  The multivariate probit is popular for modeling correlated binary data, with
an attractive balance of flexibility and simplicity. However, considerable
challenges remain in computation and in devising a clear statistical framework.
Interest in the multivariate probit has increased in recent years. Current
applications include genomics and precision medicine, where simultaneous
modeling of multiple traits may be of interest, and computational efficiency is
an important consideration. We propose a fast method for multivariate probit
estimation via a two-stage composite likelihood. We explore computational and
statistical efficiency, and note that the approach sets the stage for
extensions beyond the purely binary setting.
