A new test for random effects in linear mixed models with longitudinal data

Zaixing Li, Lixing ZHU*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

6 Citations (Scopus)


As it is known, testing the existence of random effects is often transferred to testing their zero variances/covariance matrices. It is a nonstandard testing problem because the hypothetical values are on the boundary of the whole space. In the literature, a difference-based test was proposed, which has asymptotically tractable null distribution and is then easy to implement. However, the projection method on which the difference-based test relies may affect and deteriorate its performance when covariates associated with fixed effects and covariates associated with random effects are highly correlated. In the paper, for linear mixed models (LMM) with longitudinal data, a new test is proposed to avoid this problem. The new test is also asymptotically distribution-free and more powerful than the difference-based test, particularly when the above correlation is high. The new test is consistent against all global alternatives and can detect local alternatives converging to the null at a rate as close as to m -1/2 with m being the number of subjects. Simulations are carried out to examine the performance and a real data analysis is performed for illustration.

Original languageEnglish
Pages (from-to)82-95
Number of pages14
JournalJournal of Statistical Planning and Inference
Issue number1
Publication statusPublished - Jan 2013

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

User-Defined Keywords

  • Covariance matrix
  • Difference
  • Linear mixed models


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