Best practices in multilevel modeling for within-cluster group comparisons: An evaluation of coding strategies...

In multilevel analysis, Level-1 dichotomous predictors (e.g., treatment vs. control, minority vs. majority; D) are commonly used to examine the existence of average within-cluster mean differences. To address this research question, we examine the best practices for coding D, considering within-cluster group compositions and between-cluster heterogeneity in them, as well as possible between-group heterogeneity in residual variances. We compare traditional dummy coding and unweighted effect coding with two proposed methods: overall and within-cluster weighted effect coding. Each is combined with cluster-mean centering to clearly define the within-cluster mean difference. Analytical results show that the intraclass correlation of D (ICC-D) substantially influences differences across coding methods regarding test results for the average within-cluster effect (group mean difference). When ICC-D is zero, all strategies yield identical test results (i.e., the significance tests based on the point estimates and standard error estimates) for the average within-cluster effect. However, as the ICC-D increases, test statistics (e.g., the t statistic) decrease for all coding strategies. An empirical study and simulations further confirm that ICC-D strongly influences results. Based on the simulations, we recommend dummy coding, unweighted effect coding, and overall weighted effect coding, which generally provide comparable or higher power than within-cluster weighted effect coding. The power contrast is most pronounced when both ICC-D and Level-1 residual variance heterogeneity increase, with the difference in power reaching up to 40%. Furthermore, cluster-mean centering not only disaggregates within- and between-cluster effects but also achieves generally reasonable Type I error rates even when homogeneity assumptions are not met. (PsycInfo Database Record (c) 2026 APA, all rights reserved).