Small-area estimation for the Iowa Seat-Belt Use Survey, 2017–2021
Small-area estimation for the Iowa Seat-Belt Use Survey, 2017–2021

Summary/Abstract: This study develops Bayesian small-area estimates of seat-belt use for Iowa counties from 2017 to 2021. The aim is to produce stable county-by-year estimates and measures of uncertainty for all 99 Iowa counties, although only 15 counties were directly sampled in the Iowa Seat-Belt Use Survey. The analysis focuses on two policy-relevant quantities: the percentage of belted vehicle miles traveled and the percentage of belted vehicle occupants. To address the multivariate, longitudinal, and boundary-inflated structure of the data, we compare several Bayesian hierarchical models for driver and passenger seat-belt-use proportions and combine them with a Poisson log-linear model for occupant counts. Correlated random effects are used to borrow strength across counties, years, and road segments, and posterior inference is implemented using Integrated Nested Laplace Approximations. Model performance is evaluated using WAIC, posterior predictive checks, posterior intervals, Bayesian model averaging, and comparisons with direct estimates. The empirical results show that the Bayesian estimates are generally close to direct estimates in posterior mean, while often producing substantially smaller posterior standard deviations. These gains indicate improved stability for local traffic-safety summaries, although they are interpreted as a bias–variance trade-off rather than as uniform dominance over direct estimation.

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