Sample selection models for discrete and other non-Gaussian response   variables
  Consider observation of a phenomenon of interest subject to selective sampling due to a censoring mechanism regulated by some other variable. In this context, an extensive literature exists linked to the so-called Heckman selection model. A great deal of this work has been developed under Gaussian assumption of the underlying probability distributions; considerably less work has dealt with other distributions. We examine a general construction which encompasses a variety of distributions and allows various options of the selection mechanism, focusing especially on the case of discrete response. Inferential methods based on the pertaining likelihood function are developed. 
Adelchi Azzalini, Hyoung-Moon Kim, Hea-Jung Kim
stat.ME