  We introduce a Bayesian approach for analyzing high-dimensional multinomial
data that are referenced over space and time. In particular, the proportions
associated with multinomial data are assumed to have a logit link to a latent
spatio-temporal mixed effects model. This strategy allows for covariances that
are nonstationarity in both space and time, asymmetric, and parsimonious. We
also introduce the use of the conditional multivariate logit-beta distribution
into the dependent multinomial data setting, which leads to conjugate
full-conditional distributions for use in a collapsed Gibbs sampler. We refer
to this model as the multinomial spatio-temporal mixed effects model (MN-STM).
Additionally, we provide methodological developments including: the derivation
of the associated full-conditional distributions, a relationship with a latent
Gaussian process model, and the stability of the non-stationary vector
autoregressive model. We illustrate the MN-STM through simulations and through
a demonstration with public-use Quarterly Workforce Indicators (QWI) data from
the Longitudinal Employer Household Dynamics (LEHD) program of the U.S. Census
Bureau.
