  Conventional likelihood-based information criteria for model selection rely
on the distribution assumption of data. However, for complex data that are
increasingly available in many scientific fields, the specification of their
underlying distribution turns out to be challenging, and the existing criteria
may be limited and are not general enough to handle a variety of model
selection problems. Here, we propose a robust and consistent model selection
criterion based upon the empirical likelihood function which is data-driven. In
particular, this framework adopts plug-in estimators that can be achieved by
solving external estimating equations, not limited to the empirical likelihood,
which avoids potential computational convergence issues and allows versatile
applications, such as generalized linear models, generalized estimating
equations, penalized regressions and so on. The formulation of our proposed
criterion is initially derived from the asymptotic expansion of the marginal
likelihood under variable selection framework, but more importantly, the
consistent model selection property is established under a general context.
Extensive simulation studies confirm the out-performance of the proposal
compared to traditional model selection criteria. Finally, an application to
the Atherosclerosis Risk in Communities Study illustrates the practical value
of this proposed framework.
