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Ordinal probability effect measures for group comparisons in multinomial cumulative link models.

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New probability effect measures compare ordinal distributions between groups, adjusted for covariates. These ordinal superiority measures quantify the likelihood of one group exceeding another, aiding statistical analysis.

Keywords:
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Area of Science:

  • Statistics
  • Biostatistics
  • Ordinal Data Analysis

Background:

  • Comparing distributions between groups is crucial in various scientific fields.
  • Existing methods often lack specific measures for ordinal data adjusted for covariates.
  • Probability effect measures offer a robust way to quantify group differences.

Purpose of the Study:

  • To introduce and define novel ordinal model-based probability effect measures.
  • To extend existing measures for comparing two groups with ordinal outcomes.
  • To provide methods for estimating these measures and their confidence intervals.

Main Methods:

  • Development of ordinal superiority measures based on latent variable models.
  • Application of probit, log-log, and logit link functions for cumulative probabilities.
  • Formulation of measures for both latent and observed ordinal response models.
  • Derivation of confidence intervals for the proposed measures.

Main Results:

  • The ordinal superiority measure is shown to be Φ(β/2) for normal latent variable models with probit link.
  • For general latent variable models, the measure equals exp(β)/[1+exp(β)] with log-log link and approx. exp(β/2)/[1+exp(β/2)] with logit link.
  • New measures are presented for directly modeling observed ordinal responses.
  • Confidence intervals are derived and illustrated with an example.

Conclusions:

  • The proposed ordinal superiority measures provide a flexible and interpretable way to compare ordinal distributions.
  • These measures are valuable for adjusted comparisons in the presence of explanatory variables.
  • The methods offer a significant advancement in the analysis of ordinal data.