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

arXiv: https://arxiv.org/abs/1812.03555 · HTML: https://mlsanity.com/paper/1812.03555/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2018.

## Built on by (most cited first, 1 of 1)

- [Logistic-beta processes for dependent random probabilities with beta marginals](https://mlsanity.com/paper/2402.07048/) (2024)

## Abstract (arXiv)

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.