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Using Cook's distance in polytomous logistic regression.

Nirian Martín1

  • 1Department of Statistics, Carlos III University of Madrid, Spain.

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This study establishes the asymptotic distribution for Cook's distance in polytomous logistic regression, enabling robust analysis of influential covariates and improved prediction accuracy.

Keywords:
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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Cook's distance is a key diagnostic in regression analysis.
  • Its asymptotic distribution in polytomous logistic regression was previously unknown.
  • Assessing influential covariates is crucial for model reliability.

Purpose of the Study:

  • To determine the asymptotic distribution of Cook's distance in polytomous logistic regression.
  • To develop a comprehensive method for analyzing influential covariates.
  • To introduce a novel measure for prediction accuracy.

Main Methods:

  • Derivation of the asymptotic distribution of Cook's distance.
  • Establishing it as a linear combination of independent chi-square variables.
  • Developing an analytical framework for influential covariate analysis.

Main Results:

  • The asymptotic distribution of Cook's distance was identified as a linear combination of chi-square variables.
  • A novel approach for analyzing influential covariates was successfully developed.
  • A new measure for assessing prediction accuracy was introduced.

Conclusions:

  • The established distribution provides a theoretical foundation for diagnostic analysis in polytomous logistic regression.
  • The developed methods enhance the understanding and identification of influential covariates.
  • The new prediction accuracy measure offers improved model evaluation capabilities.