A criterion for model selection in the presence of incomplete data based on Kullback's symmetric divergence

A criterion is proposed for model selection in the presence of incomplete data. It's construction is based on the motivations provided for the KIC criterion that has been recently developed and for the PDIO (predictive divergence for incomplete observation models) criterion. The proposed criterion serves as an asymptotically unbiased estimator of the complete data Kullback-Leibler symmetric divergence between a candidate model and the generating model. It is therefore a natural extension of KIC to settings where the observed data is incomplete and is equivalent to KIC when there is no missing data. The proposed criterion differs from PDIO in its goodness of fit term and its complexity term, but it differs from AICcd (where the notation “cd” stands for “complete data”) only in its complexity term. Unlike AIC, KIC and PDIO this criterion can be evaluated using only complete data tools, readily available through the EM and SEM algorithms. The performance of the proposed criterion relative to other well-known criteria are examined in a simulation study.