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

¹Measurement and Statistics, College of Education, University of Washington, 312E Miller Hall, 2012 Skagit Ln, Seattle, WA 98105, USA. wang4066@uw.edu.

|January 15, 2021

Summary

This summary is machine-generated.

This study introduces a new cognitive diagnostic model (CDM) to track how students master attributes over time, considering attribute relationships. The penalized expectation-maximization (PEM) algorithm effectively identifies learning trajectories.

Keywords:

cognitive diagnostic models latent transition analysis learning trajectory penalized expectation-maximization

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Area of Science:

Psychometrics
Educational Measurement
Learning Analytics

Background:

Cognitive Diagnostic Models (CDMs) are advanced psychometric tools for measuring attribute mastery.
Existing longitudinal CDMs often model attributes independently, neglecting inter-attribute relationships and attribute changes.
There's a need for models that capture dynamic attribute mastery and transitions over time.

Purpose of the Study:

To propose a profile-level latent transition cognitive diagnostic model (TCDM) that accounts for attribute relationships.
To develop penalized expectation-maximization (PEM) algorithms for estimating transition probabilities in longitudinal CDMs.
To explore attribute relationships and learning trajectories in a longitudinal setting.

Main Methods:

Developed a profile-level latent transition cognitive diagnostic model (TCDM).
Proposed two versions of penalized expectation-maximization (PEM) algorithms to identify attribute transition pathways.
Utilized simulation studies to evaluate the performance of the PEM algorithms.

Main Results:

The proposed TCDM can model transitions across the same attributes and pathways between different attributes over time.
The PEM algorithms successfully shrink probabilities of impermissible transition pathways to zero.
Simulation results indicate that PEM with a group penalty is effective in identifying learning trajectories.

Conclusions:

The TCDM offers a more comprehensive approach to understanding student learning over time by incorporating attribute relationships.
The developed PEM algorithms provide a robust method for analyzing longitudinal attribute mastery and transitions.
This research advances the application of CDMs in educational assessment and learning analytics.