TY - JOUR
T1 - Restricted likelihood ratio testing for zero variance components in linear mixed models
AU - Greven, Sonja
AU - Crainiceanu, Ciprian M.
AU - Küchenhoff, Helmut
AU - Peters, Annette
N1 - Funding Information:
We thank two reviewers and an associate editor for their careful reading of the original manuscript and for their comments, which helped to improve the article. This work was conducted while the first author was visiting Johns Hopkins University on a fellowship from the German Academic Exchange Service (DAAD). Ciprian Crainiceanu’s work was supported by NIH grant AG025553-02 on the Effects of Aging on Sleep Architecture. We also thank Yu-Jen Cheng and Fabian Scheipl for discussions related to the topic of this article. The AIRGENE study was funded as part of the European Union’s 5th Framework Programme, key action number 4: “ Environment and Health,” contract number QLRT-2002-02236. We would like to thank all members of the AIRGENE study group.
PY - 2009
Y1 - 2009
N2 - The goal of our article is to provide a transparent, robust, and computationally fea sible statistical platform for restricted likelihood ratio testing (RLRT) for zero variance components in linear mixed models. This problem is nonstandard because under the null hypothesis the parameter is on the boundary of the parameter space. Our proposed approach is different from the asymptotic results of Stram and Lee who assumed that the outcome vector can be partitioned into many independent subvectors. Thus, our methodology applies to a wider class of mixed models, which includes models with a moderate number of clusters or nonparametric smoothing components. We propose two approximations to the finite sample null distribution of the RLRT statistic. Both approximations converge weakly to the asymptotic distribution obtained by Stram and Lee when their assumptions hold. When their assumptions do not hold, we show in extensive simulation studies that both approximations outperform the Stram and Lee approximation ad the parametric bootstrap. We also identify and address numerical problems associated with standard mixed model software. Our methods are motivated by and applied to a large longitudinal study on air pollution health effects in a highly susceptible cohort. Relevant software is posted as an online supplement.
AB - The goal of our article is to provide a transparent, robust, and computationally fea sible statistical platform for restricted likelihood ratio testing (RLRT) for zero variance components in linear mixed models. This problem is nonstandard because under the null hypothesis the parameter is on the boundary of the parameter space. Our proposed approach is different from the asymptotic results of Stram and Lee who assumed that the outcome vector can be partitioned into many independent subvectors. Thus, our methodology applies to a wider class of mixed models, which includes models with a moderate number of clusters or nonparametric smoothing components. We propose two approximations to the finite sample null distribution of the RLRT statistic. Both approximations converge weakly to the asymptotic distribution obtained by Stram and Lee when their assumptions hold. When their assumptions do not hold, we show in extensive simulation studies that both approximations outperform the Stram and Lee approximation ad the parametric bootstrap. We also identify and address numerical problems associated with standard mixed model software. Our methods are motivated by and applied to a large longitudinal study on air pollution health effects in a highly susceptible cohort. Relevant software is posted as an online supplement.
KW - Nonparametric smoothing
KW - Nonregular problem
KW - Parametric Bootstrap
KW - Penalized splines
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U2 - 10.1198/106186008X386599
DO - 10.1198/106186008X386599
M3 - Article
AN - SCOPUS:64249145967
SN - 1061-8600
VL - 17
SP - 870
EP - 891
JO - Journal of Computational and Graphical Statistics
JF - Journal of Computational and Graphical Statistics
IS - 4
ER -