  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.
