clustMD {clustMD}

Model Based Clustering for Mixed Data

Description

A function that 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,
  scale = FALSE, startCL = "hc_mclust", autoStop = FALSE, ma.band = 50,
  stop.tol = NA)

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. Irrelevant if there are no nominal variables.

MaxIter

the maximum 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, VVI or BD.

store.params

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

scale

a logical argument indicating if the continuous variables should be standardised.

startCL

a string indicating which clustering method should be used to initialise the (MC)EM algorithm. This may be one of "kmeans" (K means clustering), "hclust" (hierarchical clustering), "mclust" (finite mixture of Gaussian distributions), "hc_mclust" (model-based hierarchical clustering) or "random" (random cluster allocation).

autoStop

a logical argument indicating whether the (MC)EM algorithm should use a stopping criterion to decide if convergence has been reached. Otherwise the algorithm will run for MaxIter iterations.

If only continuous variables are present the algorithm will use Aitken's acceleration criterion with tolerance stop.tol.

If categorical variables are present, the stopping criterion is based on a moving average of the approximated log likelihood values. Let t denote the current interation. The average of the ma.band most recent approximated log likelihood values is compared to the average of another ma.band iterations with a lag of 10 iterations. If this difference is less than the tolerance the algorithm will be said to have converged.

ma.band

the number of iterations to be included in the moving average calculation for the stopping criterion.

stop.tol

the tolerance of the (MC)EM stopping criterion.

Value

An object of class clustMD is returned. The output components are as follows:

model

The covariance model fitted to the data.

G

The number of clusters fitted to the data.

Y

The observed data matrix.

cl

The cluster to which each observation belongs.

tau

A N x G matrix of the probabilities of each observation blonging to each cluster.

means

A D x G matrix of the cluster means. Where D is the dimension of the combined observed and latent continuous space.

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.

ICLhat

The estimated integrated classification likelihood 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.

Varnames

A character vector of names corresponding to the columns of Y

Varnames_sht

A truncated version of Varnames. Used for plotting.

likelihood.store

A vector containing the estimated log likelihood at each iteration.

References

McParland, D. and Gormley, I.C. (2016). Model based clustering for mixed data: clustMD. Advances in Data Analysis and Classification, 10 (2):155-169.

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

    ## Not run: 
    res <- clustMD(X = Y, G = 3, CnsIndx = 8, OrdIndx = 11, Nnorms = 20000,
    MaxIter = 500, model = "EVI", store.params = FALSE, scale = TRUE, 
    startCL = "kmeans", autoStop= TRUE, ma.band=30, stop.tol=0.0001)
    
## End(Not run)