Estimation of multivariate probit models: A mixed generalized estimating/pseudo-score equations approach and some finite sample results

In the present paper a mixed approach is proposed for the
simultaneously estimation of regression and correlation structure
parameters in multivariate probit models using generalized
estimating equations for the former and pseudo-score equations for
the latter. The finite sample properties of the corresponding
estimators are compared to estimators proposed by Qu, Williams,
Beck and Medendorp (1992) and Qu, Piedmonte and Williams (1994)
using generalized estimating equations for both sets of parameters
via a Monte Carlo experiment. As a `reference' estimator for an
equicorrelation model, the maximum likelihood (ML) estimator of the
random effects probit model is calculated. The results show the
mixed approach to be the most robust approach in the sense that the
number of datasets for which the corresponding estimates converged
was largest relative to the other two approaches. Furthermore, the
mixed approach led to the most efficient non-ML estimators and to
very efficient estimators for regression and correlation structure
parameters relative to the ML estimator if individual covariance
matrices were used.