Accounting for Random Slopes Using Cluster-Robust Standard Errors in Multilevel Models

Although random intercept (RI) multilevel models (MLMs) are commonly used, the inclusion of random slopes, when warranted, is necessary to avoid Type I errors for variables that randomly vary by group. However, instead of explicitly modeling the random slope, an alternative approach could be to use a more parsimonious RI model together with cluster-robust standard errors (CRSEs). Although the traditionally used CRSEs (CR0) can still underestimate standard errors when only a few clusters are present, we investigate a variant (i.e., the CR2) that has been shown to be effective with a limited number of clusters. Results of a Monte Carlo simulation show that using a RI model together with the CR2 can effectively account for violations of homoscedasticity, resulting in acceptable coverage probability rates for all conditions tested. However, when used with a limited number of clusters, a properly specified random slope model has more power to detect effects for level-2 predictors and cross-level interaction (CLI) terms.