Joint Maximum Likelihood Estimation for Cognitive Diagnostic Models

• Activity Number: 165
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Committee on Applied Statisticians
• Author(s): Chia-Yi Chiu*+ and Yi Zheng and Robert Henson
• Companies: Rutgers University and University of Illinois at Urbana-Champaign and University of North Carolina at Greensboro
• Keywords: cognitive diagnosis ; joint maximum likelihood estimation ; nonparametric classification ; consistency

Abstract

Current methods for fitting cognitive diagnosis models to item responses include the Expectation Maximization (EM) algorithm and the Markov chain Monte Carlo (MCMC) technique. The joint maximum likelihood estimation (JMLE) is another alternative to estimate the item parameters and examinees' attribute patterns. Unfortunately, JMLE has not been successfully implemented due to the potential inconsistency of the parameter estimators, despite its attractive advantage of simple likelihood functions. In this study, we propose a JMLE method that overcomes the theoretical deficiency from which the traditional JMLE suffers by taking the classification result obtained by applying the nonparametric classification method (Chiu & Douglas, 2013) as initial input. Two asymptotic consistency theorems for the item parameter estimators are proven. The algorithm is empirically evaluated with simulation studies and an application to real data. The results show that the propose JMLE method can effectively remedy the issues the existing estimation methods have and estimate the item parameters and examinees' attribute patterns with high efficiency and accuracy.