logpost.cat {cat}

Log-posterior density for incomplete categorical data

Description

Calculates the observed-data loglikelihood or log-posterior density for incomplete categorical data under a specified value of the underlying cell probabilities, e.g. as resulting from em.cat or ecm.cat.

Usage

logpost.cat(s, theta, prior)

Arguments

s

summary list of an incomplete categorical dataset created by the function prelim.cat.

theta

an array of cell probabilities of dimension s$d

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 evaluation of the loglikelihood. If structural zeros appear in the table, a prior should be supplied with NAs in those cells and ones (or other hyperparameters) elsewhere.

Details

This is the loglikelihood or log-posterior density that ignores the missing-data mechanism.

Value

the value of the observed-data loglikelihood or log-posterior density function at theta

References

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

See Also

prelim.cat, em.cat, ecm.cat

Examples

data(older)                            # load data
older[1:2,c(1:4,7)]                    # see partial content; older.frame also
                                       # available.
s <- prelim.cat(older[,1:4],older[,7]) # preliminary manipulations
m <- c(1,2,0,3,4)                      # margins for restricted model
thetahat1 <- ecm.cat(s,margins=m)      # mle 
logpost.cat(s,thetahat1)               # loglikelihood at thetahat1