We derive explicit formulae for estimation in logistic regression models where some of the covariates are missing. Our approach allows for modeling the distribution of
the missing covariates either as a multivariate normal or 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 amongst these distributions. In addition we consider versions of AIC that are based on
the EM algorithm and on multiple imputation methods that have a wide applicability to model selection in likelihood models in general.