Inference under Informative Sampling

Survey data are frequently used for analytic inference about statistical models holding for the corresponding population data. Familiar examples include the estimation of income elasticities from household surveys, the analysis of labor market dynamics from labor force surveys, and the study of the relationships between risk factors and disease incidence from health surveys. The data are usually collected for samples drawn by probability sampling. This induces a set of base weights for the sampled units reflecting unequal selection probabilities. When the sampling weights are related to the values of the model outcome variable even after conditioning on the model covariates, the observed outcomes are no longer representative of the population outcomes due to the sampling or response process and the model holding for the sample data is then different from the model holding in the population. The sample distribution refers to the distribution of the sample measurements, as defined by the population model and the sampling design, with the realized sample of respondents held fixed.