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Logistic Regression Model for a Bivariate Binomial Distribution with Applications in Baseball Data Analysis.

Yewon Han1, Jaeho Kim2, Hon Keung Tony Ng3

  • 1Department of Applied Mathematics, Hanyang University, Ansan 15588, Korea.

Entropy (Basel, Switzerland)
|August 26, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a bivariate binomial regression model for analyzing two simultaneous success probabilities, extending conventional models. The new Bayesian approach with random effects is validated using Major League Baseball data and simulations.

Keywords:
Metropolis–Hastings algorithmbivariate binomial distributiongibbs samplinglogistic regressionposterior meanrandom effect

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Conventional binomial regression models typically analyze a single success probability.
  • Many real-world datasets, such as sports analytics, involve multiple, simultaneous success probabilities.
  • Existing models are insufficient for scenarios requiring the analysis of dual probabilities.

Purpose of the Study:

  • To develop and apply a bivariate binomial regression model for analyzing two distinct success probabilities concurrently.
  • To incorporate random effects within a Bayesian framework for enhanced model flexibility.
  • To demonstrate the model's utility using Major League Baseball (MLB) offensive performance data.

Main Methods:

  • Utilized a bivariate binomial distribution to model two success probabilities.
  • Employed a Bayesian framework with random effects for regression analysis.
  • Applied the methodology to Major League Baseball (MLB) player statistics.

Main Results:

  • The bivariate binomial regression model effectively handles datasets with dual success probabilities.
  • The Bayesian approach with random effects provides robust performance.
  • Analysis of MLB data demonstrated the practical applicability of the proposed methodology.

Conclusions:

  • The bivariate binomial regression model offers a significant advancement over traditional single-probability models.
  • The Bayesian framework with random effects is suitable for complex probability analyses.
  • This approach provides valuable insights for fields like sports analytics and performance prediction.