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Discussion Lead: Andrew Gelman (Columbia)
Topic: Incorporating weights in Bayesian analysis using a joint model and poststratification
Link:http://www.stat.columbia.edu/~gelman/research/unpublished/weight_regression.pdf
Abstract: A well-known rule in practical survey research is to include weights when estimating a population average but not to use weights when fitting a regression model—as long as the regression includes as predictors all the information that went into the sampling weights. But what if you don’t know where the weights came from? We propose a quasi-Bayesian approach using a joint regression of the outcome and the sampling weight, followed by poststratifcation on the two variables, thus using design information within a model-based context to obtain inferences for small-area estimates, regressions, and other population quantities of interest.