Regression Analysis for Categorical Variables with Outcome Subject to Nonignorable Nonresponse

Abstract We develop a log-linear model for categorical response subject to nonignorable nonresponse. The paper differs from Fay (1986) in its focus on estimation and hypothesis testing in a regression setting, as opposed to imputation in a multivariate setting. We present several new results concerning the existence of solutions on the boundary of the parameter space and the construction of confidence intervals for estimates. We illustrate the method by estimating the proportion of voters preferring Truman in a 1948 preelection poll (Mosteller, Hyman, McCarthy, Marks, and Truman 1949). Results may depend strongly on the model assumed for nonresponse; goodness-of-fit tests are available for comparing alternative models.