The seat-belt use rate study, based on Iowa's Data

The seat-belt use rate, defined as the ratio of the total number of individuals wearing a seat-belt to the total number of individuals in vehicles, is an important statistic for understanding the safety of a transportation system. The annual Iowa Seat-Belt Use survey is designed to produce estimates of seat-belt use rates at the state level. We consider county estimation. Because the county sample sizes are small, this is a small area estimation problem. Previously, we used a frequentist approach that only provided estimates of the seat-belt use rate among drivers for a single year. We extend the model to include both passengers and drivers for multiple years. To accomplish this, we transfer to the Bayesian paradigm. We use a two-part model with a beta component for sampling units where not everyone is belted and a binary component for units where all passengers or drivers are belted. We incorporate multivariate latent variables to capture correlations between the passengers and drivers as well as correlations over time. We evaluate the goodness of fit of alternative models using the posterior predictive p-value. We present estimated seat-belt use rates for a selected model.