Three-level clustered data commonly occur in social and behavioral research and are prominently analyzed using multilevel modeling. The influence of the clustering on estimation results is assessed with the intraclass correlation coefficients (ICCs), which indicate the fraction of variance in the outcome located at each higher level. However, ICCs are prone to bias due to high requirements regarding the overall sample size and the sample size at each data level. In Monte Carlo simulations, we investigate how these sample characteristics influence the bias of the ICCs and statistical power of the variance components using robust ML-estimation. Results reveal considerable underestimation on Level-3 and the importance of the Level-3 sample size in combination with the ICC sizes. Based on our results, we derive concise sampling recommendations and discuss limits to our inferences.
Keywords: hierarchical linear modeling; Monte Carlo simulation; statistical power; sample size; bias