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Random effects in paired-comparison experiments using the Bradley-Terry model.

J F Lancaster, D Quade

    Biometrics
    |March 1, 1983
    PubMed
    Summary
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    This study introduces a generalized Bradley-Terry model for paired comparisons. It accounts for judge-specific preferences, improving analysis of treatment variations and non-independent judgments in experiments.

    Area of Science:

    • Statistics
    • Experimental Design

    Background:

    • The standard Bradley-Terry model assumes consistent treatment ratings across all comparisons.
    • This assumption may not hold when multiple judges with varying preferences participate.

    Purpose of the Study:

    • To generalize the Bradley-Terry model by incorporating random effects for judges.
    • To enable the separation of judge-specific variation from true treatment variation.
    • To address the non-independence of judgments arising from repeated use of judges.

    Main Methods:

    • Developed a hierarchical extension of the Bradley-Terry model.
    • Treated judge preference parameters as random variables.
    • Incorporated judge-specific random effects into the model framework.

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    Main Results:

    • The generalized model successfully models correlations between judgments from the same judge.
    • It allows for the estimation of both treatment effects and judge variability.
    • Demonstrated the utility in distinguishing true treatment differences from judge bias.

    Conclusions:

    • The proposed model offers a more nuanced approach to paired-comparison data analysis.
    • It enhances the ability to isolate treatment effects by accounting for judge heterogeneity.
    • This method is valuable for experiments involving multiple judges and potential non-independent observations.