The paper shows results obtained when using a hierarchical log-linear model to produce item imputations based on the maximum likelihood estimator. We compare the results with those obtained using the sequential hot-deck imputation procedure. We apply the two procedures on the data collected in Sacramento for the 1998 dress rehearsal for Census 2000. To measure the relative differences between the two methodologies, we simulate the posterior and predictive distributions associated with the model. We run our simulation through data augmentation bayesian iterative proportional fitting (DABIPF). Gelman and Rubin (1991) first proposed a bayesian iterative proportional fitting (BIPF) to generate posterior conjugates for categorical log-linear models. Schafer (1997) proposes a variant of BIPF for direct application to hierarchical models. Schafer (1997) also extends the technique to DABIPF. In our situation Schafer's version of DABIPF yields: 1. An approximation for the posterior distribution of the inclusion probabilities. 2. An approximation for the predictive distribution of the population counts. The predictive distribution makes it possible to give a full inferential assessment of the unreported population counts, and to compare our item imputation procedure with the sequential hot-deck.
