Accelerating computation: A pairwise fitting technique for multivariate probit models

Abstract

Fitting multivariate probit models via maximum likelihood presents considerable computational challenges, particularly in terms of computation time and convergence difficulties, even for small numbers of responses. These issues are exacerbated when dealing with ordinal data. An efficient computational approach is introduced, based on a pairwise fitting technique within a pseudo-likelihood framework. This methodology is applied to clinical case studies, specifically using a trivariate probit model. Additionally, the correlation structure among outcomes is allowed to depend on covariates, enhancing both the flexibility and interpretability of the model. By way of simulation and real data applications, the proposed approach demonstrates superior computational efficiency as the dimension of the outcome vector increases. The method's ability to capture covariate-dependent correlations makes it particularly useful in medical research, where understanding complex associations among health outcomes is of scientific importance.