Han Yewon, Kim Jaeho, Ng Hon Keung Tony, Kim Seong W
Department of Applied Mathematics, Hanyang University, Ansan 15588, Korea.
Department of Economics, Hanyang University, Ansan 15588, Korea.
Entropy (Basel). 2022 Aug 17;24(8):1138. 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.
关于使用诸如逻辑、概率单位和互补对数-对数函数等著名链接函数的二项回归模型，已有大量文献。传统的二项模型仅关注代表一种成功概率的单个参数。然而，我们经常遇到同时对两个不同成功概率感兴趣的数据。例如，在棒球中有几种进攻性指标来预测击球手的未来表现。在这种情况下，考虑多个成功概率是有意义的。在本文中，我们采用具有两个成功概率的双变量二项分布，在贝叶斯框架下纳入随机效应进行回归分析。通过分析美国职业棒球大联盟的数据来展示我们的方法。进行了广泛的模拟研究以调查模型性能。
