Small Area Estimation Based on Repeated Surveys: Using Semiparametric Models to Estimate Trends

• Activity Number: 413
• Type: Contributed
• Date/Time: Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Dawei Xie*+
• Companies: University of Michigan
• Keywords: borrowing strength ; correlated sampling error ; Gibbs sampling ; empirical Bayesian ; hierarchical Bayesian

Abstract

Many surveys are repeated in time with or without partial replacement of the sample elements. For such repeated surveys considerably gain in efficiency can be achieved by borrowing strength across both small areas and time. Current literature focuses on time series models, which assumes surveys are repeated in equal time intervals and make parametric assumption on time effects. It fails when one of the assumptions is not satisfied. Hence, it is of potential interest to model the trends nonparametrically. This paper proposes a model to estimate the means of a continuous outcome of interest in small areas and their trends. In this model, the trends are modeled nonparametrically while the area level auxiliary variables are modeled parametrically. The empirical Bayesian and Bayesian estimation of the model parameters are given. The model is illustrated based on two national surveys, the Behavioral Risk Factors Surveillance Survey (BRFSS) and the Current Population Survey (CPS), where BRFSS is a repeated survey without replacement of sample elements and CPS is one with replacement of sample elements. Standard Bayesian model-checking and sensitivity analysis are applied to the model.