Estimating the Effect of Nonignorable Nonresponse in Sample Surveys

Rubin (1977) developed a method for estimating, in a subjective sense, the effect of nonignorable nonresponse in sample surveys. Based on Bayesian techniques, this method produces a subjective probability interval for the statistic, such as the mean of a response variable, that would have been calculated if all nonrespondents had responded. Demographic and socioeconomic background information that is recorded for both respondents and nonrespondents plays an important role in sharpening the subjective interval - through the adjustment of a regression equation that uses this information. In this article, Rubin's method-sometimes called the mixture modeling approach to drawing inferences from self-selected samples-is reviewed and applied to real survey and experimental data on community standards for sexually explicit material in which respondents were asked to judge the material's appeal to prurient interest and patent offensiveness (two of the three legal criteria for a determination of obscenity). A critically important substantive issue in this context is whether or not the sample self-selection processes governing the willingness of individuals to participate in the experiment have so truncated the frequency distributions of participant judgments about obscenity that they are grossly biased and inaccurate. It is shown how the mixture modeling approach sheds light on the possible extent of such biases.