Missing covariates in logistic regression, estimation and distribution selection

Abstract

We derive explicit formulae for estimation in logistic regression models where some of the covariates are missing. Our approach allows for modelling the distribution of the missing covariates either as a multivariate normal or as a multivariate t-distribution. A main advantage of this method is that it is fast and does not require the use of iterative procedures. A model selection method is derived which allows to choose among these distributions. In addition, we consider versions of Akaike’s information criterion that are based on the expectation–maximization algorithm and multiple imputation methods that have a wide applicability to model selection in likelihood models in general.