Using Penalized EM Algorithm to Infer Learning Trajectories in Latent Transition CDM

• Activity Number: 307 - Challenges and Advances in Psychological and Behavioral Data Analysis
• Type: Topic-Contributed
• Date/Time: Wednesday, August 11, 2021 : 3:30 PM to 5:20 PM
• Sponsor: Mental Health Statistics Section
• Author(s): Chun Wang*
• Companies: University of Washington
• Keywords: cognitive diagnostic modeling; penalized EM; learning trajectories; latent class models; latent transition analysis

Abstract

Cognitive diagnostic models (CDMs) have arisen as advanced psychometric models in the past few decades for assessments that intend to measure students’ mastery of a set of attributes. Recently quite a few studies attempted to extend CDMs to longitudinal versions, and they all tended to model transition probabilities from non-mastery to mastery or vice versa for each attribute separately, with an exception of a few studies. However, these pioneering works have not taken into consideration the attribute relationships and the ever-changing attributes in a learning period. In this paper, we consider a profile-level latent transition CDM (TCDM hereafter), which can not only identify transition probabilities across the same attributes over time, but also the transition pathways across different attributes. Two versions of the penalized expectation-maximization (PEM) algorithms are proposed to shrink the probabilities associated with impermissible transition pathways to 0, thereby, help explore attribute relationships in a longitudinal setting. Simulation results reveal that PEM with group penalty holds great promise for identifying learning trajectories.