Cluster-robust standard errors with three-level data

Using cluster robust standard errors (CRSEs) is a common approach used when analyzing clustered datasets. When using three-level models (e.g., students within classrooms within schools), the highest level generally has fewer clusters than the intermediate level and, with clustered data using CRSEs, the general advice is to cluster at the highest level. However, traditional CRSEs are still known to be underestimated when used with a low number of clusters resulting in higher type I error rates. We investigated the use of two different CRSE formulations together with degrees of freedom (<i>df</i>) adjustments using a Monte Carlo simulation. We found that even though CRSEs may be downwardly biased with a low number of clusters, when the CR2 estimator of Bell and McCaffrey (2002) was used with the Satterthwaite <i>df</i> adjustment, coverage rates were acceptable even with a few clusters using three-level data. Traditional CRSEs should not be relied on with three-level data if there are only a few clusters at the highest level. An applied example is provided as well.