Model explicit item imputation for demographic categories

We proposed an item imputation method for categorical data based on a Maximum Likelihood Estimator (MLE) derived from a conditional probability model (Besag 1974). We also defined a measure for the item non-response error that was useful in evaluating the bias relative to other imputation methods. To compute this measure, we used Bayesian iterative proportional fitting (Gelman and Rubin 1991; Schafer 1997). We implemented our imputation method for the 1998 dress rehearsal of the Census 2000 in Sacramento, and we used the error measure to compare item imputations between our method and a version of the nearest neighbour hot-deck method (Fay 1999; Chen and Shao 1997, 2000) at aggregate levels. Our results suggest that our method gives additional protection against imputation biases caused by heterogeneities between domains of study, relative to the hot-deck method.