  Longitudinal data are common in clinical trials and observational studies,
where missing outcomes due to dropouts are always encountered. Under such
context with the assumption of missing at random, the weighted generalized
estimating equations (WGEE) approach is widely adopted for marginal analysis.
Model selection on marginal mean regression is a crucial aspect of data
analysis, and identifying an appropriate correlation structure for model
fitting may also be of interest and importance. However, the existing
information criteria for model selection in WGEE have limitations, such as
separate criteria for the selection of marginal mean and correlation
structures, unsatisfactory selection performance in small-sample set-ups and so
on. In particular, there are few studies to develop joint information criteria
for selection of both marginal mean and correlation structures. In this work,
by embedding empirical likelihood into the WGEE framework, we propose two
innovative information criteria named a joint empirical Akaike information
criterion (JEAIC) and a joint empirical Bayesian information criterion (JEBIC),
which can simultaneously select the variables for marginal mean regression and
also correlation structure. Through extensive simulation studies, these
empirical-likelihood-based criteria exhibit robustness, flexibility, and
outperformance compared to the other criteria including the weighted
quasi-likelihood under the independence model criterion, the missing
longitudinal information criterion and the joint longitudinal information
criterion. In addition, we provide a theoretical justification of our proposed
criteria, and present two real data examples in practice for further
illustration.
