Restricted likelihood ratio testing for zero variance components in linear mixed models

Sonja Greven, Ciprian M Crainiceanu, Helmut Küchenhoff, Annette Peters

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)870-891
Number of pages22
JournalJournal of Computational and Graphical Statistics
Volume17
Issue number4
DOIs
StatePublished - 2009

Fingerprint

Linear Mixed Model
Variance Components
Likelihood Ratio
Testing
Mixed Model
Zero
Approximation
Nonparametric Smoothing
Parametric Bootstrap
Software
Air Pollution
Longitudinal Study
Null Distribution
Number of Clusters
Null hypothesis
Asymptotic distribution
Statistic
Parameter Space
Standard Model
Health

Keywords

  • Nonparametric smoothing
  • Nonregular problem
  • Parametric Bootstrap
  • Penalized splines

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Restricted likelihood ratio testing for zero variance components in linear mixed models. / Greven, Sonja; Crainiceanu, Ciprian M; Küchenhoff, Helmut; Peters, Annette.

In: Journal of Computational and Graphical Statistics, Vol. 17, No. 4, 2009, p. 870-891.

Research output: Contribution to journalArticle

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