A mixed approach for the estimation of probit models with correlated responses: some finite sample results

Abstract

In the present paper a mixed approach for the simultaneous estimation of regression and correlation structure parameters in probit models with correlated responses proposed by Spiess and Hamerle (1996a) is compared to an approach proposed by Qu, Williams, Beck and Medendorp (1992) and Qu, Piedmonte and Williams (1994) via a Monte Carlo experiment. Whereas in the former approach generalized estimating equations for the estimation of regression parameters and pseudo-score equations for the estimation of association parameters are used, in the latter approach both sets of parameters are estimated using generalized estimating equations. As a ‘reference’ estimator for an equicorrelation model, the maximum likelihood (ML) estimator of a random effects pro bit model is calculated. The results show that the mixed approach leads to the most efficient non-ML estimators for regression and correlation structure parameters if individual covariance matrices are used. Furthermore, for the equicorrelation model, the loss of efficiency is small relative to the ML estimator.