Selection of prior distributions for multivariate small area models with application to small area health insurance estimates

• Activity Number: 665
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Ryan Janicki*+
• Companies: U.S. Census Bureau
• Keywords: small area modeling ; proper posterior ; generalized linear models ; errors-in-variables ; mixed models ; multivariate analysis

Abstract

In sample surveys, it is often the case that there is insufficient sample size to obtain reliable direct estimates for a parameter of interest for certain domains. Precision can be increased by introducing small area models which ``borrow strength' by connecting different areas and incrporating auxiliary covariate information. This article considers multivariate generalized linear models for analyzing survey data, with special attention given to the mixed effect multinomial logistic regression model. A comparison of the model where area-specific random effects are correlated is made with the model where area-specific random effects are assumed to have independent components. A general theorem is presented which gives necessary and sufficient conditions for the propriety of the posterior. An example is given where a simulated data set is analyzed using the model to estimate the proportion in different income levels for different demograph groups. The results of this example indicate that we can have improved estimates over estimates based on a small area model for single components when we use area-specific random effects with correlated components.