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Elaboration Models with Symmetric Information Divergence.

Majid Asadi1,2, Karthik Devarajan3, Nader Ebrahimi4

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|May 22, 2023
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Summary
This summary is machine-generated.

This study introduces novel link functions for statistical elaboration models, enabling symmetric divergence measures. These methods improve covariate efficacy assessment in probability distributions.

Keywords:
Covariate selectionKullback-LeiblerRényigeneralized logitgeneralized probitphi-divergenceproportional odds

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Area of Science:

  • Statistics
  • Probability Theory
  • Mathematical Modeling

Background:

  • Statistical methodologies often embed probability distributions into more flexible elaboration models.
  • Asymmetric measures like likelihood ratio and Kullback-Leibler information are commonly used but can be problematic.
  • There is a need for robust methods to evaluate these model elaborations.

Purpose of the Study:

  • To introduce two formal link functions for embedding baseline distributions into elaboration models.
  • To establish conditions for these link functions to yield symmetric divergence measures (Kullback-Leibler, Rényi, phi-divergence).
  • To demonstrate the advantages of symmetric divergence measures in assessing covariate efficacy.

Main Methods:

  • Development of two novel link functions: a quantile-based elaboration and a survival function-based elaboration.
  • Derivation of conditions for achieving symmetric Kullback-Leibler, Rényi, and phi-divergences.
  • Identification of the logistic distribution as satisfying conditions for both link functions.
  • Application of the methodology to assess covariate efficacy.

Main Results:

  • The proposed link functions successfully embed baseline distributions into elaboration models.
  • Conditions were derived for symmetric divergence measures, overcoming limitations of asymmetric ones.
  • The logistic distribution uniquely satisfies the criteria for both quantile and survival function elaborations.
  • The application highlighted the benefits of symmetric divergence for covariate assessment.

Conclusions:

  • The introduced link functions provide a formal and flexible approach to statistical model elaboration.
  • Symmetric divergence measures offer a more reliable evaluation of model fit and covariate effects.
  • This work advances the understanding and application of probability distribution families in statistical modeling.