A User-Friendly Introduction to Link-Probit-Normal Models

Probit-normal models have attractive properties compared to logit-normal models. In particular, they allow for easy specification of marginal links of interest while permitting a conditional random effects structure. Moreover, programming fitting algorithms for probit-normal models can be trivial with the use of well-developed algorithms for approximating multivariate normal quantiles. In typical settings, data cannot distinguish between probit and logit conditional link functions. Therefore, if marginal interpretations are desired, the default conditional link should be the most convenient one. We refer to models with a probit conditional link, an arbitrary marginal link, and a normal random effect distribution as link-probit-normal models. In this article we outline these models and discuss appropriate situations for using multivariate normal approximations for estimation. Unlike other articles in this area that focus on very general situations and implement Markov chain or MCEM algorithms, we focus on ...