longclustEM {longclust}

Model-Based Clustering and Classification for Longitudinal Data

Description

Carries out model-based clustering or classification using multivariate t or Gaussian mixture models with Cholesky decomposed covariance structure. EM algorithms are used for parameter estimation and the BIC is used for model selection.

Usage

longclustEM(x, Gmin, Gmax, class=NULL, linearMeans = FALSE, 
modelSubset = NULL, initWithKMeans = FALSE, criteria = "BIC", 
equalDF = FALSE, gaussian=FALSE,  userseed=1004)

Arguments

x

A matrix or data frame such that rows correspond to observations and columns correspond to variables.

Gmin

A number giving the minimum number of components to be used.

Gmax

A number giving the maximum number of components to be used.

class

If NULL then model-based clustering is performed. If a vector with length equal to the number of observations, then model-based classification is performed. In this latter case, the ith entry of class is either zero, indicating that the component membership of observation i is unknown, or it corresponds to the component membership of observation i.

linearMeans

If TRUE, then means are modelled using linear models.

modelSubset

A vector of strings giving the models to be used. If set to NULL, all models are used.

initWithKMeans

If TRUE, the components are initialized using k-means algorithm.

criteria

A string that denotes the criteria used for evaluating the models. Its value should be "BIC" or "ICL".

equalDF

If TRUE, the degrees of freedom of all the components will be the same.

gaussian

If TRUE, a mixture of Gaussian distributions is used in place of a mixture of t-distributions.

userseed

The random number seed to be used.

Value

Gbest

The number of components for the best model.

zbest

A matrix that gives the probabilities for any data element to belong to any component in the best model.

nubest

A vector of Gbest integers, that give the degrees of freedom for each component in the best model.

mubest

A matrix containing the means of the components for the best model (one per row).

Tbest

A list of Gbest matrices, giving the T matrices of the components for the best model.

Dbest

A list of Gbest matrices, giving the D matrices of the components for the best model.

Author(s)

Paul D. McNicholas, K. Raju Jampani and Sanjeena Subedi

References

Paul D. McNicholas and T. Brendan Murphy (2010). Model-based clustering of longitudinal data. The Canadian Journal of Statistics 38(1), 153-168.

Paul D. McNicholas and Sanjeena Subedi (2012). Clustering gene expression time course data using mixtures of multivariate t-distributions. Journal of Statistical Planning and Inference 142(5), 1114-1127.

Examples

library(mvtnorm)
m1 <- c(23,34,39,45,51,56)
S1 <- matrix(c(1.00, -0.90, 0.18, -0.13, 0.10, -0.05, -0.90, 
1.31, -0.26, 0.18, -0.15, 0.07, 0.18, -0.26, 4.05, -2.84, 
2.27, -1.13, -0.13, 0.18, -2.84, 2.29, -1.83, 0.91, 0.10, 
-0.15, 2.27, -1.83, 3.46, -1.73, -0.05, 0.07, -1.13, 0.91, 
-1.73, 1.57), 6, 6)
m2 <- c(16,18,15,17,21,17)
S2 <- matrix(c(1.00, 0.00, -0.50, -0.20, -0.20, 0.19, 0.00, 
2.00, 0.00, -1.20, -0.80, -0.36,-0.50, 0.00, 1.25, 0.10, 
-0.10, -0.39, -0.20, -1.20, 0.10, 2.76, 0.52, -1.22,-0.20, 
-0.80, -0.10, 0.52, 1.40, 0.17, 0.19, -0.36, -0.39, -1.22, 
0.17, 3.17), 6, 6)
m3 <- c(8, 11, 16, 22, 25, 28)
S3 <- matrix(c(1.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 
1.00, -0.20, -0.64, 0.26, 0.00, 0.00, -0.20, 1.04, -0.17, 
-0.10, 0.00, 0.00, -0.64, -0.17, 1.50, -0.65, 0.00, 0.00, 
0.26, -0.10, -0.65, 1.32, 0.00, 0.00, 0.00, 0.00, 0.00, 
0.00, 1.00), 6, 6)
m4 <- c(12, 9, 8, 5, 4 ,2)
S4 <- diag(c(1,1,1,1,1,1))
data <- matrix(0, 40, 6)
data[1:10,] <- rmvnorm(10, m1, S1)
data[11:20,] <- rmvnorm(10, m2, S2)
data[21:30,] <- rmvnorm(10, m3, S3)
data[31:40,] <- rmvnorm(10, m4, S4)
clus <- longclustEM(data, 3, 5, linearMeans=TRUE)
summary(clus)
plot(clus,data)