A comparison of methods for centering covariates in cross-classified random effects models

The cross-classified random-effects model (CCREM) is used to handle cross-classified data in which units are nested within multiple higher-level dimensions that are not clustered within each other. The focus of interest in this study is the exogeneity assumption in CCREM, which refers to the assumed independence between covariates and random effects at level-2. If the exogeneity assumption is violated, it affects the robustness of the statistical inferences made when estimating the CCREM. Certain methods for centering a covariate can reduce the impact of violating exogeneity. For unbalanced cross-classified data, Raudenbush (2009) proposed the general model of the adaptive centering approach using cluster-mean centering. However, there are several alternatives in addition to this model, including the correlated random effects (RE) model, cell-mean centering, fixed effects (FE) using cluster robust variance estimation (CRVE), and the FE-RE hybrid model. The correlated RE model explicitly models between-cluster variability of the level-1 covariate as level-2 predictors, simultaneously estimating both within- and between-cluster effects. Another approach called cell-mean centering centers covariates around the cell mean instead of the cluster mean and considers the interaction between the two dimensions of the data. If a researcher is interested primarily in level-1 covariates, the FE approach has often been used for handling violations of exogeneity (Wooldridge, 2010). The FE model can be used along with two-way CRVE, an extension of one-way CRVE that accounts for the dependence of errors within clusters (Cameron et al., 2011). The final alternative is an FE-RE hybrid model, which incorporates the FE and RE approaches by modeling one dimension as fixed effects and the other dimension as random effects. This approach requires fewer assumptions while benefiting from the use of the RE model for the selected dimension. However, covariate-centering strategies have only been examined for the hierarchical linear model, not for the CCREM. Thus, extended research on CCREM is needed to demonstrate and evaluate the impact of centering options on the model’s performance and statistical inferences. In this dissertation, I first reviewed the current practice of centering with the CCREM and described the benefits and limitations of covariate centering methods with the CCREM. Next, I presented the results of two empirical applications comparing the use of different centering alternatives. Then, I conducted a systematic review examining how assumptions were tested and how centering was used when estimating the CCREM in applied education and social science research. Finally, I performed a simulation study to compare the performance of alternative centering approaches in scenarios in which the exogeneity assumption is violated.