{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:28:40Z","timestamp":1760146120586,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,5]],"date-time":"2024-10-05T00:00:00Z","timestamp":1728086400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FAP-DF (Funda\u00e7\u00e3o de Apoio \u00e0 Pesquisa do Distrito Federal)","award":["309674\/2020-4","304716\/2023-5"],"award-info":[{"award-number":["309674\/2020-4","304716\/2023-5"]}]},{"name":"University of Brasilia","award":["309674\/2020-4","304716\/2023-5"],"award-info":[{"award-number":["309674\/2020-4","304716\/2023-5"]}]},{"name":"CNPq (Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico)","award":["309674\/2020-4","304716\/2023-5"],"award-info":[{"award-number":["309674\/2020-4","304716\/2023-5"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper introduces bivariate log-symmetric models for analyzing the relationship between two variables, assuming a family of log-symmetric distributions. These models offer greater flexibility than the bivariate lognormal distribution, allowing for better representation of diverse distribution shapes and behaviors in the data. The log-symmetric distribution family is widely used in various scientific fields and includes distributions such as log-normal, log-Student-t, and log-Laplace, among others, providing several options for modeling different data types. However, there are few approaches to jointly model continuous positive and explanatory variables in regression analysis. Therefore, we propose a class of generalized linear model (GLM) regression models based on bivariate log-symmetric distributions, aiming to fill this gap. Furthermore, in the proposed model, covariates are used to describe its dispersion and correlation parameters. This study uses a dataset of anthropometric measurements of newborns to correlate them with various biological factors, proposing bivariate regression models to account for the relationships observed in the data. Such models are crucial for preventing and controlling public health issues.<\/jats:p>","DOI":"10.3390\/sym16101315","type":"journal-article","created":{"date-parts":[[2024,10,7]],"date-time":"2024-10-07T06:23:18Z","timestamp":1728282198000},"page":"1315","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Bivariate Log-Symmetric Regression Models Applied to Newborn Data"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4467-8652","authenticated-orcid":false,"given":"Helton","family":"Saulo","sequence":"first","affiliation":[{"name":"Department of Statistics, Universidade de Bras\u00edlia, Bras\u00edlia 70910-900, Brazil"},{"name":"Department of Economics, Federal University of Pelotas, Pelotas 96010-610, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1073-0114","authenticated-orcid":false,"given":"Roberto","family":"Vila","sequence":"additional","affiliation":[{"name":"Department of Statistics, Universidade de Bras\u00edlia, Bras\u00edlia 70910-900, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1854-5805","authenticated-orcid":false,"given":"Rubens","family":"Souza","sequence":"additional","affiliation":[{"name":"Department of Statistics, Universidade de Bras\u00edlia, Bras\u00edlia 70910-900, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3039","DOI":"10.1016\/j.jspi.2007.11.006","article-title":"On reciprocal symmetry","volume":"138","author":"Jones","year":"2008","journal-title":"J. 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(2023). Bivariate logistic regression model diagnostics applied to analysis of outlier cancer patients with comorbid diabetes and hypertension in Malawi. Sci. Rep., 13.","DOI":"10.1038\/s41598-023-35475-z"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6972","DOI":"10.1080\/03610926.2022.2037645","article-title":"Regression to the mean: Estimation and adjustment under the bivariate normal distribution","volume":"52","author":"Khan","year":"2023","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Umair, M., Khan, M., and Olivier, J. (2024). Accounting for regression to the mean under the bivariate t-distribution. Stat. Methods Med. Res.","DOI":"10.1177\/09622802241267808"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1214\/20-BJPS490","article-title":"A bivariate fatigue-life regression model and its application to fracture of metallic tools","volume":"35","author":"Saulo","year":"2021","journal-title":"Braz. J. Probab. Stat."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6032","DOI":"10.1080\/03610926.2019.1626425","article-title":"On mean-based bivariate Birnbaum-Saunders distributions: Properties, inference and application","volume":"49","author":"Saulo","year":"2020","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Paulsen, C., Nielsen, B., Msemo, O., M\u00f8ller, S., Ekmann, J., Theander, T., Bygbjerg, I., Lusingu, J., Minja, T., and Schmiegelow, C. (2019). Anthropometric measurements can identify small for gestational age newborns: A cohort study in rural Tanzania. BMC Pediatr., 19.","DOI":"10.1186\/s12887-019-1500-0"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Fenton, T.R., and Kim, J.H. (2013). A systematic review and meta-analysis to revisethe Fenton growth chart for preterm infants. BMC Pediatr., 13.","DOI":"10.1186\/1471-2431-13-59"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Haksari, E., Lafeber, H., Hakimi, M., Pawirohartono, E., and Nystr\u00f6m, L. (2016). Reference curves of birth weight, length, and head circumference for gestational ages in Yogyakarta, Indonesia. BMC Pediatr., 16.","DOI":"10.1186\/s12887-016-0728-1"},{"key":"ref_13","first-page":"e66291","article-title":"Reference Curves of Birth Weight, Length, and Head Circumference for Gestational Age in Iranian Singleton Births","volume":"28","author":"Rashidi","year":"2018","journal-title":"Iran. J. Pediatr."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1290","DOI":"10.1002\/bimj.202000200","article-title":"Quantile modeling through multivariate log-normal\/independent linear regression models with application to newborn data","volume":"63","author":"Ferrari","year":"2021","journal-title":"Biom. J."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Fang, K.T., Kotz, S., and Ng, K.W. (1990). Symmetric Multivariate and Related Distributions, Chapman and Hall.","DOI":"10.1007\/978-1-4899-2937-2"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Kotz, S., Kozubowski, T.J., and Podg\u00f3rski, K. (2001). The Laplace Distribution and Generalizations, Wiley.","DOI":"10.1007\/978-1-4612-0173-1"},{"key":"ref_17","first-page":"758","article-title":"On the existence and uniqueness of the maximum likelihood estimate of a vector-valued parameter in fixed-size samples","volume":"9","author":"Schmidt","year":"1981","journal-title":"Ann. Stat."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Cram\u00e9r, H. (1946). Mathematical Methods of Statistics, Princeton University Press.","DOI":"10.1515\/9781400883868"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1093\/biomet\/65.3.457","article-title":"Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher Information","volume":"65","author":"Efron","year":"1978","journal-title":"Biometrika"},{"key":"ref_20","unstructured":"Hu, S., Murphy, T.B., and O\u2019Hagan, A. (2019). Bivariate Gamma Mixture of Experts Models for Joint Insurance Claims Modeling. arXiv."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1080\/1350485042000293121","article-title":"Analysing household bottled water and water purifier expenditures: Simultaneous equation bivariate Tobit model","volume":"12","author":"Yoo","year":"2005","journal-title":"Appl. Econ. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1111\/stan.12243","article-title":"Log-symmetric quantile regression models","volume":"76","author":"Saulo","year":"2022","journal-title":"Stat. Neerl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1111\/j.1541-0420.2008.01058.x","article-title":"Joint Regression Analysis of Correlated Data Using Gaussian Copulas","volume":"65","author":"Song","year":"2009","journal-title":"Biometrics"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/10\/1315\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:11:06Z","timestamp":1760112666000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/10\/1315"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,5]]},"references-count":23,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,10]]}},"alternative-id":["sym16101315"],"URL":"https:\/\/doi.org\/10.3390\/sym16101315","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,10,5]]}}}