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Global cross-ratio models for bivariate, discrete, ordered responses.

J R Dale

    Biometrics
    |December 1, 1986
    PubMed
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    This study introduces new statistical models for analyzing ordered categorical data with two components. These models use global cross-ratios to quantify associations, extending previous work for discrete response analysis.

    Area of Science:

    • Statistics
    • Biostatistics
    • Statistical Modeling

    Background:

    • Analyzing bivariate discrete responses with ordered categories presents statistical challenges.
    • Existing models may not fully capture the complex associations between response components.

    Purpose of the Study:

    • To present a family of statistical models for bivariate, ordered categorical response data.
    • To extend and generalize previous statistical modeling approaches.

    Main Methods:

    • Utilizing global cross-ratios to express association between response components.
    • Defining models based on cross-product ratios of quadrant probabilities.
    • Extending work by Plackett and Mantel and Brown.
    • Incorporating linear logistic or generalized linear models for marginal probabilities.

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    Main Results:

    • The proposed models effectively analyze bivariate, ordered categorical data.
    • Association is quantified using global cross-ratios.
    • Marginal probabilities can be modeled using generalized linear models.

    Conclusions:

    • The presented statistical models offer a flexible framework for analyzing bivariate ordered categorical data.
    • These models provide a robust method for understanding associations in complex discrete response scenarios.
    • The approach is illustrated with a practical example of patient pain and medication data.