On generalized estimating equations for vector regression

TL;DR

This paper explores generalized estimating equations (GEE) for vector regression, demonstrating their flexibility and robustness for mixed and same-type response vectors, with theoretical insights and empirical evaluations.

Contribution

It extends GEE methodology to vector regression, showing its advantages as a semiparametric alternative and a plug-in for existing models, with proven asymptotic correctness.

Findings

GEE provides asymptotically correct inferences regardless of variance-covariance model specification.

Simulation studies show good finite-sample performance across datasets.

Application examples demonstrate GEE's practical utility in diverse contexts.

Abstract

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.