Selection Modeling Versus Mixture Modeling with Nonignorable Nonresponse

It is sometimes suspected that nonresponse to a sample survey is related to the primary outcome variable. This is the case, for example, in studies of income or of alcohol consumption behaviors. If nonresponse to a survey is related to the level of the outcome variable, then the sample mean of this outcome variable based on the respondents will generally be a biased estimate of the population mean. If this outcome variable has a linear regression on certain predictor variables in the population, then ordinary least squares estimates of the regression coefficients based on the responding units will generally be biased unless nonresponse is a stochastic function of these predictor variables. The purpose of this paper is to discuss the performance of two alternative approaches, the selection model approach and the mixture model approach, for obtaining estimates of means and regression estimates when nonresponse depends on the outcome variable. Both approaches extend readily to the situation when values of the outcome variable are available for a subsample of the nonrespondents, called “follow-ups.” The availability of follow-ups are a feature of the example we use to illustrate comparisons.