Abstract: In probability sampling, the first-order inclusion probabilities are available for each unit in the sample. If the first-order inclusion probability is correlated with the study variable at hand, even after adjusting for the covariates in the model, then the sampling design becomes informative and the naive analysis ignoring the sampling design can lead to biased estimation. How to handle informative sampling for analytic inference with survey data is an important practical problem.
Bayesian inference under informative sampling is challenging because the likelihood function under informative sampling is not generally available. In this talk, we tackle this problem by developing a sample-level weight model. The sample-level weight model can also be derived from a beta regression model on the first-order inclusion probability at the population level.
The conditional likelihood function using the sample-based weight model can be further applied to develop a valid Bayesian posterior distribution. Some extensions to the semiparametric weight model are discussed. Results from extensive simulation studies are also presented. An application using Canadian workforce data is presented.