A comparison of GEE and random effects models for distinguishing heterogeneity, nonstationarity and state dependence in a collection of short binary event series

Abstract

GEE transition models and Markov random effect models are applied to a simple panel data set on depression. In each case, the precise specifications adopted were derived from the authors’ interpretation of best practice in the literature. The two approaches result in quite different inference on the three process characteristics of interest: state dependence, heterogeneity and nonstationarity. The design of the analyses permits indirect goodness of fit measures to be derived for the GEE models and these indicate serious deficiencies in this approach. It is shown through simulation and further analyses of the depression data that these deficiencies may be corrected by including the initial observation properly in the analyses and by adopting an appropriate variance-covariance structure. The former problem is widely understood in random effects modelling and is relatively straightforward to address within GEE. The latter problem is more difficult because, without model selection or goodness of fit measures generally available for GEE models, it is not clear how one may select empirically between alternative variance-covariance structures. Inappropriate variance-covariance specifications prejudice consistent estimation of state dependence and nonstationarity.