repnormmixEM: EM Algorithm for Mixtures of Normals with Repeated Measurements

Description

Returns EM algorithm output for mixtures of normals with repeated measurements and arbitrarily many components.

Usage

repnormmixEM(x, lambda = NULL, mu = NULL, sigma = NULL, k = 2,  arbmean = TRUE, arbvar = TRUE, epsilon = 1e-08,  maxit = 10000, verb = FALSE)

Arguments

An mxn matrix of data. The columns correspond to the subjects and the rows correspond to the repeated measurements.

lambda

Initial value of mixing proportions. Entries should sum to 1. This determines number of components. If NULL, then lambda is random from uniform Dirichlet and number of components is determined by mu.

A k-vector of component means. If NULL, then mu is determined by a normal distribution according to a binning method done on the data. If both lambda and mu are NULL, then number of components is determined by sigma.

sigma

A vector of standard deviations. If NULL, then $1/\code{sigma}^2$ has random standard exponential entries according to a binning method done on the data. If lambda, mu, and sigma are NULL, then number of components is determined by k.

Number of components. Ignored unless all of lambda, mu, and sigma are NULL.

arbmean

If TRUE, then the component densities are allowed to have different mus. If FALSE, then a scale mixture will be fit.

arbvar

If TRUE, then the component densities are allowed to have different sigmas. If FALSE, then a location mixture will be fit.

epsilon

The convergence criterion.

maxit

The maximum number of iterations.

verb

If TRUE, then various updates are printed during each iteration of the algorithm.

Value

x: The raw data.
lambda: The final mixing proportions.
mu: The final mean parameters.
sigma: The final standard deviations. If arbmean = FALSE, then only the smallest standard deviation is returned. See scale below.
scale: If arbmean = FALSE, then the scale factor for the component standard deviations is returned. Otherwise, this is omitted from the output.
loglik: The final log-likelihood.
posterior: An nxk matrix of posterior probabilities for observations.
all.loglik: A vector of each iteration's log-likelihood.
restarts: The number of times the algorithm restarted due to unacceptable choice of initial values.
ft: A character vector giving the name of the function.

References

Hettmansperger, T. P. and Thomas, H. (2000) Almost Nonparametric Inference for Repeated Measures in Mixture Models, Journal of the Royals Statistical Society, Series B 62(4) 811--825.

Examples

Run this code

## EM output for the water-level task data set.

data(Waterdata)
set.seed(100)
water <- t(as.matrix(Waterdata[,3:10]))
em.out <- repnormmixEM(water, k = 2, verb = TRUE, epsilon = 1e-03)
em.out