{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T14:53:50Z","timestamp":1774277630571,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,10,30]],"date-time":"2024-10-30T00:00:00Z","timestamp":1730246400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"PhD scholarship of the Universidad de Valpara\u00edso (Chile)","award":["1241881-E2024"],"award-info":[{"award-number":["1241881-E2024"]}]},{"name":"Chilean national ANID-Fondecyt","award":["1241881-E2024"],"award-info":[{"award-number":["1241881-E2024"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A critical aspect of modeling binomial response data is selecting an appropriate link function, as an improper choice can significantly affect model precision. This paper introduces the skew\u2013t link model, an extension of the skew\u2013probit model, offering increased flexibility by incorporating both asymmetry and heavy tails, making it suitable for asymmetric and complex data structures. A penalized likelihood-based estimation method is proposed to stabilize parameter estimation, particularly for the asymmetry parameter. Extensive simulation studies demonstrate the model\u2019s superior performance in terms of lower bias, root mean squared error (RMSE), and robustness compared to traditional symmetric models like probit and logit. Furthermore, the model is applied to two real-world datasets: one concerning women\u2019s labor participation and another related to cardiovascular disease outcomes, both showing superior fitting capabilities compared to more traditional models (with probit and the skew\u2013probit links). These findings highlight the model\u2019s applicability to socioeconomic and medical research, characterized by skew and asymmetric data. Moreover, the proposed model could be applied in various domains where data exhibit asymmetry and complex structures.<\/jats:p>","DOI":"10.3390\/axioms13110749","type":"journal-article","created":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T13:09:27Z","timestamp":1730466567000},"page":"749","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Maximum Penalized Likelihood Estimation of the Skew\u2013t Link Model for Binomial Response Data"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6490-7491","authenticated-orcid":false,"given":"Omar","family":"Chocotea-Poca","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Universidad de Santiago de Chile, Avenida Libertador Bernardo O\u2019Higgins 3363, Santiago 9170022, Chile"},{"name":"Statistical Institute, Universidad de Valpara\u00edso, Avenida Gran Breta\u00f1a 1111, Valpara\u00edso 2360102, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8046-6983","authenticated-orcid":false,"given":"Orietta","family":"Nicolis","sequence":"additional","affiliation":[{"name":"Engineering Faculty, Universidad Andres Bello, Calle Quillota 980, Vi\u00f1a del Mar 2520000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6038-2149","authenticated-orcid":false,"given":"Germ\u00e1n","family":"Ibacache-Pulgar","sequence":"additional","affiliation":[{"name":"Statistical Institute, Universidad de Valpara\u00edso, Avenida Gran Breta\u00f1a 1111, Valpara\u00edso 2360102, Chile"},{"name":"Centro de Estudios Atmosf\u00e9ricos y Cambio Clim\u00e1tico, Universidad de Valpara\u00edso, Avenida Gran Breta\u00f1a 644, Valpara\u00edso 2360102, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1177\/0008068320020113","article-title":"On robustness of choice of links in binomial regression","volume":"53","author":"Chen","year":"2022","journal-title":"Calcutta Stat. Assoc. Bull."},{"key":"ref_2","first-page":"861","article-title":"A skew item response model","volume":"1","author":"Bolfarine","year":"2006","journal-title":"Bayesian Anal."},{"key":"ref_3","first-page":"678","article-title":"A framework for skew-probit links in binary regression","volume":"4","author":"Bolfarine","year":"2010","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1621","DOI":"10.1080\/00949655.2019.1590579","article-title":"Identifiability and bias reduction in the skew-probit model for a binary response","volume":"89","author":"Lee","year":"2019","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_5","first-page":"171","article-title":"A class of distributions which includes the normal ones","volume":"12","author":"Azzalini","year":"1985","journal-title":"Scand. J. Stat."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/j.jspi.2004.06.062","article-title":"A note on reference priors for the scalar skew-normal distribution","volume":"136","author":"Liseo","year":"2006","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4259","DOI":"10.1016\/j.jspi.2005.08.043","article-title":"Bias prevention of maximum likelihood estimates for scalar skew normal and skew t distributions","volume":"136","author":"Sartori","year":"2006","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/j.jspi.2012.06.022","article-title":"Maximum penalized likelihood estimation for skew-normal and skew-t distributions","volume":"143","author":"Azzalini","year":"2013","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1006\/jmva.2000.1960","article-title":"A general class of multivariate skew-elliptical distributions","volume":"79","author":"Branco","year":"2001","journal-title":"J. Multivar. Anal."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1111\/1467-9868.00391","article-title":"Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution","volume":"65","author":"Azzalini","year":"2003","journal-title":"J. R. Stat. Soc. B Stat. Methodol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"370","DOI":"10.2307\/2344614","article-title":"Generalized linear models","volume":"135","author":"Nelder","year":"1972","journal-title":"J. R. Stat. Soc. Ser. A"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1488","DOI":"10.1016\/j.spl.2006.03.008","article-title":"A new class of skew-cauchy distributions","volume":"76","author":"Behboodian","year":"2006","journal-title":"Stat. Probab. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1016\/j.csda.2008.11.002","article-title":"Recurrence relations for distributions of a skew-t and a linear combination of order statistics from a bivariate-t","volume":"53","author":"Jamalizadeh","year":"2009","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1111\/j.2517-6161.1996.tb02103.x","article-title":"The cost of adding parameters to a model","volume":"58","author":"Taylor","year":"1996","journal-title":"J. R. Stat. Soc. B Stat. Methodol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1093\/aje\/kwt245","article-title":"Maximum likelihood, profile likelihood, and penalized likelihood: A primer","volume":"179","author":"Cole","year":"2013","journal-title":"Am. J. Epidemiol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1111\/1467-9469.00317","article-title":"Penalized maximum likelihood estimator for normal mixtures","volume":"30","author":"Ciuperca","year":"2003","journal-title":"Scand. J. Stat."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1923","DOI":"10.1016\/j.jmva.2007.05.005","article-title":"Penalized empirical likelihood estimation of semiparametric models","volume":"98","author":"Otsu","year":"2007","journal-title":"J. Multivar. Anal."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2065","DOI":"10.1016\/j.jmva.2009.06.010","article-title":"On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding","volume":"100","author":"Leeb","year":"2009","journal-title":"J. Multivar. Anal."},{"key":"ref_19","unstructured":"Eggermont, P.P., and LaRiccia, V.N. (2009). Maximum Penalized Likelihood Estimation: Volume II: Regression, Springer. [1st ed.]."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Abadir, K.M., and Magnus, J.R. (2005). Matrix Algebra, Cambridge University Press. [1st ed.].","DOI":"10.1017\/CBO9780511810800"},{"key":"ref_21","unstructured":"R Core Team (2024). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1007\/s00180-010-0217-1","article-title":"maxLik: A package for maximum likelihood estimation in R","volume":"26","author":"Henningsen","year":"2010","journal-title":"Comput. Stat."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1080\/01621459.2000.10474219","article-title":"On profile likelihood","volume":"95","author":"Murphy","year":"2000","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Rodriguez-Segura, M., Nicolis, O., Peralta-Marquez, B., and Carrillo-Azocar, J. (2020, January 16\u201320). Predicting cardiovascular disease by combining optimal feature selection methods with machine learning. Proceedings of the 2020 39th International Conference of the Chilean Computer Science Society (SCCC), Coquimbo, Chile.","DOI":"10.1109\/SCCC51225.2020.9281168"},{"key":"ref_25","first-page":"1077","article-title":"The sleep heart health study: Design, rationale, and methods","volume":"20","author":"Quan","year":"1997","journal-title":"Sleep"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1111\/j.1467-9469.2011.00779.x","article-title":"Objective bayesian analysis of skew-t distributions","volume":"40","author":"Branco","year":"2012","journal-title":"Scand. J. Stat."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1093\/biomet\/asn001","article-title":"Objective bayesian analysis for the Student-t regression model","volume":"95","author":"Fonseca","year":"2008","journal-title":"Biometrika"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/11\/749\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:24:29Z","timestamp":1760113469000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/11\/749"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,30]]},"references-count":27,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["axioms13110749"],"URL":"https:\/\/doi.org\/10.3390\/axioms13110749","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,30]]}}}