Detecting Intervention Effects in a Cluster-Randomized Design Using Multilevel Structural Equation Modeling for Binary Responses

Multilevel modeling (MLM) is frequently used to detect group differences, such as an intervention effect in a pre-test–post-test cluster-randomized design. Group differences on the post-test scores are detected by controlling for pre-test scores as a proxy variable for unobserved factors that predict future attributes. The pre-test and post-test scores that are most often used in MLM are summed item responses (or total scores). In prior research, there have been concerns regarding measurement error in the use of total scores in using MLM. To correct for measurement error in the covariate and outcome, a theoretical justification for the use of multilevel structural equation modeling (MSEM) has been established. However, MSEM for binary responses has not been widely applied to detect intervention effects (group differences) in intervention studies. In this article, the use of MSEM for intervention studies is demonstrated and the performance of MSEM is evaluated via a simulation study. Furthermore, the consequences of using MLM instead of MSEM are shown in detecting group differences. Results of the simulation study showed that MSEM performed adequately as the number of clusters, cluster size, and intraclass correlation increased and outperformed MLM for the detection of group differences.