Since the pioneer works of Henderson (1973, 1984), linear mixed effects models are the cornerstone of statistical analysis in animal breeding. Later Laird and Ware (1982) and Diggle (1988) developped random effects models to analyse longitudinal data. In that framework it is often interesting to test the significance of some fixed or random coefficients in a model (see for example Foulley et al., 2000). For that purpose, likelihood ratio tests method appears to be a natural and relevant technique. However, though tests of fixed effects are classical and well known, tests of variance components are nonstandard and often misunderstood. The purpose of this article is to discuss the problem of likelihood ratio tests for variance components and to give some new interpretations in terms of model selection. Our discussion is based on the results for nonstandard testing situations by Self and Liang (1987) and Stram and Lee (1994
Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume 2002. Session 16, , 16.09, 2002
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