  Markov Chain Monte Carlo (MCMC) is a popular class of statistical methods for
simulating autocorrelated draws from target distributions, including posterior
distributions in Bayesian analysis. An important consideration in using
simulated MCMC draws for inference is that the sampling algorithm has converged
to the distribution of interest. Since the distribution is typically of a
non-standard form, convergence cannot generally be proven and, instead, is
assessed with convergence diagnostics. Although parameters used in the MCMC
framework are typically continuous, there are many situations in which
simulating a categorical variable is desired. Examples include indicators for
model inclusion in Bayesian variable selection and latent categorical component
variables in mixture modeling. Traditional convergence diagnostics are designed
for continuous variables and may be inappropriate for categorical variables. In
this paper two convergence diagnostic methods are considered which are
appropriate for MCMC data. The diagnostics discussed in the paper utilize
chi-squared test statistics for dependent data. Performance of the convergence
diagnostics is evaluated under various simulations. Finally, the diagnostics
are applied to a real data set where reversible jump MCMC is used to sample
from a finite mixture model.
