Thurstonian Scaling of Compositional Questionnaire Data.

Area of Science:

• Psychological Measurement
• Quantitative Psychology
• Statistical Modeling

Background:

• Personality questionnaires often use comparative response formats to mitigate response bias.
• Existing Thurstonian models primarily address binary choice data.
• There is a need to extend these models to compositional data formats.

Purpose of the Study:

• To extend Thurstonian modeling to compositional response formats in personality assessment.
• To develop a statistical framework for analyzing "proportion-of-total" data.
• To evaluate the performance of the proposed model in capturing latent structures and person scores.

Main Methods:

• Compositional item data were transformed into log ratios, representing differences in latent item utilities.
• Confirmatory Factor Analysis (CFA) was used to model the mean and covariance structure of these log ratios.
• A simulation study with N = 300 and N = 1,000, alongside empirical data from N = 317 students, was employed for validation.

Main Results:

• The proposed Thurstonian modeling approach demonstrated excellent recovery of true parameters in simulations.
• Near-nominal rejection rates were observed, indicating good model fit and statistical power.
• Empirical data analysis confirmed the model's ability to capture latent structures and person scores effectively.

Conclusions:

• The extended Thurstonian model provides a robust method for analyzing personality data from compositional response formats.
• This approach offers a valuable tool for more accurate personality assessment by addressing response bias.
• The model successfully integrates item utilities and personal attributes within a unified statistical framework.