Likelihood ratio tests in linear mixed models with one variance component

Ciprian M. Crainiceanu, David Ruppert

Research output: Contribution to journalArticle

Abstract

We consider the problem of testing null hypotheses that include restrictions on the variance component in a linear mixed model with one variance component and we derive the finite sample and asymptotic distribution of the likelihood ratio test and the restricted likelihood ratio test. The spectral representations of the likelihood ratio test and the restricted likelihood ratio test statistics are used as the basis of efficient simulation algorithms of their null distributions. The large sample χX2 mixture approximations using the usual asymptotic theory for a null hypothesis on the boundary of the parameter space have been shown to be poor in simulation studies. Our asymptotic calculations explain these empirical results. The theory of Self and Liang applies only to linear mixed models for which the data vector can be partitioned into a large number of independent and identically distributed subvectors. One-way analysis of variance and penalized splines models illustrate the results.

Original languageEnglish (US)
Pages (from-to)165-185
Number of pages21
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume66
Issue number1
DOIs
StatePublished - Feb 24 2004
Externally publishedYes

Keywords

  • Degrees of freedom
  • Non-regular problems
  • Penalized splines

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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