The results of two simulation studies suggest a mixed `generalized estimating/pseudo-score equations' approach to lead to more efficient estimators than a GEE approach proposed by Qu, Williams, Beck and Medendorp (1992) or a three-stage approach as proposed e.g. by Schepers, Arminger and Küsters (1991) in panel probit models with binary responses. Furthermore, the mixed approach led to very efficient estimators of regression and correlation structure parameter estimators in an assumed underlying model relative to the ML estimator for an equicorrelation structure. Using the mixed approach, the regression parameters are estimated using generalized estimating equations and the correlation structure parameters are simultaneously estimated using pseudo-score equations. Both sets of parameters are calculated as if they were orthogonal, thereby preserving the robustness of the regression parameter estimators with respect to misspecification of the correlation matrix. Based on the above simulation results, the mixed approach is extended for the estimation of more general structural equation models with ordered categorical or mixed continuous/ordered categorical responses.
Multivariate probit model generalized estimating equations correlated categorical and continuous responses structural equation models