Abstract: The Akaike Information Criterion, which is based on maximum likelihood estimation and cannot be applied directly to the situations when likelihood
functions are not available, has been modified for variable selection in longitudinal data with generalized estimating equations via a working independence model. This paper proposes another modification to AIC, the difference between the quasilikelihood functions of a candidate model and of a narrow model plus a penalty term. Such a difference avoids calculating complex integration from quasi-likelihood, but inherits theoretical asymptotic properties from AIC. We also propose a focused information criterion for variable selection on the basis of the quasi-score function. Further, this paper develops a frequentist model average estimator for longitudinal data with generalized estimating equations. Simulation studies provide evidence of the superiority of the proposed procedures. The procedures are further applied to a data example.

Key words and phrases: FIC, local misspecification, marginal likelihood, model averaging, QIC, quasi-likelihood, working independence.