Testing random effects in linear mixed models

another look at the F-test (with discussion)

F. K. C. Hui*, Samuel Müller, A. H. Welsh

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Citations (Scopus)


This article re-examines the F-test based on linear combinations of the responses, or FLC test, for testing random effects in linear mixed models. In current statistical practice, the FLC test is underused and we argue that it should be reconsidered as a valuable method for use with linear mixed models. We present a new, more general derivation of the FLC test which applies to a broad class of linear mixed models where the random effects can be correlated. We highlight three advantages of the FLC test that are often overlooked in modern applications of linear mixed models, namely its computation speed, its generality, and its exactness as a test. Empirical studies provide new insight into the finite sample performance of the FLC test, identifying cases where it is competitive or even outperforms modern methods in terms of power, as well as settings in which it performs worse than simulation-based methods for testing random effects. In all circumstances, the FLC test is faster to compute.

Original languageEnglish
Pages (from-to)61-84
Number of pages24
JournalAustralian and New Zealand Journal of Statistics
Issue number1
Publication statusPublished - Mar 2019
Externally publishedYes


  • bootstrap
  • error contrasts
  • hypothesis testing
  • restricted maximum likelihood
  • variance components

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