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Cross-classified random effects modeling (CCREM) is a common approach for analyzing cross-classified data in education. However, when the focus of a study is on the regression coefficients at level-1 rather than on the random effects, ordinary least squares regression with cluster robust variance estimators (OLS-CRVE) or fixed effects regression with CRVE (FE-CRVE) could also be appropriate approaches. These alternatives have the advantage of working under weaker assumptions than CCREM. We conducted a Monte Carlo Simulation study to compare the performance of CCREM, OLS-CRVE, and FE-CRVE in models with crossed random effects, including conditions where assumptions held and where they were violated. In the results, CCREM performed the best when its assumptions are all met. However, when homoscedasticity assumptions are violated, OLS-CRVE and FE-CRVE provided similar or better performance than CCREM. FE-CRVE even showed the best performance when the exogeneity assumption is violated. Thus, we recommend two-way FE-CRVE as a good alternative to CCREM.
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