Hierarchical Models for the Probabilities of a Survey Classification and Nonresponse: An Example from the National Crime Survey

Abstract

A goal in many survey sampling problems is to estimate the probability that elements of the population within various small areas or domains have some characteristic or fall in some particular survey classification. The estimation problem is typically complicated by nonrandom nonresponse in that the probability that a unit responds to the survey may be related to the characteristic of interest. This article presents a random parameter or hierarchical model approach to modeling the small-domain probabilities of the characteristic of interest and the probabilities of nonresponse. The general model allows nonresponse probabilities to depend on a unit's survey classification. A special case of the model treats nonresponse as occurring at random. Empirical Bayes methods are used to obtain parameter estimates under the hierarchical models. The method is illustrated using data from the National Crime Survey.

Key Words:

• Categorical data
• Empirical Bayes
• Nonrandom nonresponse
• Small-domain estimation