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A diagnostic tree model for polytomous responses with multiple strategies.

Wenchao Ma1

  • 1The University of Alabama, Tuscaloosa, AL, USA.

The British Journal of Mathematical and Statistical Psychology
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This study introduces a two-digit scoring scheme and a diagnostic tree model (DTM) for cognitive diagnostic assessments. This approach enhances the analysis of student strategies and partial credits, improving psychometric analysis for constructed-response items.

Keywords:
TIMSScognitive diagnosisconstructed-responsediagnostic treeitem responsemultiple strategiessequential G-DINAtree structuretwo-digit scoring

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Area of Science:

  • Educational Measurement
  • Psychometrics
  • Cognitive Psychology

Background:

  • Constructed-response items offer insights into student problem-solving for diagnostic assessments.
  • Analyzing diverse student strategies in these items presents scoring and psychometric challenges.

Purpose of the Study:

  • To introduce a novel two-digit scoring scheme for capturing partial credits and strategies in diagnostic assessments.
  • To propose a diagnostic tree model (DTM) for analyzing items scored with the two-digit rubric.
  • To evaluate the effectiveness of the DTM and scoring scheme through simulation and real-world data.

Main Methods:

  • Developed a two-digit scoring scheme to record partial credits and student strategies.
  • Integrated cognitive diagnosis models with tree structures to create the diagnostic tree model (DTM).
  • Employed the Maximum Marginal Likelihood Estimation/Expectation-Maximization (MMLE/EM) algorithm for DTM parameter estimation.

Main Results:

  • The two-digit scoring scheme effectively records both partial credits and student strategies.
  • The diagnostic tree model (DTM) provides a robust framework for analyzing scored items.
  • Simulation studies demonstrated good parameter recovery for the DTM under various conditions.
  • Analysis of TIMSS 2007 mathematics data illustrated the practical application of the proposed methods.

Conclusions:

  • The two-digit scoring scheme and DTM offer a viable solution for the psychometric challenges in cognitively diagnostic assessments.
  • These methods enhance the analysis of constructed-response items, providing richer diagnostic information.
  • The approach is effective and applicable to large-scale assessments like TIMSS.