A comparison of different methods for the estimation of regression models with correlated binary responses

Abstract

In the present paper results of a simulation study designed to evaluate the small sample properties of three different estimators for regression models with correlated binary responses are presented. Throughout, binary panel probit models are considered, where an underlying latent continuous random variable crosses a threshold. The estimation procedures considered are (1) marginal maximum likelihood (ML) estimation using Gauss–Hermite quadrature, (2) generalized estimating equations (GEE) techniques and, (3) the MECOSA (‘mean and covariance structure analysis’ (1991)) approach proposed by Schepers et al. (1991) (The analysis of non-metric endogenous variables in latent variable models: the MECOSA approach. In: Gruber, J. (Ed.), Econometric Decision Models: New Methods of Modelling and Applications, Lecture Notes in Economics and Mathematical Systems, Vol. 366. Springer, Berlin, pp. 459–472.) for hierarchical mean and covariance structure models. The results show that for small and moderate sample sizes calculation of the MECOSA estimators is problematic because of convergence problems and a tendency to underestimate the root mean squared errors. On the other hand, the portion of data sets for which the ML and GEE estimation procedures failed to converge was low. In general, the MECOSA estimators are not as efficient as ML or GEE estimators. For small ‘true’ correlations, differences between ML and GEE estimators with respect to efficiency are negligible. However, for larger correlations, the ML estimator is more efficient than the GEE estimator.