Issues Associated With the Formulation of a Small Area Model for Estimation of State-Level Crime Victimization Rates

Subnational estimation is an important and challenging problem in the context of the National Crime Victimization Survey (NCVS). Direct estimates for subnational domains are often unreliable due to small sample sizes. Model-based procedures have potential to improve upon direct estimators. However, model-based estimation presents several new challenges. One must identify suitable covariates, and an appropriate model form must be specified. This article discusses issues associated with the formulation of a small area model for production of state-level estimates of crime victimization rates. An analysis of direct estimates and covariates motivates the development of a Bayesian multivariate model. A model in the original scale is compared to a model in the log scale. Efficiency gains from the model relative to the direct estimators are examined. One challenge is that direct estimates can equal zero. Two ways of handling zero direct estimates are discussed.