{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T22:59:11Z","timestamp":1783119551933,"version":"3.54.6"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,16]],"date-time":"2021-02-16T00:00:00Z","timestamp":1613433600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The Ministry of Research and Technology\/National Agency for Research and Innovation of the Republic of Indonesia","award":["3\/E1\/KP.PTNBH\/2020"],"award-info":[{"award-number":["3\/E1\/KP.PTNBH\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This article provides a bivariate binary logit model and statistical inference procedures for parameter estimation and hypothesis testing. The bivariate binary logit (BBL) model is an extension of the binary logit model that has two correlated binary responses. The BBL model responses were formed using a 2 \u00d7 2 contingency table, which follows a multinomial distribution. The maximum likelihood and Berndt\u2013Hall\u2013Hall\u2013Hausman (BHHH) methods were used to obtain the BBL model. Hypothesis testing of the BBL model contains the simultaneous test and the partial test. The test statistics of the simultaneous test and the partial test were determined using the maximum likelihood ratio test method. The likelihood ratio statistics of the simultaneous test and the partial test were approximately asymptotically chi-square distributed with 3p degrees of freedom. The BBL model was applied to a real dataset, and the BBL model with the single covariate was better than the BBL model with multiple covariates.<\/jats:p>","DOI":"10.3390\/sym13020326","type":"journal-article","created":{"date-parts":[[2021,2,16]],"date-time":"2021-02-16T22:13:38Z","timestamp":1613513618000},"page":"326","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Logit Model for Bivariate Binary Responses"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1592-6645","authenticated-orcid":false,"given":"Purhadi","family":"Purhadi","sequence":"first","affiliation":[{"name":"Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5993-4196","authenticated-orcid":false,"given":"M.","family":"Fathurahman","sequence":"additional","affiliation":[{"name":"Department of Statistics, Mulawarman University, Samarinda 75123, Indonesia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"McCullagh, P., and Nelder, J.A. 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