Weighting in the regression analysis of survey data with a cross-national application

A class of survey weighting methods provides consistent estimation of regression coefficients under unequal probability sampling. The minimization of the variance of the estimated coefficients within this class is considered. A series of approximations leads to a simple modification of the usual design weight. One type of application where unequal probabilities of selection arise is in cross-national comparative surveys. In this case, our argument suggests the use of a certain kind of within-country weight. We investigate this idea in an application to data from the European Social Survey, where we fit a logistic regression model with vote in an election as the dependent variable and with various variables of political science interest included as explanatory variables. We show that the use of the modified weights leads to a considerable reduction in standard errors compared to design weighting.