{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T03:38:04Z","timestamp":1777606684483,"version":"3.51.4"},"reference-count":26,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T00:00:00Z","timestamp":1769817600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T00:00:00Z","timestamp":1769817600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Stat Anal Data Min: An ASA Data Sci Journal"],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>We propose a penalized Dirichlet regression framework for modeling compositional data, using a softmax link to ensure that the mean vector lies on the simplex and to avoid log\u2010ratio transformations or zero replacement. The model is formulated in a GLM\u2010like setting and incorporates an  (ridge) penalty on the regression coefficients to improve stability in the presence of multicollinearity, high\u2010dimensional covariate spaces and weak effects. The classical Dirichlet regression is recovered as the special case with zero penalty, so that the proposed estimator nests the standard approach. Estimation is carried out via a gradient\u2010based block coordinate ascent algorithm, for which we derive closed\u2010form expressions for the log\u2010likelihood gradient and for the Jacobian of the softmax transformation. We investigate the performance of the method through a simulation study that includes orthogonal and correlated designs, different noise levels and a sparse high\u2010dimensional scenario. The results show that the penalized and unpenalized estimators are essentially equivalent in simple well\u2010posed settings, while the ridge\u2010penalized model achieves systematically lower coefficient RMSE and higher log\u2010likelihood in more challenging configurations. Finally, we apply the method to US male cause\u2010of\u2010death data, where cross\u2010validated penalization yields improved fit and smooth, interpretable age\u2013cause profiles supported by bootstrap confidence intervals.<\/jats:p>","DOI":"10.1002\/sam.70062","type":"journal-article","created":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T12:12:17Z","timestamp":1769861537000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Stabilizing Inference in Dirichlet Regression via Ridge\u2010Penalized Model"],"prefix":"10.1002","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2707-3678","authenticated-orcid":false,"given":"Andrea","family":"Nigri","sequence":"first","affiliation":[{"name":"Department of Social Sciences University of Foggia  Foggia Italy"}]}],"member":"311","published-online":{"date-parts":[[2026,1,31]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-4109-0"},{"key":"e_1_2_11_3_1","volume-title":"Proceedings of the 28th Panhellenic Statistics Conference","author":"Tsagris M.","year":"2015"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1198\/000313008X270448"},{"key":"e_1_2_11_5_1","first-page":"77","article-title":"Modelling compositional data using dirichlet regression models","volume":"4","author":"Hijazi R.","year":"2009","journal-title":"Journal of Applied Probability and Statistics"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1982.tb01195.x"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.2307\/2335470"},{"key":"e_1_2_11_8_1","first-page":"20","volume-title":"Proceedings of IAMG'01\u2014The VII Annual Conference of the International Association for Mathematical Geology","author":"Barcel\u00f3\u2010Vidal C.","year":"2001"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11004-005-7381-9"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.2307\/2986142"},{"key":"e_1_2_11_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11004-005-1308-3"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1475-4754.2006.00270.x"},{"key":"e_1_2_11_13_1","first-page":"157","volume-title":"Proceedings of the 3rd Annual Conference of the International Association for Mathematical Geology","author":"Woronow A.","year":"1997"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610920600974021"},{"key":"e_1_2_11_15_1","volume-title":"CoDaWork'11: 4th International Workshop on Compositional Data Analysis","author":"Tsagris M.","year":"2011"},{"key":"e_1_2_11_16_1","first-page":"338","volume-title":"Proceedings of the IEEE International Conference on Information Reuse and Integration (IRI)","author":"Ankam D.","year":"2018"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1080\/03461238.2024.2425723"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1970.10488634"},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1993.tb01470.x"},{"key":"e_1_2_11_20_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974997"},{"key":"e_1_2_11_21_1","volume-title":"Nonlinear Programming: A Unified Approach","author":"Zangwill W.","year":"1969"},{"key":"e_1_2_11_22_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1970-0274029-X"},{"key":"e_1_2_11_23_1","volume-title":"Asymptotic Statistics","author":"Vaart A. W.","year":"2000"},{"key":"e_1_2_11_24_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511802843"},{"key":"e_1_2_11_25_1","doi-asserted-by":"crossref","unstructured":"R.GrazianiandA.Nigri \u201cAn Age\u2013Period\u2013Cohort Model in a Dirichlet Framework: A Coherent Causes of Death Estimation \u201dInsurance: Mathematics & Economics 2025 https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0167668725001404.","DOI":"10.1016\/j.insmatheco.2025.103194"},{"key":"e_1_2_11_26_1","unstructured":"Human Mortality Database \u201cMortality Data \u201d2025 https:\/\/www.mortality.org\/."},{"key":"e_1_2_11_27_1","unstructured":"Human Cause of Death Database \u201cCause of Death Statistics \u201d2025 https:\/\/www.causesofdeath.org\/cgi\u2010bin\/main.php."}],"container-title":["Statistical Analysis and Data Mining: An ASA Data Science Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sam.70062","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/sam.70062","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sam.70062","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T21:06:58Z","timestamp":1777410418000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sam.70062"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,31]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["10.1002\/sam.70062"],"URL":"https:\/\/doi.org\/10.1002\/sam.70062","archive":["Portico"],"relation":{},"ISSN":["1932-1864","1932-1872"],"issn-type":[{"value":"1932-1864","type":"print"},{"value":"1932-1872","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,31]]},"assertion":[{"value":"2025-08-10","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-01-19","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-01-31","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70062"}}