Structural equation modeling of paired-comparison and ranking data

Area of Science:

• Psychology
• Statistics
• Decision Science

Background:

• L. L. Thurstone's (1927) model offers a robust framework for analyzing individual differences in choice behavior.
• Thurstonian models are essential for understanding comparative judgment data.

Purpose of the Study:

• To provide an overview of Thurstonian models for comparative data.
• To demonstrate embedding these models within a structural equation modeling (SEM) framework.
• To facilitate efficient estimation and testing of complex models for comparative judgments.

Main Methods:

• Overview of classical Thurstonian models (Case V, Case III) and general choice models.
• Integration of Thurstonian models into the structural equation modeling (SEM) framework.
• Utilizing popular SEM statistical packages for estimation.

Main Results:

• Demonstration of embedding Thurstonian models within SEM.
• Successful estimation of various Thurstonian model special cases, including factor analysis for paired comparisons and rankings.
• Minor modifications enable accommodation of diverse data types within the SEM framework.

Conclusions:

• Thurstonian models can be effectively estimated and tested using SEM.
• SEM provides a unified and efficient approach for complex comparative judgment analysis.
• This integration enhances the accessibility and application of Thurstonian models in research.