‘On the behaviour of marginal and conditional AIC in linear mixed models’

By Sonja Greven, Thomas Kneib. Biometrika, 2010

222 citations recorded by the source corpus.

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion, aic , have been used, based either on the marginal or on the conditional distribution. We show that the marginal aic is not an asymptotically unbiased estimator of the Akaike information, and favours smaller models without random effects. For the conditional aic , we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that can lead to the selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional aic , which avoids the high computational cost and imprecision of available numerical approximations. An implementation in an R package (R Development Core Team, 2010) is provided. All theoretical results are illustrated in simulation studies, and their impact in practice is investigated in an analysis of childhood malnutrition in Zambia. Copyright 2010, Oxford University Press.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1db0b44e92f3494566d5ee3e218d8263a9638bd6

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Citations in the corpus

A unifying approach to the estimation of the conditional Akaike information in generalized linear mixed models (2014, methodology): “Even under the marginal model it is not an (asymptotically) unbiased estimator of the Akaike information as shown for the Gaussian case by Greven & Kneib (2010).”
Cross-Validation for Correlated Data (2019, background): “This topic is also discussed in context of conditional AIC (Vaida and Blanchard 2005; Liang, Wu, and Zou 2008; Greven and Kneib 2010; Rabinowicz and Rosset 2020) where the bias correction term also contains the covariance matrix.”
Spatial weights matrix selection and model averaging for spatial autoregressive models (2017, background): “Similar to the proof of Theorem 3 by Greven and Kneib (2010), from normality of ε and Stein’s Lemma (1981), we have”
Generalized additive models for location, scale and shape for high dimensional data—a flexible approach based on boosting (2012, background): “This approach, however, has several shortcomings that are partially inherited from problems that are associated with the traditional AIC (Ripley (2004) and Greven and Kneib (2010); see Section 2.2 for a detailed discussion).”