexmix")
library("flexord")
library("flexclust")

# example data
data("iris", package = "datasets")
my_iris <- subset(iris, select=setdiff(colnames(iris), "Species")) |>
    as.matrix()

# cluster one model with a scale parameter similar to the default for 3 components
params <- FLXMCregnorm_defaults(my_iris, zeta_p = c(0.23, 0.06, 1.04, 0.19))
m1 <- stepFlexmix(my_iris ~ 1, k = 3, 
    model=FLXMCregnorm(params = params))
summary(m1)

# rand index of clusters vs species
randIndex(clusters(m1), iris$Species)

# cluster one model with default scale parameter
params <- FLXMCregnorm_defaults(my_iris, k = 3)
m2 <- stepFlexmix(my_iris ~ 1, k = 3,
    model = FLXMCregnorm(params = params))
summary(m2)

# rand index of clusters vs species
randIndex(clusters(m2), iris$Species)

# rand index between both models (should be >= 0.8)
randIndex(clusters(m1), clusters(m2))

Data-Driven Default Parameters for Regularized Normal Mixtures

Description

Determines the default values for regularized univariate normal mixtures as proposed by Fraley and Raftery (2007) based on the data set to be clustered and the number of components in the mixture model.

Usage

FLXMCregnorm_defaults(x, zeta_p = NULL, kappa_p = 0.01, nu_p = 3, k = NULL)

Arguments

Value

A named list with values for mu_p, kappa_p, nu_p and zeta_p.

Centroid Functions for K-Centroids Clustering of (Ordinal) Categorical/Mixed Data

Description

Functions to calculate cluster centroids for K-centroids clustering that extend the options available in package flexclust.

centMode calculates centroids based on the mode of each variable. centMin determines centroids within a specified range which minimize the supplied distance metric. centOptimNA replicates the behaviour of flexclust::centOptim() but removes missing values.

These functions are designed for use with flexclust::kcca() or functions that are built upon it. Their use is easiest via the wrapper kccaExtendedFamily().

Usage

centMode(x)

centMin(x, dist, xrange = NULL)

centOptimNA(x, dist)

Arguments

Details

• centMode: Column-wise modes are used as centroids, and ties are broken randomly. In combination with Simple Matching Distance (distSimMatch), this results in the kmodes algorithm.

• centMin: Column-wise centroids are calculated by minimizing the specified distance measure between the values in x and all possible levels of x.

• centOptimNA: Column-wise centroids are calculated by minimizing the specified distance measure via a general purpose optimizer. Unlike in flexclust::centOptim(), NAs are removed from the starting search values and disregarded in the distance calculation.

Value

A named numeric vector containing the centroid values for each column of x.

See Also

kccaExtendedFamily(), flexclust::kcca()

Examples

# Example: Mode as centroid
dat <- data.frame(A = rep(2:5, 2),
                  B = rep(1:4, 2),
                  C = rep(c(1, 2, 4, 5), 2))
centMode(dat)
## within kcca
flexclust::kcca(dat, 3, family=kccaExtendedFamily('kModes')) #default centroid

# Example: Centroid is level for which distance is minimal
centMin(dat, flexclust::distManhattan, xrange = 'all')
## within kcca
flexclust::kcca(dat, 3,
                family=flexclust::kccaFamily(dist=flexclust::distManhattan,
                                             cent=\(y) centMin(y, flexclust::distManhattan,
                                                               xrange='all')))
                             
# Example: Centroid calculated by general purpose optimizer with NA removal
nas <- sample(c(TRUE, FALSE), prod(dim(dat)),
              replace=TRUE, prob=c(0.1,0.9)) |> 
       matrix(nrow=nrow(dat))
dat[nas] <- NA
centOptimNA(dat, flexclust::distManhattan)
## within kcca
flexclust::kcca(dat, 3, family=kccaExtendedFamily('kGower')) #default centroid

Distance Functions for K-Centroids Clustering of (Ordinal) Categorical/Mixed Data

Description

Functions to calculate the distance between a matrix x and a matrix c, which can be used for K-centroids clustering via flexclust::kcca().

distSimMatch implements Simple Matching Distance (most frequently used for categorical, or symmetric binary data) for K-centroids clustering.

distGower implements Gower's Distance after Gower (1971) and Kaufman & Rousseeuw (1990) for mixed-type data with missings for K-centroids clustering.

distGDM2 implements GDM2 distance for ordinal data introduced by Walesiak et al. (1993) and adapted to K-centroids clustering by Ernst et al. (2025).

These functions are designed for use with flexclust::kcca() or functions that are built upon it. Their use is easiest via the wrapper kccaExtendedFamily(). However, they can also easily be used to obtain a distance matrix of x, see Examples.

Usage

distGDM2(x, centers, genDist, xrange = NULL)

distGower(x, centers, genDist)

distSimMatch(x, centers)

Arguments

Details

• distSimMatch: Simple Matching Distance between two observations is calculated as the proportion of disagreements acros all variables. Described, e.g., in Kaufman & Rousseeuw (1990), p. 24. If this is used in K-centroids analysis in combination with mode centroids (as implemented in centMode), this results in the kModes algorithm. A wrapper for this algorithm is obtained with kccaExtendedFamily(which='kModes').

• distGower: Distances are calculated for each column (Euclidean distance, distEuclidean, is recommended for numeric, Manhattan distance, distManhattan for ordinal, Simple Matching Distance, distSimMatch for categorical, and Jaccard distance, distJaccard for asymmetric binary variables), and they are summed up as:

  d(x_i, x_k) = \frac{\sum_{j=1}^p \delta_{ikj} d(x_{ij}, x_{kj})}{\sum_{j=1}^p \delta_{ikj}}

  where p is the number of variables and with the weight \delta_{ikj} being 1 if both values x_{ij} and x_{kj} are not missing, and in the case of asymmetric binary variables, at least one of them is not 0. Please note that for calculating Gower's distance, scaling of numeric/ordered variables is required (as f.i. by .ScaleVarSpecific). A wrapper for K-centroids analysis using Gower's distance in combination with a numerically optimized centroid is found in kccaExtendedFamily(which='kGower').

• distGDM2: GDM2 distance for ordinal variables conducts only relational operations on the variables, such as \leq, \geq and =. By translating x to its relative frequencies and empirical cumulative distributions, we are able to extend this principle to compare two arbitrary values, and thus use it within K-centroids clustering. For more details, see Ernst et al. (2025). A wrapper for this algorithm in combination with a numerically optimized centroid is found in kccaExtendedFamily(which='kGDM2').

The distances functions presented here can also be used in clustering algorithms that rely on distance matrices (such as hierarchical clustering and PAM), if applied accordingly, see Examples.

Value

A matrix of dimensions c(nrow(x), nrow(centers)) that contains the distance between each row of x and each row of centers.

References

• Ernst, D, Ortega Menjivar, L, Scharl, T, Grün, B (2025). Ordinal Clustering with the flex-Scheme. Austrian Journal of Statistics. Submitted manuscript.

• Gower, JC (1971). A General Coefficient for Similarity and Some of Its Properties. Biometrics, 27(4), 857-871. doi:10.2307/2528823

• Kaufman, L, Rousseeuw, P (1990). Finding Groups in Data: An Introduction to Cluster Analysis. Wiley Series in Probability and Statistics. doi:10.1002/9780470316801

• Leisch, F (2006). A Toolbox for K-Centroids Cluster Analysis. Computational Statistics and Data Analysis, 17(3), 526-544. doi:10.1016/j.csda.2005.10.006

• Kaufman, L, Rousseeuw, P (1990.) Finding Groups in Data: An Introduction to Cluster Analysis. Wiley Series in Probability and Statistics, New York: John Wiley & Sons. doi:10.1002/9780470316801

• Walesiak, M (1993). Statystyczna Analiza Wielowymiarowa w Badaniach Marketingowych. Wydawnictwo Akademii Ekonomicznej, 44-46.

• Weihs, C, Ligges, U, Luebke, K, Raabe, N (2005). klaR Analyzing German Business Cycles. In Baier D, Decker, R, Schmidt-Thieme, L (eds.). Data Analysis and Decision Support, 335-343. Berlin: Springer-Verlag. doi:10.1007/3-540-28397-8_36

See Also

flexclust::kcca(), klaR::kmodes(), cluster::daisy(), clusterSim::dist.GDM()

Examples

# Example 1: Simple Matching Distance
set.seed(123)
dat <- data.frame(question1 = factor(sample(LETTERS[1:4], 10, replace=TRUE)),
                  question2 = factor(sample(LETTERS[1:6], 10, replace=TRUE)),
                  question3 = factor(sample(LETTERS[1:4], 10, replace=TRUE)),
                  question4 = factor(sample(LETTERS[1:5], 10, replace=TRUE)),
                  state = factor(sample(state.name[1:10], 10, replace=TRUE)),
                  gender = factor(sample(c('M', 'F', 'N'), 10, replace=TRUE,
                                         prob=c(0.45, 0.45, 0.1))))
datmat <- data.matrix(dat)
initcenters <- datmat[sample(1:10, 3),]
distSimMatch(datmat, initcenters)
## within kcca
flexclust::kcca(dat, k=3, family=kccaExtendedFamily('kModes'))
## as a distance matrix
as.dist(distSimMatch(datmat, datmat))

# Example 2: GDM2 distance
flexclust::kcca(dat, k=3, family=kccaExtendedFamily('kGDM2'))

# Example 3: Gower's distance
# Ex. 3.1: single variable type case with no missings:
flexclust::kcca(datmat, 3, kccaExtendedFamily('kGower'))

# Ex. 3.2: single variable type case with missing values:
nas <- sample(c(TRUE, FALSE), prod(dim(dat)), replace = TRUE,
   prob=c(0.1, 0.9)) |> 
   matrix(nrow = nrow(dat))
dat[nas] <- NA
flexclust::kcca(dat, 3, kccaExtendedFamily('kGower', cent=centMode))

#Ex. 3.3: mixed variable types (with or without missings): 
dat <- data.frame(cont = sample(1:100, 10, replace=TRUE)/10,
                  bin_sym = as.logical(sample(0:1, 10, replace=TRUE)),
                  bin_asym = as.logical(sample(0:1, 10, replace=TRUE)),                     
                  ord_levmis = factor(sample(1:5, 10, replace=TRUE),
                                      levels=1:6, ordered=TRUE),
                  ord_levfull = factor(sample(1:4, 10, replace=TRUE),
                                       levels=1:4, ordered=TRUE),
                  nom = factor(sample(letters[1:4], 10, replace=TRUE),
                               levels=letters[1:4]))
dat[nas] <- NA
flexclust::kcca(dat, 3, kccaExtendedFamily('kGower'))

Extending K-Centroids Clustering to (Mixed-with-)Ordinal Data

Description

This wrapper creates objects of class "kccaFamily", which can be used with flexclust::kcca() to conduct K-centroids clustering using the following methods:

• kModes (after Weihs et al., 2005)

• kGower (Gower's distance after Kaufman & Rousseeuw, 1990, and a user specified centroid)

• kGDM2 (GDM2 distance after Walesiak et al., 1993, and a user specified centroid)

Usage

kccaExtendedFamily(which = c('kModes', 'kGDM2', 'kGower'),
                   cent = NULL,
                   preproc = NULL,
                   xrange = NULL,
                   xmethods = NULL,
                   trim = 0, groupFun = 'minSumClusters')

Arguments

This argument is ignored for `which='kModes'`, and `centMode`
is used.  For `'kGDM2'` and `'kGower'`, `cent=NULL` defaults to
a general purpose optimizer.

This argument is ignored for `which='kGower'`. In this case,
the default preprocessing proposed by Gower (1971) and Kaufman
& Rousseeuw (1990) is conducted. For `'kGDM2'` and `'kModes'`,
users can specify preprocessing steps here, though this is not
recommended.

Default is `'minSumClusters'`, see [flexclust::kccaFamily()].

Details

Wrappers for defining families are obtained by specifying which using:

• which='kModes' creates an object for kModes clustering, i.e., K-centroids clustering using Simple Matching Distance (counts of disagreements) and modes as centroids. Argument cent is ignored for this method.

• which='kGower' creates an object for performing clustering using Gower's method as described in Kaufman & Rousseeuw (1990):

  • Numeric and/or ordinal variables are scaled by \frac{\mathbf{x}-\min{\mathbf{x}}}{\max{\mathbf{x}-\min{\mathbf{x}}}}. Note that for ordinal variables the internal coding with values from 1 up to their maximum level is used.

  • Distances are calculated for each column (Euclidean distance, distEuclidean, is recommended for numeric, Manhattan distance, distManhattan for ordinal, Simple Matching Distance, distSimMatch for categorical, and Jaccard distance, distJaccard for asymmetric binary variables), and they are summed up as:

    d(x_i, x_k) = \frac{\sum_{j=1}^p \delta_{ikj} d(x_{ij}, x_{kj})}{\sum_{j=1}^p \delta_{ikj}}

    where p is the number of variables and with the weight \delta_{ikj} being 1 if both values x_{ij} and x_{kj} are not missing, and in the case of asymmetric binary variables, at least one of them is not 0.

    The columnwise distances used can be influenced in two ways: By passing a character vector of length p to xmethods that specifies the distance for each column. Options are: distEuclidean, distManhattan, distJaccard, and distSimMatch. Another option is to not specify any methods within kccaExtendedFamily, but rather pass a "data.frame" as argument x in kcca, where the class of the column is used to infer the distance measure. distEuclidean is used on numeric and integer columns, distManhattan on columns that are coded as ordered factors, distSimMatch is the default for categorically coded columns, and distJaccard is the default for binary coded columns.

    For this method, if cent=NULL, a general purpose optimizer with NA omission is applied for centroid calculation.

• which='kGDM2' creates an obejct for clustering using the GDM2 distance for ordinal variables. The GMD2 distance was first introduced by Walesiak et al. (1993), and adapted in Ernst et al. (2025), as the distance measure within flexclust::kcca().

  This distance respects the ordinal nature of a variable by conducting only relational operations to compare values, such as \leq, \geq and =. By obtaining the relative frequencies and empirical cumulative distributions of x, we allow for comparison of two arbitrary values, and thus are able to conduct K-centroids clustering. For more details, see Ernst et al. (2025).

Also for this method, if cent=NULL, a general purpose optimizer with NA omission will be applied for centroid calculation.

Scale handling. In 'kModes', all variables are treated as unordered factors. In 'kGDM2', all variables are treated as ordered factors, with strict assumptions regarding their ordinality. 'kGower' is currently the only method designed to handle mixed-type data. For ordinal variables, the assumptions are more lax than with GDM2 distance.

NA handling. NA handling via omission and upweighting non-missing variables is currently only implemented for 'kGower'. Within 'kModes', the omission of NA responses can be avoided by coding missings as valid factor levels. For 'kGDM2', currently the only option is to omit missing values completely.

Value

An object of class "kccaFamily".

References

• Ernst, D, Ortega Menjivar, L, Scharl, T, Grün, B (2025). Ordinal Clustering with the flex-Scheme. Austrian Journal of Statistics. Submitted manuscript.

• Gower, JC (1971). A General Coefficient for Similarity and Some of Its Properties. Biometrics, 27(4), 857-871. doi:10.2307/2528823

• Kaufman, L, Rousseeuw, P (1990). Finding Groups in Data: An Introduction to Cluster Analysis. Wiley Series in Probability and Statistics. doi:10.1002/9780470316801

• Leisch, F (2006). A Toolbox for K-Centroids Cluster Analysis. Computational Statistics and Data Analysis, 17(3), 526-544. doi:10.1016/j.csda.2005.10.006

• Walesiak, M (1993). Statystyczna Analiza Wielowymiarowa w Badaniach Marketingowych. Wydawnictwo Akademii Ekonomicznej, 44-46.

• Weihs, C, Ligges, U, Luebke, K, Raabe, N (2005). klaR Analyzing German Business Cycles. In: Data Analysis and Decision Support, Springer: Berlin. 335-343. doi:10.1007/3-540-28397-8_36

See Also

flexclust::kcca(), flexclust::stepFlexclust(), flexclust::bootFlexclust()

Examples

# Example 1: kModes
set.seed(123)
dat <- data.frame(cont = sample(1:100, 10, replace=TRUE)/10,
                  bin_sym = as.logical(sample(0:1, 10, replace=TRUE)),
                  bin_asym = as.logical(sample(0:1, 10, replace=TRUE)),                     
                  ord_levmis = factor(sample(1:5, 10, replace=TRUE),
                                      levels=1:6, ordered=TRUE),
                  ord_levfull = factor(sample(1:4, 10, replace=TRUE),
                                       levels=1:4, ordered=TRUE),
                  nom = factor(sample(letters[1:4], 10, replace=TRUE),
                               levels=letters[1:4]))
flexclust::kcca(dat, k=3, family=kccaExtendedFamily('kModes'))

# Example 2: kGDM2
flexclust::kcca(dat, k=3, family=kccaExtendedFamily('kGDM2',
                                                    xrange='columnwise'))
# Example 3: kGower
flexclust::kcca(dat, 3, kccaExtendedFamily('kGower'))
nas <- sample(c(TRUE,FALSE), prod(dim(dat)), replace=TRUE, prob=c(0.1,0.9)) |> 
   matrix(nrow=nrow(dat))
dat[nas] <- NA
flexclust::kcca(dat, 3, kccaExtendedFamily('kGower',
                                           xrange='all'))
flexclust::kcca(dat, 3, kccaExtendedFamily('kGower',
                                           xmethods=c('distEuclidean',
                                                      'distEuclidean',
                                                      'distJaccard',
                                                      'distManhattan',
                                                      'distManhattan',
                                                      'distSimMatch')))
#the case where column 2 is a binary variable, but is symmetric

Low Back Pain Diagnoses and Diagnosis Criteria

Description

In a 2011 study, Smart et al. (2011) collected information on 464 Irish and British patients suffering from low back pain regarding:

• the type of low back pain (classified into "nociceptive", "peripheral neuropathic", and "central neuropathic")

• the presence/absence of 38 clinical criteria and symptoms relating to low back pain.

Fop et al. (2017) conducted Latent Class Analysis on this data set to retrieve the experts' classifications; and by comparing nested models they were able to select 11 out of 38 criteria which contain the most of the relevant grouping information while avoiding redundancy.

Usage

data('lowbackpain')

Format

A list containing:

data:

A 464x11 binary matrix indicating the presence/absence of the 11 selected criteria for each of the 464 patients.

group:

A factor of length 464 indicating the diagnosis each patient received, numerically coded (order has no meaning).

index:

The index for the criteria explaining which symptom they refer to.

Source

Supplemental Content for Fop et al. (2017): doi:10.1214/17-AOAS1061SUPP

References

• Fop, M, Smart, K, Murphy, TB (2017). Variable Selection for Latent Class Analysis with Application to Low Back Pain Diagnosis. The Annals of Applied Statitics. 11(4), 2080-2110. doi:10.1214/17-aoas1061

• Smart, K, Blake, C, Staines, A, Doody, C (2011). The Discriminative Validity of "Nociceptive", "Peripheral Neuropathic", and "Central Sensitization" as Mechanisms-Based Classifications of Musculoskeletal Pain. The Clinical Journal of Pain. 27, 655-663. doi:10.1097/AJP.0b013e318215f16a

Risk Aversion

Description

Survey data from 563 respondents on frequency of risk taking on six different types. Taken from the companion package to Market Segmentation Analysis: Understanding It, Doing It, and Making It Useful (Dolnicar et al., 2018, doi:10.1007/978-981-10-8818-6).

Usage

data('risk')

Format

A matrix with 563 respondents (rows) and 6 variables (columns) named Recreational, Health, Career, Financial, Safety and Social.

Details

The data was collected by academic researchers using a permission based online panel.

The sample was taken from adult Australian residents who have undertaken at least one holiday in the last year which involved staying away from home for at least four nights.

The respondents were asked: "Which risks have you taken in the past?" and answered on a 5-point scale with options:

• Never (1)

• Rarely (2)

• Quite often (3)

• Often (4)

• Very often (5)

The six types of risk were:

• Recreational: e.g. rock-climbing, scuba diving

• Health: e.g., smoking, poor diet, high alcohol consumption

• Career: e.g., quitting a job without another to go to

• Financial: e.g., gambling, risky investments

• Safety: e.g., speeding

• Social: e.g., standing for election, publicly challenging a rule or decision

Source

Sara Dolnicar.

Data and help page are taken from the companion package to Market Segmentation Analysis: Understanding It, Doing It, and Making It Useful (Dolnicar et al., 2018, doi:10.1007/978-981-10-8818-6).

URL: https://statistik.boku.ac.at/nachlass_leisch/MSA/

References

• Hajibaba H, Dolnicar S (2017). Helping When Disaster Hits. In: Dolnicar S (ed) Peer-to-Peer Accomodation Networks: Pushing the Boundaries, Goodfellow Publishers, Oxford, chap.21, 235-243. doi:10.23912/9781911396512-3619

• Hajibaba H, Karlsson L, Dolnicar S (2017) Residents Open Their Homes to Tourists When Disaster Strikes. Journal of Travel Research. 58(8), 1065-1078. doi:10.1177/0047287516677167