Spiess, M.; Nagl, W.; Hamerle, Alfred
(1997):
Probit models: Regression parameter estimation using the ML principle despite misspecification of the correlation structure.
Collaborative Research Center 386, Discussion Paper 67

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Abstract
In this paper it is shown that using the maximum likelihood (ML) principle for the estimation of multivariate probit models leads to consistent and normally distributed pseudo maximum likelihood regression parameter estimators (PML estimators) even if the `true' correlation structure of the responses is misspecified. As a consequence, e.g. the PML estimator of the random effects probit model may be used to estimate the regression parameters of a model with any `true' correlation structure. This result is independent of the kind of covariates included in the model. The results of a Monte Carlo experiment show that the PML estimator of the independent binary probit model is inefficient relative to the PML estimator of the random effects binary panel probit model and two alternative estimators using the `generalized estimating equations' approach proposed by Liang and Zeger (1986), if the `true' correlations are high. If the `true' correlations are low, the differences between the estimators are small in finite samples and for the models used. Generally, the PML estimator of the random effects probit panel model is very efficient relative to the GEE estimators. Therefore, if correlations between binary responses cannot be ruled out and the `true' structure of association is unknown or infeasible to estimate, the PML estimator of the random effects probit model is recommended.