da.mix {mix}

Data Augmentation for Unrestricted General Location Model

Description

Markov Chain Monte Carlo method for generating posterior draws of the parameters of the unrestricted general location model, given a matrix of incomplete mixed data. At each step, missing data are randomly imputed under the current parameter, and a new parameter value is drawn from its posterior distribution given the completed data. After a suitable number of steps are taken, the resulting value of the parameter may be regarded as a random draw from its observed-data posterior distribution. May be used together with imp.mix to create multiple imputations of the missing data.

Usage

da.mix(s, start, steps=1, prior=0.5, showits=FALSE)

Arguments

s

summary list of an incomplete data matrix created by the function prelim.mix.

start

starting value of the parameter. This is a parameter list such as one created by the function em.mix.

steps

number of data augmentation steps to be taken.

prior

Optional vector or array of hyperparameter(s) for a Dirichlet prior distribution. The default is the Jeffreys prior (all hyperparameters = .5). If structural zeros appear in the table, prior counts for these cells should be set to NA.

showits

if TRUE, reports the iterations so the user can monitor the progress of the algorithm.

Details

The prior distribution used by this function is a combination of a Dirichlet prior for the cell probabilities, an improper uniform prior for the within-cell means, and the improper Jeffreys prior for the covariance matrix. The posterior distribution is not guaranteed to exist, especially in sparse-data situations. If this seems to be a problem, then better results may be obtained by imposing restrictions on the parameters; see ecm.mix and dabipf.mix.

Value

A new parameter list. The parameter can be put into a more understandable format by the function getparam.mix.

Note

The random number generator seed must be set at least once by the function rngseed before this function can be used.

References

Schafer, J. L. (1996) Analysis of Incomplete Multivariate Data. Chapman & Hall, Chapter 9.

See Also

prelim.mix, getparam.mix, em.mix, and rngseed.

Examples

data(stlouis)
s <- prelim.mix(stlouis,3)  # preliminary manipulations
thetahat <- em.mix(s) # find ML estimate
rngseed(1234567)   # set random number generator seed
newtheta <- da.mix(s, thetahat, steps=100, showits=TRUE)  # take 100 steps
ximp1 <- imp.mix(s, newtheta) # impute under newtheta