Poststrati cation Into Many Categories Using HierarchicalLogistic Regression
A standard method for correcting for unequal sampling probabilities and nonresponse in sample surveys is poststratiication: that is, dividing the population into several categories, estimating the distribution of responses in each category, and then counting each category in proportion to its size in the population. We consider poststratiication as a general framework that includes many weighting schemes used in survey analysis (see Little, 1993). We construct a hierarchical logistic regression model for the mean of a binary response variable conditional on poststratiication cells. The hierarchical model allows us to t many more cells than is possible using classical methods, and thus to include much more population-level information, while at the same time including all the information used in standard survey sampling inferences. We are thus combining the modeling approach often used in small-area estimation with the population information used in poststratiication. We apply the method to a set of U.S. pre-election polls, poststratiied by state as well as the usual demographic variables. We evaluate the models graphically by comparing to state-level election outcomes.