Variance Component Testing in Multilevel Models

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Power struggles (2018, background): “Moreover, the choice of statistical test can affect the calculation of the standard error and corresponding estimates of power (Berkhof & Snijders, 2001).”
The effect of estimation method and sample size in multilevel structural equation modeling (2010, background): “Other studies focusing on multilevel regression also found that the Wald test for variances is not very accurate; for a discussion, see Berkhof and Snijders (2001).”
Hierarchical CUB Models for Ordinal Variables (2012, background): “However, the null hypothesis specifies a parameter on the boundary of the admissible parametric space, and classical LRT asymptotic theory is not more valid (Berkhof and Snijders, 2001; Verbeke and Molenberghs, 2007).”
Diagnostic Checks for Multilevel Models (2008, background): “The score test also has good power properties in a small sample setting [6].”
Sufficient Sample Sizes for Multilevel Modeling (2005, background): “A variety of alternative approaches have been proposed (cf. Berkhof & Snijders, 2001, for a review ).”
An Introduction to Growth Modeling (2004, unknown): “As noted by Berkhof and Snijders (2001), this bias can largely be corrected by dividing the p-value obtained from the likelihood ratio test (of variance terms) by 2.”