Sample selection models for discrete and other non-Gaussian response variables

TL;DR

This paper develops a general framework for sample selection models applicable to non-Gaussian and discrete response variables, extending existing methods beyond the traditional Gaussian assumption.

Contribution

It introduces a flexible construction for selection models covering various distributions and proposes likelihood-based inference methods for these models.

Findings

Framework accommodates diverse distributions including discrete responses.

Likelihood inference methods are developed for the proposed models.

Extends the applicability of sample selection models beyond Gaussian cases.

Abstract

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.