The Effects of Including Observed Means or Latent Means as Covariates in Multilevel Models for Cluster Randomized Trials

Aydin B., LEITE W. L., Algina J.

EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT, vol.76, no.5, pp.803-823, 2016 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 76 Issue: 5
  • Publication Date: 2016
  • Doi Number: 10.1177/0013164415618705
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus
  • Page Numbers: pp.803-823
  • Recep Tayyip Erdoğan University Affiliated: Yes


We investigated methods of including covariates in two-level models for cluster randomized trials to increase power to detect the treatment effect. We compared multilevel models that included either an observed cluster mean or a latent cluster mean as a covariate, as well as the effect of including Level 1 deviation scores in the model. A Monte Carlo simulation study was performed manipulating effect sizes, cluster sizes, number of clusters, intraclass correlation of the outcome, patterns of missing data, and the squared correlations between Level 1 and Level 2 covariates and the outcome. We found no substantial difference between models with observed means or latent means with respect to convergence, Type I error rates, coverage, and bias. However, coverage could fall outside of acceptable limits if a latent mean is included as a covariate when cluster sizes are small. In terms of statistical power, models with observed means performed similarly to models with latent means, but better when cluster sizes were small. A demonstration is provided using data from a study of the Tools for Getting Along intervention.