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A Testlet Diagnostic Classification Model with Attribute Hierarchies.

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A new Testlet Hierarchical Diagnostic Classification Model (TH-DCM) accounts for attribute hierarchies and item bundles. Simulation results show ignoring testlet effects impacts parameter recovery, with THO-DCM being a robust alternative in some cases.

Keywords:
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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Cognitive Diagnosis

Background:

  • Cognitive Diagnostic Models (CDMs) are essential for understanding student mastery of specific skills.
  • Existing CDMs often do not fully account for complex data structures like attribute hierarchies and item bundles (testlets).
  • Accurate parameter estimation is crucial for the validity of diagnostic classifications.

Purpose of the Study:

  • To introduce a Testlet Hierarchical Diagnostic Classification Model (TH-DCM) that integrates attribute hierarchies and testlet structures.
  • To evaluate the parameter recovery of TH-DCM using a simulation study.
  • To compare TH-DCM with the Testlet Higher-Order CDM (THO-DCM).

Main Methods:

  • Development of the TH-DCM incorporating attribute hierarchies and testlet effects.
  • Parameter estimation using the expectation-maximization algorithm with analytic dimension reduction.
  • Simulation studies under various conditions to assess parameter recovery and model comparison.

Main Results:

  • Ignoring significant testlet effects negatively impacts parameter recovery.
  • CDMs with equal testlet effects performed comparably to those with unequal effects.
  • Misspecifying the joint attribute distribution differentially affected parameter recovery.
  • THO-DCM demonstrated robustness as an alternative to TH-DCM under certain hierarchical conditions.

Conclusions:

  • The proposed TH-DCM offers a way to model complex attribute and item structures in cognitive diagnosis.
  • Model misspecifications, particularly regarding testlet effects and attribute distributions, can bias parameter estimates.
  • THO-DCM presents a viable and robust alternative for cognitive diagnosis when hierarchical structures are present.