Hierarchical modeling of paired comparison data

Area of Science:

• Decision Sciences
• Psychometrics
• Statistical Modeling

Background:

• Paired comparison methods offer explicit insights into choice consistency.
• Existing models often focus on individual choices, with less emphasis on group-level aggregation.
• Understanding the link between individual and group judgments is crucial for robust decision analysis.

Purpose of the Study:

• To extend R. D. Luce's (1959) model for individual choice behavior to a mixed-effects paired comparison model.
• To investigate the relationship between individual and group-level judgments in paired comparisons.
• To demonstrate the utility of hierarchical approaches in analyzing multiple pairwise judgments.

Main Methods:

• Extension of R. D. Luce's (1959) model to a mixed-effects paired comparison framework.
• Utilizing standard multilevel software designed for binary data for model estimation.
• Detailed discussion on the interpretation of paired comparison parameters and statistical model tests.

Main Results:

• The proposed mixed-effects paired comparison model effectively links individual and group-level judgments.
• Standard multilevel software is suitable for estimating this hierarchical model.
• The hierarchical approach provides a powerful tool for analyzing complex pairwise judgment data.

Conclusions:

• The developed mixed-effects paired comparison model offers a robust method for analyzing choice consistency at both individual and group levels.
• The findings highlight the applicability of multilevel modeling techniques in decision science and psychometrics.
• This hierarchical approach enhances the understanding and modeling of complex decision-making processes involving multiple pairwise comparisons.