Testing and adjusting for informativeness in analytic inference
by Professor Jean Opsomer
Abstract: Survey data are often collected through complex surveys with stratification, clustering, and unequal probabilities. Weighting is used to account for these design complexities, and also incorporates additional adjustments for nonresponse and for calibration to known population information. Researchers working with complex survey data may be tempted to ignore these sampling and weighting aspects when conducting statistical analyses and fitting models, but traditional methods often are not appropriate unless these aspects are accounted for.
We describe a likelihood-based testing approach to detect informativeness that is simple to implement and has good statistical properties. We obtain the asymptotic distribution of the test, and use both the asymptotic distribution and a more convenient bootstrap distribution in implementing the procedure. Because the approach relies on a comparison of the weighted and unweighted estimators, it is applicable for secondary analysts who have access to previously created weights. Following testing, we discuss a nonparametric approach for incorporating the informativeness in the analytic inference.
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