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  • 1KU Leuven, Kortrijk, Belgium.

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Summary

The General Hyperbolic Cosine Model (GHCM) offers a simpler alternative for ideal point item response theory (IRT) measurement. This study introduces a new estimation algorithm and finds a sample size of 400 adequate for reliable parameter estimation.

Keywords:
General Hyperbolic Cosine ModelIRTMML-EMideal point

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Area of Science:

  • Psychometrics
  • Item Response Theory (IRT)
  • Noncognitive Measurement

Background:

  • Ideal point item response theory (IRT) models are increasingly recognized for noncognitive measurement.
  • While the Generalized Graded Unfolding Model (GGUM) is common, Andrich's Hyperbolic Cosine Models (HCM and GHCM) offer simpler alternatives.
  • HCM and GHCM have been underutilized due to estimation and parameter metric concerns.

Purpose of the Study:

  • To develop a marginal maximum likelihood (MML) estimation algorithm for the General Hyperbolic Cosine Model (GHCM).
  • To explore parameter estimation requirements for GHCM through a Monte Carlo simulation.
  • To address the underutilization of GHCM in applied research.

Main Methods:

  • Developed a marginal maximum likelihood (MML) estimation algorithm for the GHCM.
  • Conducted a Monte Carlo simulation study.
  • Manipulated sample size, scale length, and data types (dichotomous/polytomous) to assess parameter estimation.

Main Results:

  • A sample size of 400 was found to be adequate for GHCM parameter estimation.
  • Parameter estimation was superior under polytomous conditions, consistent with GGUM findings.
  • The new MML algorithm facilitates more accessible GHCM application.

Conclusions:

  • The GHCM is a viable and mathematically simpler alternative for ideal point IRT.
  • The developed MML estimation algorithm overcomes previous technical barriers.
  • Renewed consideration of GHCM is warranted for noncognitive measurement applications.