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

Regression Models with Correlated Binary Response Variables: A Comparison of Different Methods in Finite Samples

The present paper deals with the comparison of the performance of different estimation methods for regression models with correlated binary responses. Throughout, we consider probit models where an underlying latent continous random variable crosses a threshold. The error variables in the unobservable latent model are assumed to be normally distributed. The estimation procedures considered are (1) marginal maximum likelihood estimation using Gauss-Hermite quadrature, (2) generalized estimation equations (GEE) techniques with an extension to estimate tetrachoric correlations in a second step, and, (3) the MECOSA approach proposed by Schepers, Arminger and Küsters (1991) using hierarchical mean and covariance structure models. We present the results of a simulation study designed to evaluate the small sample properties of the different estimators and to make some comparisons with respect to technical aspects of the estimation procedures and to bias and mean squared error of the estimators. The results show that the calculation of the ML estimator requires the most computing time, followed by the MECOSA estimator. For small and moderate sample sizes the calculation of the MECOSA estimator is problematic because of problems of convergence as well as a tendency of underestimating the variances. In large samples with moderate or high correlations of the errors in the latent model, the MECOSA estimators are not as efficient as ML or GEE estimators. The higher the `true' value of an equicorrelation structure in the latent model and the larger the sample sizes are, the more is the efficiency gain of the ML estimator compared to the GEE and MECOSA estimators. Using the GEE approach, the ML estimates of tetrachoric correlations calculated in a second step are biased to a smaller extent than using the MECOSA approach

Semiparametric EM-estimation of censored linear regression models for durations

This paper investigates the sensitivity of maximum quasi likelihood estimators of the covariate effects in duration models in the presence of misspecification due to neglected heterogeneity or misspecification of the hazard function. We consider linear models for r(T) where T is duration and r is a known, strictly increasing function. This class of models is also referred to as location-scale models. In the absence of censoring, Gould and Lawless (1988) have shown that maximum likelihood estimators of the regression parameters are consistent and asymptotically normally distributed under the assumption that the location-scale structure of the model is of the correct form. In the presence of censoring, however, model misspecification leads to inconsistent estimates of the regression coefficients for most of the censoring mechanisms that are widely used in practice. We propose a semiparametric EM-estimator, following ideas of Ritov (1990), and Buckley and James (1979). This estimator is robust against misspecification and is highly recommended if there is heavy censoring and if there may be specification errors. We present the results of simulation experiments illustrating the performance of the proposed estimator

Probit models: Regression parameter estimation using the ML principle despite misspecification of the correlation structure

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