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Score-based tests for parameter instability in ordinal factor models.

Franz Classe1, Rudolf Debelak2, Christoph Kern3

  • 1Deutsches Jugendinstitut e.V., Munich, Germany.

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|April 23, 2025
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Summary
This summary is machine-generated.

A new method efficiently computes parameter instability tests for ordinal factor models using limited information estimation. This approach offers a faster, powerful alternative to full information estimation for complex models.

Keywords:
multidimensional item response theoryordinal factor analysisparameter instabilityscore test

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Computational Statistics

Background:

  • Ordinal factor models, specifically graded response models (GRMs), are crucial for analyzing categorical data in various fields.
  • Assessing parameter stability is vital for the reliability and validity of these models.
  • Existing methods for parameter instability tests in GRMs, particularly those using full information (FI) estimation, can be computationally intensive.

Purpose of the Study:

  • To introduce a novel, computationally efficient approach for calculating model scores in ordinal factor models.
  • To enable the development of score-based tests for parameter instability in these models.
  • To facilitate rapid execution of parameter instability tests for multidimensional item response theory (MIRT) models.

Main Methods:

  • Development of a novel method for computing model scores tailored for limited information (LI) estimators in GRMs.
  • Implementation of score-based tests for parameter instability using the proposed LI estimation approach.
  • Comparative performance analysis against established methods using full information (FI) estimation.

Main Results:

  • The proposed score-based tests demonstrate good Type I error rates and high statistical power.
  • The limited information (LI) estimation method is computationally faster than traditional full information (FI) estimation.
  • The method's efficacy is validated through applications with complex models and real-world data.

Conclusions:

  • The novel LI-based score computation method provides an efficient and effective tool for parameter instability testing in ordinal factor models.
  • This approach significantly speeds up the assessment of model stability, especially for complex multidimensional item response theory (MIRT) models.
  • The implementation in the R package 'lavaan' makes this advanced statistical technique accessible for broader research applications.