Likelihood Ratio, Score, and Wald Tests in a Constrained Parameter Space

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A Family of Generalized Linear Models for Repeated Measures With Normal and Conjugate Random Effects (pp.188) (2010, methodology): “boundary problem that occurs when testing for variance components, mixtures of a χ2 0 and χ 2 1 were used, instead of the conventional χ2 1 (Molenberghs and Verbeke, 2007).”
On the Unnecessary Ubiquity of Hierarchical Linear Modeling (2017, background): “The resulting distribution of the test statistic (typically a Z or 2 statistic) for this hypothesis may not follow the appropriate test distribution, meaning that inferences made from such tests may be untrustworthy (Molenberghs & Verbeke, 2004, 2007; Stram & Lee, 1994).”
Modelling Uncertainty and Overdispersion in Ordinal Data (2014, background): “However, when we test a borderline hypothesis, the asymptotic distribution of this statistic does not converge to the standard 2 random variable (Self and Liang, 1987; Vu and Zhou, 1997; Molenberghs and Verbeke, 2007).”
The effect of number of clusters and cluster size on statistical power and Type I error rates when testing random effects variance components in multilevel linear and logistic regression models (2018, background): “As noted in the Introduction, Molenberghs and Verbeke noted that while the likelihood ratio test and theWald test are asymptotically equivalent, the former is easier to implement and should be considered the default [4].”