A Bayesian Model of Sample Selection with a Discrete Outcome Variable: Detecting Depression in Older Adults

Depression as a major mental illness among older adults has attracted a lot of research attention. However, the problem of sample selection, inevitable in most health surveys, has been largely ignored. To fill in this gap, this paper formally models selection into the sample jointly with a discrete outcome variable for depression. A Bayesian model of sample selection is developed from a multivariate probit by (i) allowing missing depression status for nonselected respondents, and (ii) using Cholesky factorization of the inverse variance matrix to avoid a Metropolis-Hastings step in the Gibbs sampler. Non-selected respondents are less likely to suffer from depression.