A note on conditional AIC for linear mixed-effects models

Liang, Hua; Wu, Hulin; Zou, Guohua

doi:10.1093/biomet/asn023

Cited by 111 publications

(115 citation statements)

References 16 publications

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“…Then, the problem is closely related to a regression model selection problem with correlated errors, and use of the marginal model does not involve defining information criteria different from those derived in the context of linear regression models. When the random effects are themselves of interest, then the conditional or hierarchical model should be used, and the conventional information criteria may be inappropriate (Liang, Wu, & Zou, 2008;Vaida & Blanchard, 2005).…”

Section: Information Criteria For Model Selectionmentioning

confidence: 99%

Selecting the best unbalanced repeated measures model

et al. 2010

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This study examined the performance of selection criteria available in the major statistical packages for both mean model and covariance structure. Unbalanced designs due to missing data involving both a moderate and large number of repeated measurements and varying total sample sizes were investigated. The study also investigated the impact of using different estimation strategies for information criteria, the impact of different adjustments for calculating the criteria, and the impact of different distribution shapes. Overall, we found that the ability of consistent criteria in any of the their examined forms to select the correct model was superior under simple covariance patterns than under complex covariance patterns, and vice versa for the efficient criteria. The simulation studies covered in this paper also revealed that, regardless of method of estimation used, the consistent criteria based on number of subjects were more effective than the consistent criteria based on total number of observations, and vice versa for the efficient criteria. Furthermore, results indicated that, given a dataset with missing values, the efficient criteria were more affected than the consistent criteria by the lack of normality.

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Section: Information Criteria For Model Selectionmentioning

confidence: 99%

Selecting the best unbalanced repeated measures model

et al. 2010

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“…Further, when variance components τ are unknown, Vaida and Blanchard (2005) proposed that ρ can be replaced with estimated version ρ = ρ(Σ). Liang et al (2008) provided an alternative presentation for cAIC by using Stein's formula (Stein, 1981) and when the error variance σ 2 is known but variance components τ are unknown, cAIC is derived as…”

Section: Review Of Model Selection Methods Based On Akaike Informatiomentioning

confidence: 99%

“…Vaida and Blanchard (2005) proposed the conditional model selection formation in terms of cAIC with effective degrees of freedom that account for certain shrinkage weight in the random effects under assumption of known variance parameters for random effects. Liang et al (2008) proposed a bias-corrected cAIC that accounts for uncertainty in the estimation of the variance parameters, but its implementation could be computationally intensive since it uses numerical differentiation. Greven and Kneib (2010) developed and explicit formulation of bias-corrected cAIC by Liang et al (2008) so that the corrected cAIC good be obtained without numerical differentiation.…”

Section: Introductionmentioning

confidence: 99%

“…Liang et al (2008) proposed a bias-corrected cAIC that accounts for uncertainty in the estimation of the variance parameters, but its implementation could be computationally intensive since it uses numerical differentiation. Greven and Kneib (2010) developed and explicit formulation of bias-corrected cAIC by Liang et al (2008) so that the corrected cAIC good be obtained without numerical differentiation.…”

Section: Introductionmentioning

confidence: 99%

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A Note on Performance of Conditional Akaike Information Criteria in Linear Mixed Models

Lee

2015

CSAM

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It is not easy to select a linear mixed model since the main interest for model building could be different and the number of parameters in the model could not be clearly defined. In this paper, performance of conditional Akaike Information Criteria and its bias-corrected version are compared with marginal Bayesian and Akaike Information Criteria through a simulation study. The results from the simulation study indicate that bias-corrected conditional Akaike Information Criteria shows promising performance when candidate models exclude large models containing the true model, but bias-corrected one prefers over-parametrized models more intensively when a set of candidate models increases. Marginal Bayesian and Akaike Information Criteria also have some difficulty to select the true model when the design for random effects is nested.

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“…Vaida and Balanchard (2005) proposed conditional AIC for model selection in linear mixed effect models when the prediction of random effects is of primary interest. Theoretical properties of cAIC and related criteria have been investigated by Liang et al (2008) and Greven and Kneib (2010). However, all of the simulation studies were performed under a balanced design.…”

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confidence: 99%

Simulation Study on Model Selection Based on AIC under Unbalanced Design in Linear Mixed Effect Models

Lee¹

2010

Korean Journal of Applied Statistics

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서론선형혼합모형(Linear Mixed-Effects Models)은 서로 독립이 아닌 다양한 형태의 상관관계를 가지는 자 료들에 적용할 수 있는 매우 유용한 통계적 모형이다. 예로 반복측정 자료나 군집 자료에서는 관측값들 이 서로 독립이 아니며 또한 동일한 분포를 가지지 않기 때문에 단순한 선형모형을 적용할 수 없다. 이 러한 경우 선형혼합모형은 임의효과(random effects)를 이용하여 자료들 간에 다양한 상관관계를 설명 할 수 있다. 선형혼합모형하에서의 통계적 추론은 분산분석(ANOVA; Analysis of Variance)의 제곱합 을 이용한 적률추정방법에서 시작되었으며 Hartley와 Rao (1967)에 의해 우도함수방법이 제안되면서 다양한 추정 방법과 그 계산법이 개발되어 왔다 (Harville, 1977; Searle 등, 1992;Jiang, 2009). 특별 히 자료가 불균형(unbalanced data)인 경우에는 대부분의 추정량이 자료가 균형일 때 나타나는 최적성 질을 만족하지 않는 것이 알려져 있으며 자료가 불균형일 때 생기는 추정량 효율의 저하를 극복하기 위 하여 많은 연구가 수행되어 왔다 (Khuri 등, 1998). Blanchard, 2005; Liang 등, 2008). 선형혼합모형과 AIC에 의한 모형의 선택 선형혼합모형선형혼합모형은 임의효과를 이용하여 자료들 간에 상관관계와 분포의 이질성을 설명할 수 있으며 일반 적인 형태는 다음과 같이 나타낼 수 있다.1)모형 M1인 경우에는 mAIC와 cAIC가 동일하며 AIC는 다음과 같다. Greven과 Kneib, 2010).참고문헌 Akaike, H. (1973 AbstractThis article consider a performance model selection based on AIC under unbalanced deign in linear mixed effect models. Vaida and Balanchard (2005) proposed conditional AIC for model selection in linear mixed effect models when the prediction of random effects is of primary interest. Theoretical properties of cAIC and related criteria have been investigated by Liang et al. (2008) and Greven and Kneib (2010). However, all of the simulation studies were performed under a balanced design. Even though functional form of AIC remain same even under the unbalanced deign, it is worthwhile to investigate performance of AIC based model selection criteria under the unbalanced design. The simulation study in this article shows how unbalancedness affects model selection in linear mixed effect models.

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A note on conditional AIC for linear mixed-effects models

Cited by 111 publications

References 16 publications

Selecting the best unbalanced repeated measures model

Selecting the best unbalanced repeated measures model

A Note on Performance of Conditional Akaike Information Criteria in Linear Mixed Models

Simulation Study on Model Selection Based on AIC under Unbalanced Design in Linear Mixed Effect Models

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