Correcting for Nonavailability Bias in Surveys by Weighting Based on Number of Callbacks

Abstract

When respondents to sample surveys differ from nonrespondents, bias can result. Nonresponse is produced by both refusal and nonavailability. Here we concentrate on nonavailability. Clever weighting schemes to deal with nonavailability bias were proposed about 40 years ago by Politz and Simmons and by Simmons, but further theoretical development has been limited. In the meantime, not only have in-person surveys continued to flourish, but telephone surveys also have become common. Herein we present weighting techniques that correct for nonavailability bias yet avoid limitations of earlier methods. The weights (which depend on parameters) are based on the number of callbacks needed to obtain the interview from the sample member, and usually increase with the number of callbacks. If a sample design generated sample weights that are not all the same, those external weights are easily incorporated into the analysis. We assume a beta distribution for p, the probability or proportion of time that a sample member is available for interview. The conditional expectation of the response variable given p is assumed to be a linear (or other) function of p. Our simplest callback model, suitable for some telephone surveys, requires estimates of the two parameters of the beta distribution. Two other models, designed for surveys where interviewers use cues to infer the best times for callbacks, each have a third parameter. For a number of published empirical callback distributions (most with truncation or censoring), parameters under the different models are estimated and the results evaluated.

Key Words:

• Beta distribution
• Maximum likelihood estimation
• Nonresponse
• Not at home
• Sample survey