Mixed Membership Modeling of Student Strategies from Sequences of Actions

• Activity Number: 302
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Social Statistics Section
• Author(s): April Galyardt*+
• Companies: University of Georgia
• Keywords: Mixed Membership ; Latent Dirichlet Allocation ; Markov Chain ; Simplicial Mixture ; Cognitive Strategies ; Hidden Markov Model

Abstract

Strategy choice strongly distinguishes novice and expert performance; however identifying strategies from data is an open problem. We propose a mixed membership-Markov chain (MM-MC) model to model how students use strategies. Markov processes can model the probabilistic sequence of actions that a student using a particular strategy will take, and a mixed membership framework will allow us to model students switching strategy from task to task. An earlier model, the simplicial mixture of Markov chains (SM-MC), was unsuccessful for data sets with N=1500, a fairly large sample size for educational data. SM-MC includes an exchangeability assumption equivalent to allowing students to switch strategy between every action. MM-MC simplifies the model by only allowing students to switch strategies between tasks. Since this assumes that short sequences of actions must have all come from the same Markov process, this makes it easier to estimate the transition matrices, and makes the model more tractable. We will present results from preliminary simulation studies, and compare the structure of MM-MC to hidden Markov models.