Comparing cross-classified growth models with and without the cumulative effect of teachers to a hierarchical growth model on cross-classified data

Multilevel value-added models (VAMs) have the capability to capture the cumulative effect of students' prior teachers while simultaneously modeling the dependency of various levels. However, some researchers question the applicability of these models because of the absence of random assignment in many applied settings. For example, students are not randomly assigned to teachers and teachers are not randomly assigned to schools. Moreover, there are several obstacles in the implementation of these models, such as cross-classified data structures and limitations in the capacities of statistical software packages. Therefore, the merits of these VAMs have come into question and so the purpose of this simulation study was to compare the performance of a cross-classified VAM with a cumulative effect of teachers to two other teacher evaluation models: a non-cumulative cross-classified model; and a hierarchical model. The most notable finding was that the teacher effect in the value-added cumulative cross-classified model was generally estimated with the least amount of bias. This cross-classified model that utilized the cumulative teacher effect also had the least amounts of error, for the random within-student effect and the random student slope. These results provide supporting evidence for the value-added cumulative cross-classified model.