Cognitive Diagnosis Modeling Incorporating Item-Level Missing Data Mechanism

The aim of cognitive diagnosis is to classify respondents' mastery status of latent attributes from their responses on multiple items. Since respondents may answer some but not all items, item-level missing data often occur. Even if the primary interest is to provide diagnostic classification of respondents, misspecification of missing data mechanism may lead to biased conclusions. This paper proposes a joint cognitive diagnosis modeling of item responses and item-level missing data mechanism. A Bayesian Markov chain Monte Carlo (MCMC) method is developed for model parameter estimation. Our simulation studies examine the parameter recovery under different missing data mechanisms. The parameters could be recovered well with correct use of missing data mechanism for model fit, and missing that is not at random is less sensitive to incorrect use. The Program for International Student Assessment (PISA) 2015 computer-based mathematics data are applied to demonstrate the practical value of the proposed method.

An Application of Cognitive Diagnosis Modeling in TIMSS: A Comparison of Intuitive Definitions of Q-Matrices

Detection of students’ ability levels is one of the common aims in educational studies. Cognitive Diagnosis Modeling approach has been used recently for the purpose of ability level detection by defined Q-matrices. This paper aims to use Cognitive Diagnosis Modeling (CDM) in order to investigate the definition of a Q-matrix across the cognitive skills of different years and countries in TIMSS. There is a subjective way in defining Q-matrices; for this purpose, an application of building Q-matrices under specific CDMs, from a set of expert proposed attributes is examined. The proposed attributes are used to build Q-matrices for TIMSS mathematics questions across its cycles, and across different nations.

Assessing Change in Latent Skills Across Time With Longitudinal Cognitive Diagnosis Modeling: An Evaluation of Model Performance

Cognitive diagnosis models are diagnostic models used to classify respondents into homogenous groups based on multiple categorical latent variables representing the measured cognitive attributes. This study aims to present longitudinal models for cognitive diagnosis modeling, which can be applied to repeated measurements in order to monitor attribute stability of individuals and to account for respondent dependence. Models based on combining latent transition analysis modeling and the DINA and DINO cognitive diagnosis models were developed and then evaluated through a Monte Carlo simulation study. The study results indicate that the proposed models provide adequate convergence and correct classification rates.