# clustMD v1.2.1

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## Model Based Clustering for Mixed Data

Model-based clustering of mixed data (i.e. data which consist of continuous, binary, ordinal or nominal variables) using a parsimonious mixture of latent Gaussian variable models.

# Model based clustering for mixed data: clustMD

Damien McParland March 22, 2017

This R package allows the user to perform model based clustering of mixed data (i.e. data that consist of continuous, binary, ordinal or nominal variables) using a parsimonious mixture of latent Gaussian variable models.

This model based clustering approach assumes that underlying the observed categorical response is a latent continuous variable. A finite mixture model is used to identify sub populations or clusters within the larger population.

## Installation

The clustMD package can be easily installed in R as follows.

  install.packages("clustMD")


The Byar data set that is used in the examples is included in the package. This data set contains information on 475 prostate cancer patients. Measurements taken on these patients consist of continuous, binary, ordinal and nominal variables.

## Functions

### clustMD()

To use clustMD to cluster the Byar data set you may run the following code. The code consists of some simple pre-processing steps followed by the correct usage of the clustMD() function.

    data(Byar)
# Transformation skewed variables
Byar$Size.of.primary.tumour <- sqrt(Byar$Size.of.primary.tumour)
Byar$Serum.prostatic.acid.phosphatase <- log(Byar$Serum.prostatic.acid.phosphatase)

# Order variables (Continuous, ordinal, nominal)
Y <- as.matrix(Byar[, c(1, 2, 5, 6, 8, 9, 10, 11, 3, 4, 12, 7)])

# Start categorical variables at 1 rather than 0
Y[, 9:12] <- Y[, 9:12] + 1

# Standardise continuous variables
Y[, 1:8] <- scale(Y[, 1:8])

# Merge categories of EKG variable for efficiency
Yekg <- rep(NA, nrow(Y))
Yekg[Y[,12]==1] <- 1
Yekg[(Y[,12]==2)|(Y[,12]==3)|(Y[,12]==4)] <- 2
Yekg[(Y[,12]==5)|(Y[,12]==6)|(Y[,12]==7)] <- 3
Y[, 12] <- Yekg

res <- clustMD(X=Y, G=3, CnsIndx=8, OrdIndx=11, Nnorms=20000,
MaxIter=500, model="EVI", store.params=FALSE, scale=TRUE,
startCL="kmeans")


The clustMD() function outputs an S3 object of class clustMD. Basic S3 methods are included in the package also. The functions available are

• print.clustMD()
• summary.clustMD()
• plot.clustMD()

The plot.clustMD() function produces a number of useful summary plots of the clustMD object.

### clustMDparallel()

Another function is available to run multiple models in parallel called clustMDparallel(). This function takes a range of possible values for the number of clusters as a vector. It also takes a character vector as an input that specifies which of the covariance models are to be fitted.

  data(Byar)

# Transformation skewed variables
Byar$Size.of.primary.tumour <- sqrt(Byar$Size.of.primary.tumour)
Byar$Serum.prostatic.acid.phosphatase <- log(Byar$Serum.prostatic.acid.phosphatase)

# Order variables (Continuous, ordinal, nominal)
Y <- as.matrix(Byar[, c(1, 2, 5, 6, 8, 9, 10, 11, 3, 4, 12, 7)])

# Start categorical variables at 1 rather than 0
Y[, 9:12] <- Y[, 9:12] + 1

# Standardise continuous variables
Y[, 1:8] <- scale(Y[, 1:8])

# Merge categories of EKG variable for efficiency
Yekg <- rep(NA, nrow(Y))
Yekg[Y[,12]==1] <- 1
Yekg[(Y[,12]==2)|(Y[,12]==3)|(Y[,12]==4)] <- 2
Yekg[(Y[,12]==5)|(Y[,12]==6)|(Y[,12]==7)] <- 3
Y[, 12] <- Yekg

res <- clustMDparallel(X=Y, G=1:3, CnsIndx=8, OrdIndx=11, Nnorms=20000,
MaxIter=500, models=c("EVI", "EII", "VII"), store.params=FALSE,
scale=TRUE, startCL="kmeans")


The clustMDparallel() function outputs an S3 object of class clustMDparallel. Some S3 methods are also available for this class:

• print.clustMDparallel()
• summary.clustMDparallel()
• plot.clustMDparallel()

The plot.clustMDparallel() function outputs the same plots as plot.clustMD() but for the optimal model according to the approximated BIC criterion. An additional plot is also included that illustrated the approximated BIC values for the fitted models.

## Functions in clustMD

 Name Description Byar Byar prostate cancer data set. E.step E-step of the (MC)EM algorithm M.step M-step of the (MC)EM algorithm ObsLogLikelihood Approximates the observed log likelihood. clustMDlist Model Based Clustering for Mixed Data clustMDparallel Run multiple clustMD models in parallel clustMDparcoord Parallel coordinates plot adapted for dtmvnom Return the mean and covariance matrix of a truncated multivariate normal clustMD-package Model based clustering for mixed data: clustMD clustMD Model Based Clustering for Mixed Data perc.cutoffs Calculates the threshold parameters for ordinal variables. plot.clustMD Plotting method for objects of class z.moments Calculates the first and second moments of the latent data plot.clustMDparallel Summary plots for a clustMDparallel object print.clustMD Print basic details of npars_clustMD Calculates the number of free parameters for the patt.equal Check if response patterns are equal stable.probs Stable computation of the log of a sum getOutput_clustMDparallel Extracts relevant output from modal.value Calculate the mode of a sample summary.clustMD Summarise z.moments_diag Calculates the first and second moments of the latent data for diagonal models print.clustMDparallel Print basic details of qfun Helper internal function for z.nom.diag Transforms Monte Carlo simulated data into categorical data. Calculates summary.clustMDparallel Prints a summary of a clustMDparallel object to screen. vec.outer Calculate the outer product of a vector with itself No Results!