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 (Journal Indexed in SCI) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 76 Issue: 5
  • Publication Date: 2016
  • Doi Number: 10.1177/0013164415618705
  • Page Numbers: pp.803-823


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.