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A Machine Learning Approach to Design an Efficient Selective Screening of Mild Cognitive Impairment
12:18

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Published on: January 11, 2020

A multiple-choice SDT model for cognitive diagnosis models.

Lawrence T DeCarlo1

  • 1Department of Human Development, Teachers College, Columbia University, New York, New York, USA.

The British Journal of Mathematical and Statistical Psychology
|June 6, 2026
PubMed
Summary
This summary is machine-generated.

This study unifies multiple-choice item response theory and cognitive diagnosis models using signal detection theory. The new MC-SDT-CDM models offer parsimonious interpretations and are effective for small sample sizes.

Keywords:
CDMMC‐SDTTIMSScognitive diagnosismultiple‐choicesignal detection

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Area of Science:

  • Educational Measurement
  • Psychometrics
  • Cognitive Psychology

Background:

  • Multiple-choice (MC) item analysis often employs signal detection theory (SDT) to model examinee response processes.
  • Cognitive diagnosis models (CDMs) aim to identify specific skills or knowledge mastered by examinees.
  • Existing frameworks may lack a unified approach to understanding examinee choices within CDMs.

Purpose of the Study:

  • To integrate the multiple-choice signal detection theory (MC-SDT) model with various cognitive diagnosis models (CDMs).
  • To establish a unified theoretical framework for analyzing examinee behavior on MC items within CDMs.
  • To demonstrate the parsimony and utility of the proposed MC-SDT-CDM models.

Main Methods:

  • The study conceptualizes both MC-SDT and CDMs as hierarchical models with item-level (Level 1) and examinee-level (Level 2) components.
  • The MC-SDT model is proposed as the Level 1 model within a broader CDM framework (Level 2).
  • The methodology involves demonstrating how MC-SDT-CDM models are parsimonious sub-models of existing MC-CDMs.

Main Results:

  • The integration results in MC-SDT-CDM models that unify response processes across different CDMs.
  • These models offer straightforward interpretations at the MC-SDT (Level 1) level.
  • The proposed models avoid common estimation problems and are suitable for small sample sizes.

Conclusions:

  • The MC-SDT-CDM framework provides a unified and parsimonious approach to cognitive diagnosis for multiple-choice items.
  • The models offer clear interpretations and practical advantages, particularly for datasets with limited sample sizes.
  • The application to TIMSS 2007 data illustrates the practical utility of this integrated approach in educational measurement.