How many clusters do I need to fit a multilevel model?

In this edition of CBA Office Hours, Dan discusses a question that frequently comes up in our multilevel modeling workshop, namely, “How many clusters do I need to be able to fit a multilevel model?”  Here, clusters refers to upper-level units, so in the case of individuals nested within groups, the groups, and in the case of repeated measures, the individuals studied over time.  The discussion centers on how to appropriately estimate and obtain inferences from a multilevel model with as few as 10 clusters.

For additional information on this issue, see the excellent review paper recently published by Dan McNeish and Laura Stapleton in Educational Psychology Review.

Note: This video is an expanded remake of an earlier version on the same topic.

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A reviewer recently asked me to comment on the issue of equivalent models in my structural equation model. What is the difference between alternative models and equivalent models within an SEM?

An equivalent model can be thought of as a re-parameterization of the original model. In other words, it is just a different way of “packaging” the same information in the data and no equivalent model can be distinguished from another based on fit alone. If you were to fit a series of equivalent models to the same sample data you obtain exactly the same chi-square test statistic, RMSEA, CFI, TLI, and any other omnibus measure of fit. It is often best to treat this as a limitation of any given study and to potentially present one or a small number of equivalent model options to the reader so that these too might be considered as plausible representations of the data.