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Categorical Data Analysis Using a Skewed Weibull Regression Model.

Renault Caron1, Debajyoti Sinha2, Dipak K Dey3

  • 1Department of Statistics, Federal University of São Carlos, São Carlos 13565-905, Brazil.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a flexible Weibull link model for analyzing categorical data. The proposed model encompasses common methods like logit and probit as special cases, offering improved analysis for skewed distributions.

Keywords:
Weibull distributionasymmetric modelbinomial responsemultinomial responseskewed link

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Area of Science:

  • Statistics
  • Statistical Modeling
  • Data Analysis

Background:

  • Categorical data analysis commonly employs logit, probit, and complementary log-log models.
  • These standard models may not adequately capture asymmetry in response distributions.
  • There is a need for more flexible models to handle skewed categorical data.

Purpose of the Study:

  • To introduce and evaluate a novel Weibull link (skewed) model for categorical response data.
  • To demonstrate that established models are limiting cases of the proposed Weibull model.
  • To compare the performance of the Weibull model against other asymmetrical models.

Main Methods:

  • Development of a Weibull link model for binomial and multinomial data.
  • Derivation of logit, probit, and complementary log-log models as limiting cases.
  • Application of both Bayesian and frequentist estimation procedures.
  • Comparative analysis with existing asymmetrical statistical models.

Main Results:

  • The proposed Weibull link model effectively handles skewed categorical response data.
  • Commonly used models are shown to be special instances of the Weibull model.
  • Empirical analysis of two datasets confirms the model's efficiency and flexibility.

Conclusions:

  • The Weibull link model provides a robust and versatile alternative for categorical data analysis, particularly when skewness is present.
  • The model unifies several existing approaches, offering a broader framework.
  • The findings support the use of the Weibull model for improved statistical inference in various applications.