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This article discusses the asymptotic behavior of likelihood ratio tests for nonzero variance components in the longitudinal mixed effects linear model described by Laird and Ware (1982, Biometrics 38, 963-974). Our discussion of the large-sample behavior of likelihood ratio tests for nonzero variance components is based on the results for nonstandard testing situations by Self and Liang (1987, Journal of the American Statistical Association 82, 605-610).
Stram et al. (Thu,) studied this question.