A Lognormal Ipsative Model for Multidimensional Compositional Items

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.