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Testing random effects in linear mixed models: another look at the F‐test (with discussion)
Author(s) -
Hui F. K. C.,
Müller Samuel,
Welsh A. H.
Publication year - 2019
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12256
Subject(s) - generality , generalized linear mixed model , mixed model , test (biology) , random effects model , mathematics , linear model , computation , statistical hypothesis testing , class (philosophy) , algorithm , computer science , statistics , artificial intelligence , medicine , psychology , paleontology , meta analysis , psychotherapist , biology
Summary 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.