On the Formation of Weighting Adjustment Cells for Unit Nonresponse

1. Introduction Unit nonresponse occurs when entire interviews are missing due to noncontact of a sampled individual or refusal to answer the questionnaire. Weighting is a standard method of unit nonresponse adjustment and is a natural extension of weighting for unequal probabilities of selection. However, unlike the sample weight, the nonresponse rate is usually unknown and must be estimated. In forming nonresponse weights, respondents and nonrespondents are often classified into adjustment cells based on covariate information recorded for both groups. Respondents in cell c are then weighted by the inverse of the response rate in cell c. For example, a cell is defined as " married women living in the south " with 80 respondents and 20 nonrespondents. Then, the response rate is 80/100 = 0.8 and the response weight is 1/0.8 = 1.25. Let D = (X,Z) be all fully-observed survey variables X and design variables Z, Y be the outcome variable and R be a response indicator. In principle, adjustment cells might be based on a joint classification of the variables D. We consider here situations where this leads to too many cells, so that some cells have no respondents or a small counts of respondents that lead to excessively variable nonresponse weights. This situation is common in the case of attrition in panel surveys, where extensive survey information from earlier waves is available for creating adjustment cells for later waves. In surveys involving differential probabilities of selection, adjustment cells are often formed within which the probability of selection is not constant. The usual weighting adjustment is then proportional to the inverse of the weighted response rate, defined as the sum of the weights for respondents divided by the sum of the weights for respondents and nonrespondents. Simulations in Little and Vartivarian (2002) show that improved inferences are obtained by forming adjustment cells that crossclassify on the survey design variables, rather than incorporating these variables by weighting the rates. However, this strategy may lead to too many adjustment cells to be practical. For example in the Health Interview Survey (Botman et al, 2000), weighted response weights are calculated within second stage sampling unit (SSU), a variable that has many levels. Joint classification by Z and X would correspond to stratifying households within SSU according to race, which would yield many small adjustment cells, including perhaps some with no respondents.