On generalized estimating equations for vector regression

Generalized estimating equations (GEE; Liang & Zeger 1986) for general vector regression settings are examined. When the response vectors are of mixed type (e.g. continuous-binary response pairs), the GEE approach is a semiparametric alternative to full-likelihood copula methods, and is closely related to the mean-covariance estimation equations approach of Prentice & Zhao (1991). When the response vectors are of the same type (e.g. measurements on left and right eyes), the GEE approach can be viewed as a "plug-in" to existing methods, such as the vglm function from the state-of-the-art VGAM R package of Yee (2015). In either scenario, the GEE approach offers asymptotically correct inferences on model parameters regardless of whether the working variance-covariance model is correctly or incorrectly specified. The finite-sample performance of the method is assessed using simulation studies based on a burn injury dataset (Song 2007) and a Sorbinil eye trial dataset (Rosner et. al 2006). The method is applied to data analysis examples using the same two datasets, as well as on a presence/absence dataset on three plant species in the Hunua ranges of Auckland.