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Semi-Parametric Item Response Theory With O'Sullivan Splines for Item Responses and Response Time.

Chen-Wei Liu1

  • 1National Taiwan Normal University, Taiwan.

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|February 5, 2025
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Summary

A new semi-parametric item response theory (IRT) model using O

Keywords:
item response theoryresponse timesmoothing splines

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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Statistics

Background:

  • Item response theory (IRT) models traditionally use parametric approaches for response time (RT).
  • Parametric models may fail to capture complex, nonlinear relationships between latent traits and RT due to behavioral changes.
  • Accurate estimation of latent traits and item parameters is crucial for educational testing.

Purpose of the Study:

  • To introduce a novel semi-parametric IRT model incorporating O'Sullivan splines.
  • To flexibly model mean RT shapes and explore nonlinear relationships between latent traits and RT.
  • To improve parameter estimation accuracy and reduce measurement errors in educational assessments.

Main Methods:

  • Development of a semi-parametric IRT model using O'Sullivan splines.
  • Simulation studies to compare the proposed model with traditional parametric models.
  • Analysis of real-world data from the Programme for International Student Assessment (PISA) mathematics test.

Main Results:

  • The proposed semi-parametric model significantly improves parameter estimation accuracy compared to parametric models.
  • Parametric models exhibit biases and increased measurement errors when nonlinear RT patterns are present.
  • The PISA dataset analysis confirmed the presence of nonlinearity and demonstrated superior model fitting of the new approach.

Conclusions:

  • The novel semi-parametric IRT model offers a more flexible and accurate approach to analyzing response time data.
  • This method enhances test reliability and reduces measurement errors by capturing nonlinear relationships.
  • The model shows potential as a valuable psychometric tool for educational measurement.