Small area prediction of seat‐belt use rates using a Bayesian hierarchical unit‐level Poisson model with multivariate random effects

Abstract

SummaryThe Iowa Seat‐Belt Use Survey is an annual survey designed to provide estimates of seat‐belt use rates for the state of Iowa in the United States. A desire for county level (substate) estimates motivates the need for small area estimation. Developing a small area model for the seat‐belt survey data is challenging for two mean reasons. First, the data consist of multivariate counts. Second, the same sampling units are observed for five different time points. An appropriate model should reflect multivariate dependencies and the longitudinal data structure. We address these challenges though a unit‐level Bayesian hierarchical model. The observed counts have Poisson distributions. Latent random effects capture multivariate associations and correlations among the observations for the same sampling unit observed at different time points. We employ the posterior predictive distribution for model comparisons. Using the selected model, we construct small area predictors of two measures of seat‐belt use at the county level for 5 years.