Cognitive Diagnosis Models with Longitudinal Growth Curves for Skill Knowledge

• Activity Number: 399
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Elizabeth Ayers*+ and Sophia Rabe-Hesketh
• Companies: University of California at Berkeley and University of California at Berkeley
• Keywords: Cognitive Diagnosis ; Growth Curve Modeling ; Longitudinal

Abstract

In recent years, a number of cognitive diagnosis models have become a popular means of estimating student skill knowledge. However these models treat responses as though they are from a single time point. When data is collected throughout a school year, we expect student skill knowledge at different times to be dependent within students and the probability of skill mastery to increase over time as students learn. We have developed longitudinal cognitive growth curve models to account for the within-student dependence, as well as understand the variability in learning and how this depends on explanatory variables. The relationship between the latent binary skill knowledge indicators and the item responses is modeled as a DINA model. A logistic regression model is specified for the latent skill knowledge indicators with student characteristics and time as covariates and with a student-level random intercept and random slope of time. The model is estimated using Markov chain Monte Carlo in WinBUGS. Simulation studies show good parameter recovery. The model will be applied to data from the ASSISTment tutor, an online mathematics tutor used by eighth graders in Massachusetts.