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Using Bayesian Hierarchical Modeling and DataShop to Inform Parameter Estimation with the Predictive Performance Equation

Abstract

The Predictive Performance Equation (PPE) is a mathematical model of learning and retention that uses regularities seenin human learning to predict future performance (Walsh, Gluck, Gunzelmann, Jastrzembski, & Krusmark, in press). Togenerate predictions, PPEs free parameters must be calibrated to historical performance data, with generally inaccuratepredictions for initial performance events. Prior research (Collins, Gluck, Walsh, Krusmark & Gunzelmann, 2016; Collins,Gluck, & Walsh, 2017) explored the use of aggregate prior data to inform PPEs free parameters for initial performance pre-dictions. Here we report an extension of our prior research, using Bayesian hierarchical modeling to integrate informationfrom the historical performance of both prior data and an individual student to generate future performance predictionsover an entire instructional period. Data are sourced from DataShop an online educational data repository (Koedinger et al.2010). Adding Bayesian hierarchical modeling to the PPE will improve PPEs application in both education and trainingscenarios.

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