Case‐deletion measures for models with incomplete data

Abstract

This paper proposes several case‐deletion measures for assessing the influence of an observation for complicated models with real missing data or hypothetical missing data corresponding to latent random variables. The idea is to generalise Cook's (1977) approach to the conditional expectation of the complete‐data loglikelihood function in the EM algorithm. On the basis of the diagnostic measures, a procedure is proposed for detecting influential observations. Two examples illustrate our methodology. We show that the method can be applied efficiently to a wide variety of complicated problems that are difficult to handle by existing methods.