{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T00:48:08Z","timestamp":1773881288087,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T00:00:00Z","timestamp":1704931200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002713","name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU)","doi-asserted-by":"publisher","award":["IMSIU-RP23097"],"award-info":[{"award-number":["IMSIU-RP23097"]}],"id":[{"id":"10.13039\/501100002713","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This study introduces a new two-parameter Liu estimator (PMTPLE) for addressing the multicollinearity problem in the Poisson regression model (PRM). The estimation of the PRM is traditionally accomplished through the Poisson maximum likelihood estimator (PMLE). However, when the explanatory variables are correlated, thus leading to multicollinearity, the variance or standard error of the PMLE is inflated. To address this issue, several alternative estimators have been introduced, including the Poisson ridge regression estimator (PRRE), Liu estimator (PLE), and adjusted Liu estimator (PALE), each of them relying on a single shrinkage parameter. The PMTPLE uses two shrinkage parameters, which enhances its adaptability and robustness in the presence of multicollinearity between explanatory variables. To assess the performance of the PMTPLE compared to the four existing estimators (the PMLE, PRRE, PLE, and PALE), a simulation study is conducted that encompasses various scenarios and two empirical applications. The evaluation of the performance is based on the mean square error (MSE) criterion. The theoretical comparison, simulation results, and findings of the two applications consistently demonstrate the superiority of the PMTPLE over the other estimators, establishing it as a robust solution for count data analysis under multicollinearity conditions.<\/jats:p>","DOI":"10.3390\/axioms13010046","type":"journal-article","created":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T12:56:33Z","timestamp":1704977793000},"page":"46","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Modified Two-Parameter Liu Estimator for Addressing Multicollinearity in the Poisson Regression Model"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5758-1035","authenticated-orcid":false,"given":"Mahmoud M.","family":"Abdelwahab","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 90950, Saudi Arabia"},{"name":"Department of Basic Sciences, Higher Institute of Administrative Sciences, Osim, Cairo 12961, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6010-001X","authenticated-orcid":false,"given":"Mohamed R.","family":"Abonazel","sequence":"additional","affiliation":[{"name":"Department of Applied Statistics and Econometrics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt"}]},{"given":"Ali T.","family":"Hammad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt"}]},{"given":"Amera M.","family":"El-Masry","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Management Technology and Information Systems, Port Said University, Port Said 42521, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1162\/rest.88.4.641","article-title":"The log of gravity","volume":"88","author":"Silva","year":"2006","journal-title":"Rev. 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