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We introduce a Bayesian approach for analyzing high-dimensional multinomialdata that are referenced over space and time. In particular, the proportionsassociated with multinomial data are assumed to have a logit link to a latentspatio-temporal mixed effects model. This strategy allows for covariances thatare nonstationarity in both space and time, asymmetric, and parsimonious. Wealso introduce the use of the conditional multivariate logit-beta distributioninto the dependent multinomial data setting, which leads to conjugatefull-conditional distributions for use in a collapsed Gibbs sampler. We referto this model as the multinomial spatio-temporal mixed effects model (MN-STM).Additionally, we provide methodological developments including: the derivationof the associated full-conditional distributions, a relationship with a latentGaussian process model, and the stability of the non-stationary vectorautoregressive model. We illustrate the MN-STM through simulations and througha demonstration with public-use Quarterly Workforce Indicators (QWI) data fromthe Longitudinal Employer Household Dynamics (LEHD) program of the U.S. CensusBureau.

Spatio-Temporal Models for Big Multinomial Data using the Conditional Multivariate Logit-Beta Distribution