Asymptotic Properties and Information Criteria for Misspecified Generalized Linear Mixed Models

Yu, Dalei; Zhang, Xinyu; Yau, Kelvin K. W.

doi:10.1111/rssb.12270

Cited by 14 publications

(4 citation statements)

References 40 publications

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“…The first part of Condition 3 requires inf w∈ Q * n (w) to grow at a rate no slower than n 1∕2 and excludes the situation where the true model lies within the set of candidate models. Similar assumption was imposed in condition (8) of Ando and Li [1] and theorem 2 of Yu et al [36]. The second part of Condition 3 poses a mild assumption on the quasi-true value of the Poisson count component.…”

Section: Discussionmentioning

confidence: 93%

Frequentist model averaging for zero‐inflated Poisson regression models

Zhou

Wan

2022

Statistical Analysis

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This paper considers frequentist model averaging for estimating the unknown parameters of the zero-inflated Poisson regression model. Our proposed weight choice procedure is based on the minimization of an unbiased estimator of a conditional quadratic loss function. We prove that the resulting model average estimator enjoys optimal asymptotic property and improves finite sample properties over the two commonly used information-based model selection estimators and their model average estimators via simulation studies. The proposed method is illustrated by a real data example.

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Section: Discussionmentioning

confidence: 93%

Frequentist model averaging for zero‐inflated Poisson regression models

Zhou

Wan

2022

Statistical Analysis

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“…Pu and Niu (2006) show the asymptotic loss efficiency of GIC for selecting the fixed‐effects models given the correct random‐effects models. Yu et al (2018) show the asymptotic loss efficiency of conditional generalized information criterion (CGIC) for selecting generalized linear mixed‐effects models when the random effects are predicted by treating them as fixed ones. Although it is common to predict random effects using the empirical best linear unbiased predictors (EBLUPs)—see Robinson (1991) and Bates et al (2015)—to the best of our knowledge, no asymptotic loss efficiency has been derived for EBLUPs.…”

Section: Introductionmentioning

confidence: 99%

Selection of linear mixed‐effects models for clustered data

Chang

Huang

Ing

2023

Scandinavian J Statistics

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We consider model selection for linear mixed-effects models with clustered structure, where conditional Kullback-Leibler (CKL) loss is applied to measure the efficiency of the selection. We estimate the CKL loss by substituting the empirical best linear unbiased predictors (EBLUPs) into random effects with model parameters estimated by maximum likelihood. Although the BLUP approach is commonly used in predicting random effects and future observations, selecting random effects to achieve asymptotic loss efficiency concerning CKL loss is challenging and has not been well studied. In this paper, we propose addressing this difficulty using a conditional generalized information criterion (CGIC) with two tuning parameters. We further consider a challenging but practically relevant situation where the number, m, of clusters does not go to infinity with the sample size.Hence the random-effects variances are not consistently estimable. We show that via a novel decomposition of the CKL risk, the CGIC achieves consistency and asymptotic loss efficiency, whether m is fixed or increases to infinity with the sample size. We also conduct numerical experiments to illustrate the theoretical findings.

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“…These results are not directly applicable for generalized mixed models (Saefken, Kneib, van Waveren, & Greven, ). However Yu, Zhang, and Yau () propose a conditional generalized information criterion based on the conditional Kullback–Leibler divergence for possibly misspecified data modeled by a generalized linear mixed model. In a recent contribution, Sakamoto () introduces a bias reduction for the marginal AIC.…”

Section: Introductionmentioning

confidence: 99%

Conditional covariance penalties for mixed models

Säfken

Kneib

2019

Scandinavian J Statistics

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The prediction error for mixed models can have a conditional or a marginal perspective depending on the research focus. We introduce a novel conditional version of the optimism theorem for mixed models linking the conditional prediction error to covariance penalties for mixed models. Different possibilities for estimating these conditional covariance penalties are introduced. These are bootstrap methods, cross-validation, and a direct approach called Steinian. The behavior of the different estimation techniques is assessed in a simulation study for the binomial-, the t-, and the gamma distribution and for different kinds of prediction error. Furthermore, the impact of the estimation techniques on the prediction error is discussed based on an application to undernutrition in Zambia.

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Asymptotic Properties and Information Criteria for Misspecified Generalized Linear Mixed Models

Cited by 14 publications

References 40 publications

Frequentist model averaging for zero‐inflated Poisson regression models

Frequentist model averaging for zero‐inflated Poisson regression models

Selection of linear mixed‐effects models for clustered data

Conditional covariance penalties for mixed models

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