Monroe G. Sirken Award Lecture

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 it is not clear how to apply this advice when fitting regressions that include only some of the weighting information, nor does it tell us what to do when analyzing already-collected surveys where the weighting procedure has not been clearly explained or where the weights depend in part on information that is not available in the data. It is also not clear how one is supposed to account for clustering in such analyses. We propose a quasi-Bayesian approach using a joint regression of the outcome and the logarithm of sampling weight, poststratifying to obtain inference for the quantity of interest or regression in the population, thus using design information within a model-based context.