[Working Paper] Comparing Random Effects Models, Ordinary Least Squares, or Fixed Effects with Cluster Robust Standard Errors for Cross-Classified Data
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Description: Cross-classified random effects modeling (CCREM) is a common approach for analyzing cross-classified data in psychology, education research, and other fields. However, when the focus of a study is on the regression coefficients at level one 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 be appropriate approaches. These alternative methods are potentially advantageous because they rely on weaker assumptions than those required by CCREM. We conducted a Monte Carlo Simulation study to compare the performance of CCREM, OLS-CRVE, and FE-CRVE in models, including conditions where homoscedasticity assumptions and exogeneity assumptions held and conditions where they were violated, as well as conditions with unmodeled random slopes. We found that CCREM out-performed the alternative approaches when its assumptions are all met. However, when homoscedasticity assumptions are violated, OLS-CRVE and FE-CRVE provided similar or better performance than CCREM. When the exogeneity assumption is violated, only FE-CRVE provided adequate performance. Further, OLS-CRVE and FE-CRVE provided more accurate inferences than CCREM in the presence of un-modeled random slopes. Thus, we recommend two-way FE-CRVE as a good alternative to CCREM, particularly if the homoscedasticity or exogeneity assumptions of the CCREM might be in doubt.