An approach to categorical data with nonignorable nonresponse

Log-linear models have been used to adjust for nonresponse when categorical outcomes are subject to nonignorable nonresponse. The log models are fitted to the data in an augmented frequency table in which one index corresponds to whether the subject is a respondent. Park and Brown (1994, Journal of the American Statistical Association 89, 44-52) proposed a pseudo-Bayesian method that has the effect of smoothing the unobserved cell frequencies. Their approach assigns prior observations only to the unobserved cells. Their method was shown to perform better than the maximum likelihood method, which can produce unstable boundary estimates. Generalizing their approach, we propose a new approach that assigns prior observations to both observed and unobserved cells. Through a simulation study, we compare the proposed approach with Park and Brown's and the maximum likelihood approach.