Bayesian Analysis of Sample Surveys

Columbia University, New York NY

Investigators

Abstract

Two key concerns in sample surveys are bias, caused by inability to reach all sections of the target population (noncoverage) or nonresponse on the part of selected subjects, and variance or lack of precision, caused by inadequate sample sizes. One approach to increase precision is to fit statistical models to the survey response; however, practical application has been limited by an inability to fit sufficiently flexible models. The plan of this research is to develop models that incorporate information about the design of the survey and other knowledge, such as population distributions of covariates, that is currently used in classical weighting methods to reduce the bias and variance of sample survey estimates. A special concern of this approach is to account for the design of the data collection and to make our new methods "backward compatible" with existing design-based analysis methods for sample surveys. Statistically, developing models to account for all the features in a survey design requires research in linear and logistic regression models with complex hierarchical structures among the predictor variables. The research is intended ultimately to yield routine methods for sample survey inference that combine the flexibility of model-based inference with the reliability of design-based inference. This work will potentially advance three areas: statistical sampling inference, Bayesian methods, and the applications of sample surveys, especially in social science and public health. The modeling approach allows the partial pooling of estimates between different structural levels in the population (for instance, school classrooms and individual students), and is particularly effective for estimating small subpopulations and for dealing with nonresponse that is caused by complex combinations of factors. For example, in opinion polls a researcher may be interested in differences in opinion between different demographic groups or different regions of the country. In a public health survey of children, one may wish to identify predictors of high-risk behavior.