Selection Models

Abstract

Much of the early development of, and debate about, selection models appeared in the econometrics literature in which the Tobit model (Heckman 1976) played a central role. This combines a marginal Gaussian regression model for the response, as might be used in the absence of missing data, with a Gaussian-based threshold model for the probability of a value being missing. For simplicity, consider a single Gaussian-distributed response variable Y ∼ N(µ,σ2). The probability of Y being missing is assumed to depend on a second Gaussian variable Ym σ N(µm,σm2), where P(R = 0) = P(Ym<0).