Cluster Size in Multilevel Models: The Impact of Sparse Data Structures on Point and Interval Estimates in Two-Level Models

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Heterogeneous global crop yield response to biochar: a meta-regression analysis (2013, background): “It is nonetheless a higher level than a random effect at the common-control experiment level; given that there are 230 of these, with many singletons, specification of random effects at this level would adversely affect confidence intervals [29] while also over-fitting the model.”
The Impact of Small Cluster Size on Multilevel Models: A Monte Carlo Examination of Two-Level Models with Binary and Continuous Predictors (2010, result): “One exception is a previous study conducted by Bell, Ferron, and Kromrey (2008).”
Dancing the Sample Size Limbo with Mixed Models: How Low Can You Go? (2010, methodology): “…example, some studies have shown bias in the standard errors of the fixed effects, thus decreasing average coverage rates of the 95% confidence intervals at some extreme sample size conditions (i.e., 50 level-2 units with large proportions of singletons; Bell et al., 2008, 2009; Maas & Hox, 2004).”
Examining Relations between Mathematics Teachers’ Instructional Vision and Knowledge and Change in Practice (2017, result): “Indeed, the consistency of our estimates confirms what prior research has indicated about the robustness of parameter estimates to sparse clustered data within hierarchical linear models (e.g., Bell et al. 2008; Clarke 2008; Raudenbush and Bryk 2002).”