SummaryThe conventional model selection criterion AIC has been applied to choose candidate models in mixed-effects models by the consideration of marginal likelihood. Vaida and Blanchard (2005) demonstrated that such a marginal AIC and its small sample correction are inappropriate when the research focus is on clusters. Correspondingly, these authors suggested to use conditional AIC. The conditional AIC is derived under the assumptions of the variance-covariance matrix or scaled variance-covariance matrix of random effects being known. We develop a general conditional AIC but without these strong assumptions. This allows Vaida and Blanchard's conditional AIC to be applied in a wide range. Simulation studies show that the proposed method is promising.
There has been increasing interest recently in model averaging within the frequentist paradigm. The main benefit of model averaging over model selection is that it incorporates rather than ignores the uncertainty inherent in the model selection process. One of the most important, yet challenging, aspects of model averaging is how to optimally combine estimates from different models. In this work, we suggest a procedure of weight choice for frequentist model average estimators that exhibits optimality properties with respect to the estimator's mean squared error (MSE). As a basis for demonstrating our idea, we consider averaging over a sequence of linear regression models. Building on this base, we develop a model weighting mechanism that involves minimizing the trace of an unbiased estimator of the model average estimator's MSE. We further obtain results that reflect the finite sample as well as asymptotic optimality of the proposed mechanism. A Monte Carlo study based on simulated and real data evaluates and compares the finite sample properties of this mechanism with those of existing methods. The extension of the proposed weight selection scheme to general likelihood models is also considered. This article has supplementary material online.
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