{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T17:25:51Z","timestamp":1770225951290,"version":"3.49.0"},"reference-count":29,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,17]],"date-time":"2022-08-17T00:00:00Z","timestamp":1660694400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF-2021R1A2C1005271"],"award-info":[{"award-number":["NRF-2021R1A2C1005271"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/e24081138","type":"journal-article","created":{"date-parts":[[2022,8,17]],"date-time":"2022-08-17T21:23:56Z","timestamp":1660771436000},"page":"1138","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Logistic Regression Model for a Bivariate Binomial Distribution with Applications in Baseball Data Analysis"],"prefix":"10.3390","volume":"24","author":[{"given":"Yewon","family":"Han","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Hanyang University, Ansan 15588, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4949-9925","authenticated-orcid":false,"given":"Jaeho","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Economics, Hanyang University, Ansan 15588, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4685-2199","authenticated-orcid":false,"given":"Hon Keung Tony","family":"Ng","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Bentley University, Waltham, MA 02452, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7759-2329","authenticated-orcid":false,"given":"Seong W.","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Hanyang University, Ansan 15588, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1214\/09-BA424","article-title":"Hierarchical Bayesian modeling of hitting performance in baseball","volume":"4","author":"Jensen","year":"2009","journal-title":"Bayesian Anal."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1093\/biomet\/59.3.581","article-title":"Bayesian methods for binomial data","volume":"59","author":"Leonard","year":"1972","journal-title":"Biometrika"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1080\/00031305.1997.10473965","article-title":"Bayesian binomial regression: Predicting survival at a Trauma Center","volume":"51","author":"Bedrick","year":"1997","journal-title":"Am. 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