Bayesian modeling of temporal dependence in large sparse contingency tables

TL;DR

This paper introduces a Bayesian autoregressive tensor factorization model to analyze large, sparse contingency tables over time, effectively capturing temporal dependencies and handling missing data in categorical survey data.

Contribution

It proposes a novel Bayesian tensor factorization approach with autocorrelation for modeling temporal dependence in large sparse contingency tables.

Findings

Effective in capturing temporal trends in categorical data.

Handles missing data and variable changes over time.

Demonstrates good performance in simulations and real social survey data.

Abstract

In many applications, it is of interest to study trends over time in relationships among categorical variables, such as age group, ethnicity, religious affiliation, political party and preference for particular policies. At each time point, a sample of individuals provide responses to a set of questions, with different individuals sampled at each time. In such settings, there tends to be abundant missing data and the variables being measured may change over time. At each time point, one obtains a large sparse contingency table, with the number of cells often much larger than the number of individuals being surveyed. To borrow information across time in modeling large sparse contingency tables, we propose a Bayesian autoregressive tensor factorization approach. The proposed model relies on a probabilistic Parafac factorization of the joint pmf characterizing the categorical data distribution at each time point, with autocorrelation included across times. Efficient computational methods are developed relying on MCMC. The methods are evaluated through simulation examples and applied to social survey data.