Detecting intervention effects using a multilevel latent transition analysis with a mixture IRT model.

A multilevel latent transition analysis (LTA) with a mixture IRT measurement model (MixIRTM) is described for investigating the effectiveness of an intervention. The addition of a MixIRTM to the multilevel LTA permits consideration of both potential heterogeneity in students' response to instructional intervention as well as a methodology for assessing stage sequential change over time at both student and teacher levels. Results from an LTA-MixIRTM and multilevel LTA-MixIRTM were compared in the context of an educational intervention study. Both models were able to describe homogeneities in problem solving and transition patterns. However, ignoring a multilevel structure in LTA-MixIRTM led to different results in group membership assignment in empirical results. Results for the multilevel LTA-MixIRTM indicated that there were distinct individual differences in the different transition patterns. The students receiving the intervention treatment outscored their business as usual (i.e., control group) counterparts on the curriculum-based Fractions Computation test. In addition, 27.4 % of the students in the sample moved from the low ability student-level latent class to the high ability student-level latent class. Students were characterized differently depending on the teacher-level latent class.