A multivariate Bayesian hierarchical model for small area estimation of criminal victimization rates in domains defined by age and sex

The National Crime Victimization Survey (NCVS) gathers information on criminal victimizations for individuals in a representative sample of United States households. The NCVS provides authoritative data on the rates of many types of violent crimes, including simple assault, robbery, and aggravated assault. Estimates are of interest for small domains defined by the intersection of sex with detailed age divisions. Standard survey estimators for these domains suffer from instability due to small sample sizes. Model-based small area procedures are needed to obtain more reliable estimates. We employ a multivariate Bayesian model to obtain small area estimates for domains defined by intersections of sex with specific age categories. We construct estimates for four types of violent crimes in each of two time periods. We compare a model with a log transformation to a model fit to the data in the original scale. We compare small area predictors based on a selected model to the direct estimators.