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Coarse-graining procedures make it possible to model the movement of large numbers of objects, such as particles in a fluid. Longitudinal student performance data can be modeled similarly by sorting students into score bins and following the flow of scores through time: trajectories depict the average scores over time for initial score bins and streamlines provide an approximate way to calculate the flow of student scores over many years based on only two consecutive years of data. However, due to the partially stochastic nature of observed scores, the coarse-graining procedure that sorts students into score bins amplifies a statistical phenomenon known as regression to the mean (RTM). As a result, streamlines do not provide an accurate prediction for the future performance of students. Here we discuss a new coarse-graining procedure, regression-corrected (RC) grouping, which reduces RTM in the streamlines. We apply RC streamlines to the Texas State Longitudinal Data System, which contains standardized testing data for students throughout primary and secondary school since 2003. We show that the RC streamlines accurately predict trajectories, using two or three years of data. Therefore RC streamlines can be used to identify the e↵ects of academic interventions on a time scale comparable to that of policy changes. We illustrate this assertion by examining a particular policy intervention, Texas’ Student Success Initiative.

Longitudinal predictions using regression-corrected grouping to reduce regression to the mean