Sample Size and Accuracy of Estimates in Multilevel Models

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Keep Calm and Learn Multilevel Logistic Modeling: A Simplified Three-Step Procedure Using Stata, R, Mplus, and SPSS (2017, methodology): “In multilevel linear modeling, simulation studies show that 50 or more level-2 units are necessary to accurately estimate standard errors (Maas & Hox, 2005; see also Paccagnella, 2011).”
The Effect of Small Sample Size on Two-Level Model Estimates: A Review and Illustration (2014, background): “…and Hibbard 2009; Hox et al. 2012; Konstantopoulos 2010; Kreft 1996; Maas, C and Hox 2004; Maas and Hox 2005; McNeish 2014; Meuleman and Billiet 2009; Moineddin, Matheson, and Glazier 2007; Mok 1995; Paccagnella 2011; Scherbaum and Ferreter 2009; Snijders and Bosker 1993; Stegmueller 2013).”
The Impact of Sample Size and Other Factors When Estimating Multilevel Logistic Models (2016, background): “…guideline prescribes at least 30 level-1 units with at least 10 groups for accurate fixed effects and standard errors, 30 groups if random effects are of interest, and at least 50 groups if accurate random effects and their standard errors are desired (Maas & Hox, 2004, 2005; Pacagnella, 2011).”
Multilevel Modelling of Country Effects: A Cautionary Tale (2016, background): “There is less evidence for multilevel logit models than for linear models but the few existing studies suggest broadly similar conclusions: see, for example, Austin (2010), Moineddin, Matheson and Glazier (2007), Paccagnella (2011), and Stegmueller (2013).”