Regression Models with Correlated Binary Response Variables: a Comparison of Diierent Methods in Finite Samples

The present paper deals with the comparison of the performance of diierent 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 K usters (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 diierent estima-tors and to make some comparisons with respect to technical aspects of the estimation procedures and to bias and mean squared error of the estima-tors. 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 eecient as ML or GEE estimators. The higher thètrue' value of an equicorrelation structure in the latent model and the larger the sample sizes are, the more is the eeciency 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.