em.cat: EM algorithm for incomplete categorical data

Description

Finds ML estimate or posterior mode of cell probabilities under the saturated multinomial model.

Usage

em.cat(s, start, prior=1, showits=TRUE, maxits=1000,
eps=0.0001)

Value

array of dimension s$d containing the ML estimate or posterior mode, assuming that EM has converged by maxits iterations.

Arguments

s: summary list of an incomplete categorical dataset produced by the function prelim.cat.
start: optional starting value of the parameter. This is an array with dimensions s$d whose elements sum to one. The default starting value is a uniform array (equal probabilities in all cells). If structural zeros appear in the table, start should contain zeros in those positions and nonzero (e.g. uniform) values elsewhere.
prior: optional vector of hyperparameters for a Dirichlet prior distribution. The default is a uniform prior distribution (all hyperparameters = 1) on the cell probabilities, which will result in maximum likelihood estimation. If structural zeros appear in the table, a prior should be supplied with NAs in those cells.
showits: if TRUE, reports the iterations of EM so the user can monitor the progress of the algorithm.
maxits: maximum number of iterations performed. The algorithm will stop if the parameter still has not converged after this many iterations.
eps: convergence criterion. This is the largest proportional change in an expected cell count from one iteration to the next. Any expected cell count that drops below 1E-07 times the average cell probability (1/number of non-structural zero cells) is set to zero during the iterations.

References

Schafer (1996) Analysis of Incomplete Multivariate Data. Chapman & Hall, Section 7.3.

Examples

Run this code

data(crimes)
crimes
s <- prelim.cat(crimes[,1:2],crimes[,3])     # preliminary manipulations
thetahat <- em.cat(s)                        # mle under saturated model
logpost.cat(s,thetahat)                      # loglikelihood at thetahat