Basic Steps in Weighting

Abstract

Survey weights are a key component to producing population estimates. For example, an estimated total has the for t = s w i y i where y i is a response provided by the i th sample member and w i is the corresponding analysis weight. Without their use, estimates may reflect only nuances of a particular sample and may contain significant levels of bias. This is the first of two chapters that address techniques for calculating analysis weights currently used in survey research. Articles detailing new research on survey weighting surface in the literature constantly. Therefore, we encourage survey researchers to use these chapters as a basis of understanding and to rely on journal articles for cutting-edge techniques. There are a series of steps in weighting that are carried out in most, if not all, surveys. These include computation of base weights (also known as design weights), adjustments for unknown eligibility, nonresponse adjustments, and use of auxiliary data to reduce variances and, in some cases, correct for frame deficiencies. We cover the first three of these steps in this chapter. Chapter 14 will address the use of auxiliary data. Sections 13.1 and 13.2 give an overview of weighting and describe general theoretical approaches that are used to justify the use of weights in estimation. In probability samples, the base weights are inverses of selection probabilities. Examples of base weight calculation are presented in Sect. 13.3 for various designs. These can be used for weighting a sample to the full finite population if the frame is perfect and all sample units respond. In some applications, a complete frame of units is available for sampling and frame problems are not a concern. In others, the frame may contain some units that are ineligible and may omit units that are. Having ineligible units in a frame is a type of overcoverage. A way of adjusting for ineligible units is presented in Sect. 13.4; the problem of frame undercoverage is dealt with in Chap. 14. The failure of some units to respond is a worry in most surveys. Without adjusting for nonresponse, estimators can have significant levels of bias. There are different methods of adjustment, which we present in Sect. 13.5. Before covering specific tools used in weighting, some general comments are needed about methods of inference and how they affect weight calculation. 13.1 Overview of Weighting The general goal in weighting to find a set of weights, w i , that can be used in virtually all analyses to produce estimates for the target population under study. For example, an estimated total has the for t = s w i y i and a mean can be computed a ¯ y = s w i y i / s w i for a set of units in sample s (i.e., i ∈ s) Other statistics that can be written as combinations of estimated totals would use the same set of weights. Regression model analyses, for example, often begin with a type of estimated total