Investigating the use of robust standard errors to account for two-way clustering in cross-classified data structures

Traditional multilevel models are commonly used to analyze multilevel data with a pure nested structure. However, cross-classified data structures are present when observations are nested within two higher-level structures which in turn are not nested within each other. To capture the variations from both clustering dimensions, cross-classified random effects models (CCREMs) were developed as an extension to standard multilevel modeling. Alternatively, simpler linear regression models with cluster-robust standard errors (CRSEs) can also be effective when analyzing cross-classified data structures. However, CRSEs can be underestimated when the number of clusters is small. The present chapter extends the use of a small sample adjustment approach (i.e., CR2) of CRSEs when used with cross-classified data structures (i.e., two-way OLS-CR2) and investigates its performance under various conditions. Simulation results showed that two-way OLS-CR2 can be used for both complete and partial cross-classified data with at least 30 clusters in one of two clustering dimensions. An applied data example showed similar results using the two-way OLS-CR2 and CCREMs.