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Limited-information goodness-of-fit testing of diagnostic classification item response models.

Mark Hansen1, Li Cai2, Scott Monroe1

  • 1University of California, Los Angeles, California, USA.

The British Journal of Mathematical and Statistical Psychology
|July 13, 2016
PubMed
Summary

This study evaluates the M2 statistic for diagnostic classification models, finding it effective for detecting model misspecifications. The XLD2 statistic aids in pinpointing sources of misfit, enhancing model evaluation in educational measurement.

Keywords:
diagnostic classification modelsitem response modelslimited-information goodness of fitlocal item independence

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Area of Science:

  • Educational Measurement
  • Psychometrics
  • Statistical Modeling

Background:

  • Diagnostic classification models (DCMs) are increasingly popular in educational and psychological measurement.
  • Existing methods for testing the absolute goodness of fit for DCMs are underdeveloped.
  • Full-information fit statistics face challenges with data sparseness in realistic scenarios.

Purpose of the Study:

  • To evaluate the performance of the Maydeu-Olivares and Joe's (2006) M2 statistic for diagnostic classification models.
  • To assess the M2 statistic's sensitivity to various model misspecifications.
  • To investigate the utility of the Chen and Thissen (1997) XLD2 statistic for identifying sources of misfit.

Main Methods:

  • Simulation studies were conducted to assess the M2 statistic's calibration and sensitivity.
  • The M2 statistic was applied to diagnostic classification models with varying structures.
  • The XLD2 statistic was used to analyze local dependence and pinpoint sources of model misfit.

Main Results:

  • The M2 statistic demonstrated good calibration across diverse diagnostic model structures.
  • M2 was sensitive to specific item model misspecifications, Q-matrix errors, and local item dependence violations.
  • M2 showed limited sensitivity to higher-order latent dimension misspecifications and extraneous attributes.
  • The XLD2 statistic was found to be conservative but useful for identifying misfit sources.

Conclusions:

  • The M2 statistic is a valuable tool for assessing the overall goodness of fit for diagnostic classification models.
  • The XLD2 statistic effectively complements M2 by localizing sources of model misspecification.
  • These statistics provide a robust framework for evaluating diagnostic classification models in practice.