Multilevel data can have observations nested within two dimensions of clustering which do not follow a pure nested structure. Failure to consider both dimensions simultaneously may lead to biased results. To address this, cross-classified random effects models (CCREMs) have been developed (Goldstein, 1987) to capture the random effects from multiple dimensions. Although effective, CCREMs may encounter nonconvergence issues. Alternatively, a linear regression model with cluster robust standard errors (OLS-CRSEs) (Liang & Zeger, 1986) can provide asymptotically consistent standard errors. Cameron et al. (2011) introduced the two-way clustering case which is equivalent to the cross-classified data. However, there is a lack of a comprehensive comparison for multilevel data with two dimensions of clustering with a small number of clusters.
Zhang, B., & Huang, F. (2023). Using cluster robust standard errors to analyze cross-classified data with a small number of clusters. Poster presented at the Society for Research on Educational Effectiveness conference, Arlington, VA.