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

• Published in: Entropy (Basel, Switzerland) Vol. 24; no. 8; p. 1138
• Main Authors: Han, Yewon, Kim, Jaeho, Ng, Hon Keung Tony, Kim, Seong W.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.08.2022; MDPI
• Subjects: Algorithms; Baseball; Basketball; Binomial distribution; Bivariate analysis; bivariate binomial distribution; Book publishing; Data analysis; gibbs sampling; logistic regression; Metropolis–Hastings algorithm; Monte Carlo simulation; Optimization; Parameter estimation; Performance evaluation; posterior mean; Probability; Professional baseball; random effect; Random variables; Regression analysis; Regression models; Statistical analysis; Success; United States; United States
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e24081138

There has been a considerable amount of literature on binomial regression models that utilize well-known link functions, such as logistic, probit, and complementary log-log functions. The conventional binomial model is focused only on a single parameter representing one probability of success. However, we often encounter data for which two different success probabilities are of interest simultaneously. For instance, there are several offensive measures in baseball to predict the future performance of batters. Under these circumstances, it would be meaningful to consider more than one success probability. In this article, we employ a bivariate binomial distribution that possesses two success probabilities to conduct a regression analysis with random effects being incorporated under a Bayesian framework. Major League Baseball data are analyzed to demonstrate our methodologies. Extensive simulation studies are conducted to investigate model performances.