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Type:

Package

Title:

Multiple Imputation in Cluster Analysis

Version:

1.3.0

Description:

Implementation of a framework for cluster analysis with selection of the final number of clusters and an optional variable selection procedure. The package is designed to integrate the results of multiple imputed datasets while accounting for the uncertainty that the imputations introduce in the final results. In addition, the package can also be used for a cluster analysis of the complete cases of a single dataset. The package also includes specific methods to summarize and plot the results. The methods are described in Basagana et al. (2013) <doi:10.1093/aje/kws289>.

Depends:

R (≥ 4.1)

License:

GPL-3

Encoding:

UTF-8

LazyData:

true

Suggests:

knitr, xtable, rmarkdown

Imports:

doBy, combinat, flexclust, graphics, matrixStats, stats, utils

Author:

Jose Barrera-Gomez

[aut, cre], Xavier Basagana

[aut]

Maintainer:

Jose Barrera-Gomez <jose.barrera@isglobal.org>

Config/roxygen2/version:

8.0.0

NeedsCompilation:

Packaged:

2026-06-08 18:02:05 UTC; jbarrera

Repository:

CRAN

Date/Publication:

2026-06-08 19:00:02 UTC

miclust-package: integrating multiple imputation with cluster analysis

Description

Cluster analysis with selection of the final number of clusters and an optional variable selection procedure. The package is designed to integrate the results of multiply imputed datasets while accounting for the uncertainty that the imputations introduce in the final results. See ‘Procedure’ below for further details on how the tool works.

Procedure

The tool consists of a two-step procedure. In the first step the user provides the data to be analysed. They can be a single data.frame or a list of data.frames including the raw data and the imputed datasets. In the latter case, getdata needs to by used first to get data prepared. In the second step, the miclust performs k-means clustering with selection of the final number of clusters and an optional (backward or forward) variable selection procedure. Specific summary and plot methods are provided to summarize and visualize the impact of the imputations on the results.

Authors

Jose Barrera-Gomez (maintainer, <jose.barrera@isglobal.org>) and Xavier Basagana.

Author(s)

Maintainer: Jose Barrera-Gomez jose.barrera@isglobal.org (ORCID)

Authors:

Jose Barrera-Gomez jose.barrera@isglobal.org (ORCID)
Xavier Basagana xavier.basagana@isglobal.org (ORCID)

References

The methodology used in the package is described in

Basagana X, Barrera-Gomez J, Benet M, Anto JM, Garcia-Aymerich J. A Framework for Multiple Imputation in Cluster Analysis. American Journal of Epidemiology. 2013;177(7):718-725.

Creates a `midata` object.

Description

Creates an object of class miData to be clustered by the function miclust.

Usage

getdata(data)

Arguments

data

a list or data.frame object. If it is a data frame, it is assumed to contain just the raw data, with or without missing data. If it is a list of data frames, it is assumed that the first element contains the raw data and the remaining ones correspond to multiple imputed datasets. Since all variables are considered in the clustering procedure, no identifier variables must be present in the data. In addition, all variables need to be treated as numeric (i.e., categorical variables must be coded with numeric values). See Details below.

Details

All variables in data frames in impdata are standardized by getdata, so categorical variables need to be coded with numeric values. Standardization is performed by centering all variables at the mean and then dividing by the standard deviation (or the difference between the maximum and the minimum values for binary variables). Such a standardization is applied only to the imputed datasets. The standardization of the raw data is internally applied by the miclust if needed (which is the case of analysing just the raw data, i.e., complete cases analysis).

Value

An object of classes "list" and "midata" including the following items:

rawdata: a data frame containing the raw data.
impdata: if data is an object of class list, impdata is a list containing the standardized imputed datasets.

Examples

### data minhanes:
data(minhanes)
class(minhanes)

### number of imputed datasets:
length(minhanes) - 1

### raw data with missing values:
summary(minhanes[[1]])

### first imputed dataset:
minhanes[[2]]
summary(minhanes[[2]])

### data preparation for a complete case cluster analysis:
data1 <- getdata(minhanes[[1]])
class(data1)
names(data1)

### there are no imputed datasets:
data1$impdata

### data preparation for a multiple imputation cluster analysis:
data2 <- getdata(minhanes)
class(data2)
names(data2)

### number of imputed datasets:
length(data2$impdata)

### imputed datasets are standardized:
summary(data2$rawdata)
summary(data2$impdata[[1]])

Calculates the ranked selection frequency of the variables.

Description

Creates a ranked selection frequency for all the variables that have been selected at least once along the analysed imputed datasets. getvariablesfrequency can be useful for customizing the plot of these frequencies as it is shown in Examples below.

Usage

getvariablesfrequency(x, k = NULL)

Arguments

x

an object of class miclust obtained with the function miclust.

k

the number of clusters. The default value is the optimal number of clusters obtained by the function miclust.

Value

A list including the following items:

percfreq: vector of the selection frequencies (percentage of times) of the variables in decreasing order.
varnames: names of the variables.

Examples

### see examples in miclust.

Cluster analysis in multiple imputed datasets with optional variable selection.

Description

Performs cluster analysis in multiple imputed datasets with optional variable selection. Results can be summarized and visualized with the summary and plot methods.

Usage

miclust(
  data,
  method = "kmeans",
  search = c("none", "backward", "forward"),
  ks = 2:3,
  maxvars = NULL,
  usedimp = NULL,
  distance = c("manhattan", "euclidean"),
  centpos = c("means", "medians"),
  initcl = c("hc", "rand"),
  verbose = TRUE,
  seed = NULL
)

## S3 method for class 'miclust'
print(x, ...)

## S3 method for class 'miclust'
plot(
  x,
  k = NULL,
  metric = c("all", "nclfreq", "critcf", "nvarfreq", "varsel"),
  col.nclfreq = "gray",
  col.critcf = "gray",
  col.nvarfreq = "gray",
  col.varsel = "black",
  col.all = NULL,
  ...
)

Arguments

data

object of class midata obtained with the function getdata.

method

clustering method. Currently, only "kmeans" is accepted.

search

search algorithm for the selection variable procedure: "backward", "forward" or "none". If "none" (default), no variable selection is performed.

ks

the values of the explored number of clusters. Default is exploring 2 and 3 clusters.

maxvars

if method = "forward", the maximum number of variables to be selected.

usedimp

numeric. Which imputed datasets must be included in the cluster analysis. If NULL (default), all available imputed datasets are included. If usedimp is numeric (or a numeric vector), its values indicate which imputed datasets are included.

distance

two metrics are allowed to compute distances: "manhattan" (default) and "euclidean".

centpos

position computation of the cluster centroid. If "means" (default) the position of the centroid is computed by the mean. If "medians", by the median.

initcl

starting values for the clustering algorithm. If "rand", they are randomly selected; if "hc", they are computed via hierarchical clustering. See Details below.

verbose

a logical value indicating output status messages. Default is TRUE.

seed

a number. Seed for reproducibility of results. Default is NULL (no seed).

x

for print.miclust and plot.miclust, an object of class miclust obtained with the function miclust.

...

further arguments for print.miclust and plot.miclust.

k

for plot.miclust, number of clusters. The default value is the optimal number of clusters obtained by miclust.

metric

for plot.miclust, metrics to be represented. "all" (default, corresponding to the output provided by version 1.2.8 and earlier represents all metrics. Other options are: "nclfreq" (percentage of times each number of clusters has been selected); "critcf" (critCF distribution for each number of clusters); "nvarfreq" (distribution of the number of selected variables), and "varsel" (percentage of appearance of the variables that remained in the final set of selected variables).

col.nclfreq, col.critcf, col.nvarfreq, col.varsel

for plot.miclust, a character string or integer specifying the color for each specific metric. They control the color of the bars in the cluster frequency plot ("nclfreq"), the boxes in the CritCF plot ("critcf"), the bars in the variable frequency plot ("nvarfreq"), and the segments in the variable selection plot ("varsel"). Defaults are "gray" for all cases but "black" for "varsel".

col.all

An optional character string or integer specifying a global color. If provided, it overrides all specific color arguments listed above, applying the same color across all subplots. Defaults to NULL.

Details

The optimal number of clusters and the final set of variables are selected according to CritCF. CritCF is defined as

CritCF = \left(\frac{2m}{2m + 1} \cdot \frac{1}{1 + W / B}\right)^{\frac{1 + \log_2(k + 1)}{1 + \log_2(m + 1)}},

where m is the number of variables, k is the number of clusters, and W and B are the within- and between-cluster inertias. Higher values of CritCF are preferred (Breaban, 2011). See References below for further details about the clustering algorithm.

For computational reasons, option "rand" is suggested instead of "hc" for high dimensional data.

Value

A list with class "miclust" including the following items:

clustering: a list of lists containing the results of the clustering algorithm for each analyzed dataset and for each analyzed number of clusters. Includes information about selected variables and the cluster vector.
completecasesperc: if data contains a single data frame, percentage of complete cases in data.
data: input data.
ks: the values of the explored number of clusters.
usedimp: indicator of the imputed datasets used.
kfin: optimal number of clusters.
critcf: if data contains a single data frame, critcf contains the optimal (maximum) value of CritCF (see Details) and the number of selected variables in the reduction procedure for each explored number of clusters. If data is a list, critcf contains the optimal value of CritCF for each imputed dataset and for each explored value of the number of clusters.
numberofselectedvars: number of selected variables.
selectedkdistribution: if data is a list, frequency of selection of each analyzed number of clusters.
method: input method.
search: input search.
maxvars: input maxvars.
distance: input distance.
centpos: input centpos.
selmetriccent: an object of class kccaFamily needed by the specific summary method.
initcl: input initcl.

References

Basagana X, Barrera-Gomez J, Benet M, Anto JM, Garcia-Aymerich J. A framework for multiple imputation in cluster analysis. American Journal of Epidemiology. 2013;177(7):718-25.
Breaban M, Luchian H. A unifying criterion for unsupervised clustering and feature selection. Pattern Recognition 2001;44(4):854-65.

Examples

### data preparation:
minhanes1 <- getdata(data = minhanes)

##################
###
### Example 1:
###
### Multiple imputation clustering process with backward variable selection
###
##################

### using only the imputations 1 to 10 for the clustering process and exploring
### 2 vs. 3 clusters:
minhanes1clust <- miclust(data = minhanes1, search = "backward", ks = 2:3,
                          usedimp = 1:10, seed = 4321)
minhanes1clust
minhanes1clust$kfin  ### optimal number of clusters

### graphical summary:
plot(minhanes1clust)

### selection frequency of the variables for the optimal number of clusters:
y <- getvariablesfrequency(minhanes1clust)
y
plot(y$percfreq, type = "h", main = "", xlab = "Variable",
     ylab = "Percentage of times selected", xlim = 0.5 + c(0, length(y$varnames)),
     lwd = 15, col = "blue", xaxt = "n")
axis(1, at = 1:length(y$varnames), labels = y$varnames)

### default summary for the optimal number of clusters:
summary(minhanes1clust)

## summary forcing 3 clusters:
summary(minhanes1clust, k = 3)

##################
###
### Example 2:
###
### Same analysis but without variable selection
###
##################

minhanes2clust <- miclust(data = minhanes1, ks = 2:3, usedimp = 1:10, seed = 4321)
minhanes2clust
plot(minhanes2clust)
summary(minhanes2clust)


##################
###
### Example 3:
###
### Complete cases clustering process with backward variable selection
###
##################

nhanes0 <- getdata(data = minhanes[[1]])
nhanes2clust <- miclust(data = nhanes0, search = "backward", ks = 2:3, seed = 4321)
nhanes2clust

summary(nhanes2clust)

### nothing to plot for a single dataset analysis
# plot(nhanes2clust)

##################
###
### Example 4:
###
### Complete case clustering process without variable selection
###
##################

nhanes3clust <- miclust(data = nhanes0, ks = 2:3, seed = 4321)
nhanes3clust
summary(nhanes3clust)

Multiple imputation for nhanes data.

Description

A list with 101 datasets. The first dataset contains nhanes data from mice package. The remaining datasets were obtained by applying the multiple imputation function mice from package mice.

Usage

minhanes

Format

A list of 101 data.frames each of them with 25 observations of the following 4 variables:

age: age group (1 = 20-39, 2 = 40-59, 3 = 60+). Treated as numerical.
bmi: body mass index (kg/m^2)
hyp: hypertensive (1 = no, 2 = yes). Treated as numerical.
chl: total serum cholesterol (mg/dL)

Source

https://CRAN.R-project.org/package=mice

Examples

data(minhanes)
### raw data:
minhanes[[1]]
summary(minhanes[[1]])

### number of imputed datasets:
length(minhanes) - 1

### first imputed dataset:
minhanes[[2]]
summary(minhanes[[2]])

Summarizes the results.

Description

Performs a within-cluster descriptive analysis of the variables after the clustering process performed by the function miclust.

Usage

## S3 method for class 'miclust'
summary(object, k = NULL, quantilevars = NULL, ...)

## S3 method for class 'summary.miclust'
print(x, digits = 2, ...)

Arguments

object

object of class miclust obtained with the function miclust.

k

number of clusters. The default value is the optimal number of clusters obtained by miclust.

quantilevars

numeric. If a variable selection procedure was used, the cut-off percentile in order to decide the number of selected variables in the variable reduction procedure by decreasing order of presence along the imputations results. The default value is quantilevars = 0.5, i.e., the number of selected variables is the median number of selected variables along the imputations.

...

further arguments for summary and print.summary methods.

x

for the print.summary method, an object obtained with the method summary.

digits

digits for the print.summary method. Default is 2.

Value

A list including the following items:

allocationprobabilities: if imputations were analysed, descriptive summary of the probability of cluster assignment.
classmatrix: if imputations were analysed, the individual probabilities of cluster assignment.
cluster: if imputations were analysed, the final individual cluster assignment.
clusterssize: if imputations were analysed, size of the imputed cluster and between-imputations summary of the cluster size.
clustervector: if a single dataset (raw dataset) has been clustered, a vector containing the individuals cluster assignments.
clustervectors: if imputed datasets have been clustered, the individual cluster assignment in each imputation.
completecasesperc: if a single dataset (raw dataset) has been clustered, the percentage of complete cases in the dataset.
k: number of clusters.
kappas: if imputations were analysed, the Cohen's kappa values after comparing the cluster vector in the first imputation with the cluster vector in each of the remaining imputations.
kappadistribution: a summary of kappas.
m: number of imputations used in the descriptive analysis which is the total number of imputations provided.
quantilevars: if variable selection was performed, the input value of quantilevars.
search: search algorithm for the selection variable procedure.
selectedvariables: if variable selection was performed, the selected variables obtained considering quantilevars.
selectedvarspresence: if imputations were analysed and variable selection was performed, the presence of the selected variables along imputations.
summarybycluster: within-cluster descriptive analysis of the selected variables.
usedimp: indicator of imputations used in the clustering procedure.

Examples

### see examples in miclust.

Package {miclust}

miclust-package: integrating multiple imputation with cluster analysis

Description

Procedure

Authors

Author(s)

References

Creates a midata object.

Description

Usage

Arguments

Details

Value

See Also

Examples

Calculates the ranked selection frequency of the variables.

Description

Usage

Arguments

Value

See Also

Examples

Cluster analysis in multiple imputed datasets with optional variable selection.

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Multiple imputation for nhanes data.

Description

Usage

Format

Source

Examples

Summarizes the results.

Description

Usage

Arguments

Value

See Also

Examples

Creates a `midata` object.