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A Lognormal Ipsative Model for Multidimensional Compositional Items.

Chia-Wen Chen1, Wen-Chung Wang2, Magdalena Mo Ching Mok2,3

  • 1Centre for Educational Measurement, University of Oslo, Oslo, Norway.

Frontiers in Psychology
|October 29, 2021
PubMed
Summary
This summary is machine-generated.

A new lognormal ipsative model (LIM) effectively analyzes compositional items, overcoming limitations of the Thurstonian item response theory (IRT) model. This improved method ensures accurate latent trait estimation for forced-choice questionnaires.

Keywords:
Rasch modelscompositional itemsforced-choice itemsipsative dataitem response model

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Area of Science:

  • Psychometrics
  • Item Response Theory
  • Measurement Theory

Background:

  • Compositional items require fixed point allocation, posing analytical challenges.
  • The Thurstonian item response theory (IRT) model, while prominent, has identification and estimation issues with compositional items, particularly regarding factor loading matrices.
  • Existing models struggle with biased latent trait estimates and convergence problems when analyzing forced-choice data.

Purpose of the Study:

  • To develop a new Thurstonian item response theory (IRT) model, the lognormal ipsative model (LIM), to address the limitations of existing models for compositional items.
  • To evaluate the performance of the LIM using real-world data from an online value test and through simulation studies.
  • To provide a robust analytical tool for forced-choice questionnaires with positively phrased statements and equal factor loadings.

Main Methods:

  • Development of the lognormal ipsative model (LIM) as a novel approach to Thurstonian item response theory (IRT).
  • Application of the LIM to an online value test based on Schwartz's values theory, collecting data from 512 participants (ages 13-51).
  • Conducting a simulation study to assess parameter recovery, convergence rates, and estimation precision under various conditions.

Main Results:

  • The lognormal ipsative model (LIM) demonstrated an acceptable fit to the collected data, with reliabilities exceeding 0.85.
  • Simulation studies indicated good parameter recovery, high convergence rates, and precise estimation.
  • The LIM effectively overcame the identification and convergence issues associated with the Thurstonian IRT model for specific item types.

Conclusions:

  • The proposed lognormal ipsative model (LIM) offers a viable and effective solution for analyzing compositional items within the Thurstonian item response theory (IRT) framework.
  • The LIM provides reliable and precise latent trait estimates, particularly for tests with positively phrased statements and similar factor loadings.
  • This advancement enhances the analysis of forced-choice data, improving the accuracy and stability of psychometric measurements.