Comparison of model- and design-based approaches to detect the treatment effect and covariate by treatment interactions in three-level models for multisite cluster-randomized trials

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

BEHAVIOR RESEARCH METHODS, vol.51, no.1, pp.243-257, 2019 (SSCI) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.3758/s13428-018-1080-1
  • Journal Indexes: Social Sciences Citation Index (SSCI), Scopus
  • Page Numbers: pp.243-257
  • Recep Tayyip Erdoğan University Affiliated: Yes


In this study, we evaluated the estimation of three important parameters for data collected in a multisite cluster-randomized trial (MS-CRT): the treatment effect, and the treatment by covariate interactions at Levels 1 and 2. The Level 1 and Level 2 interaction parameters are the coefficients for the products of the treatment indicator, with the covariate centered on its Level 2 expected value and with the Level 2 expected value centered on its Level 3 expected value, respectively. A comparison of a model-based approach to design-based approaches was performed using simulation studies. The results showed that both approaches produced similar treatment effect estimates and interaction estimates at Level 1, as well as similar Type I error rates and statistical power. However, the estimate of the Level 2 interaction coefficient for the product of the treatment indicator and an arithmetic mean of the Level 1 covariate was severely biased in most conditions. Therefore, applied researchers should be cautious when using arithmetic means to form a treatment by covariate interaction at Level 2 in MS-CRT data.