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Survey Weights: A Step-by-Step Guide to Calculation, by Richard Valliant and Jill Dever, is an excellent reference for survey data analysts and researchers. This book details the reasons for weighting and shows how to perform different weight-adjustment methods in Stata.
Topics covered include nonresponse, weight adjustment and calibration, linearized and replication-based variance estimation, multiple weights, two-phase sampling, composite estimation, and quality control when computing your own survey weights.
The authors assume familiarity with Stata and some applied sampling experience and knowledge of "lite" theory, such as the concepts of with-replacement versus without-replacement sampling and single- versus multistage designs.