clustMD (version 1.0)

clustMD: Model-Based Clustering for Mixed Data

Description

A function which fits the clustMD model to a data set consisting of any combination of continuous, binary, ordinal and nominal variables.

Usage

clustMD(X, G, CnsIndx, OrdIndx, Nnorms, MaxIter, model, store.params = FALSE)

Arguments

X

A data matrix where the variables are ordered so that the continuous variables come first, the binary (coded 1 and 2) and ordinal variables (coded 1, 2,...) come second and the nominal variables (coded 1, 2,...) are in last position.

G

The number of mixture components to be fitted.

CnsIndx

The number of continuous variables in the data set.

OrdIndx

The sum of the number of continuous, binary and ordinal variables in the data set.

Nnorms

The number of Monte Carlo samples to be used for the intractable E-step in the presence of nominal data.

MaxIter

The number of iterations for which the (MC)EM algorithm should run.

model

A string indicating which clustMD model is to be fitted. This may be one of: EII, VII, EEI, VEI, EVI or VVI.

store.params

A logical variable indicating if the parameter estimates at each iteration should be saved and returned by the clustMD function.

Value

• A list is returned:
• cl
  The cluster to which each observation belongs.
• tau
  A N x G matrix of the conditional probabilities of each observation blonging to each cluster.
• means
  A D x G matrix of the cluster means.
• A
  A G x D matrix containing the diagonal entries of the A matrix corresponding to each cluster.
• Lambda
  A G x D matrix of volume parameters corresponding to each observed or latent dimension for each cluster.
• Sigma
  A D x D x G array of the covariance matrices for each cluster.
• BIChat
  The estimated Bayesian information criterion for the model fitted.
• paramlist
  If store.params is true then paramlist is a list of the stored parameter values in the order given above with the saved estimated likelihood values in last position.

Details

Model-based clustering of mixed data using a parsimonious mixture of latent Gaussian variables.

References

McParland, D. and Gormley, I.C. (2014). Model based clustering for mixed data: clustMD. Technical report, University College Dublin.

Examples

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=100, model="EVI", store.params=FALSE)