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This research presents a multidimensional principal stratification (MFLPS) framework for inference on latent measurement variables in randomized control trials (RCTs), extending a unidimensional framework and exploring its performance through Monte Carlo simulation. The aim is to enhance the analysis of rich, multivariate data derived from RCTs, especially in the context of computer-based educational interventions. Preliminary simulation results underscore the crucial role of factor reliability and sample size for accurate estimation of principal effects. With a sample size of at least 500, MFLPS correctly identified a medium effect size in over 80% of cases. This study's findings provide valuable guidelines for researchers interested in RCTs, offering insights into MFLPS application and determining optimal conditions for its use.