Modelling multilevel nonlinear treatment-by-covariate interactions in cluster randomized controlled trials using a...

Area of Science:

• Statistics
• Educational Research
• Psychometrics

Background:

• Cluster randomized controlled trials (C-RCTs) are prevalent in educational research.
• Multilevel modeling (MLM) is standard for C-RCT analysis but often conflates interaction effects.
• Existing MLM methods assume linear interactions, failing to capture complex treatment-covariate relationships.

Purpose of the Study:

• To present a generalized additive mixed model (GAMM) for estimating unconflated multilevel interaction effects in C-RCTs.
• To allow for the estimation of nonlinear treatment-by-covariate interactions without a prespecified functional form.
• To provide R code for model estimation and visualization of nonlinear interactions.

Main Methods:

• Development and application of a generalized additive mixed model (GAMM).
• Utilizing maximum likelihood estimation for parameter estimation.
• Employing simulation studies to compare GAMM with alternative approaches.
• Illustrating the model with instructional intervention data from a C-RCT.

Main Results:

• The GAMM successfully estimated unconflated multilevel interactions, outperforming alternative methods in logistic scenarios.
• Parameter recovery was satisfactory in typical educational C-RCT designs, though sensitive to small cluster numbers, sizes, and intraclass correlations.
• Modeling linear interactions with nonlinear effects using traditional MLM led to biased estimates and incorrect predictions.

Conclusions:

• The GAMM offers a flexible and accurate approach for analyzing complex interactions in C-RCTs, particularly in educational research.
• Researchers should consider GAMM for its ability to model nonlinear treatment-by-covariate effects, avoiding biases associated with linear assumptions.
• The provided R code facilitates the practical application of GAMM for advanced statistical analysis in intervention studies.