{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T19:44:12Z","timestamp":1775850252192,"version":"3.50.1"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2022,11,1]],"date-time":"2022-11-01T00:00:00Z","timestamp":1667260800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,11,1]],"date-time":"2022-11-01T00:00:00Z","timestamp":1667260800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100002322","name":"coordena\u00e7\u00e3o de aperfei\u00e7oamento de pessoal de n\u00edvel superior","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"conselho nacional de desenvolvimento cient\u00edfico e tecnol\u00f3gico","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2021\/11720-0"],"award-info":[{"award-number":["2021\/11720-0"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Stat"],"published-print":{"date-parts":[[2025,7]]},"DOI":"10.1007\/s00180-022-01297-2","type":"journal-article","created":{"date-parts":[[2022,11,1]],"date-time":"2022-11-01T07:03:02Z","timestamp":1667286182000},"page":"3007-3040","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Bayesian quantile regression models for heavy tailed bounded variables using the No-U-Turn sampler"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0588-4549","authenticated-orcid":false,"given":"Eduardo S. B.","family":"de Oliveira","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M\u00e1rio","family":"de Castro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cristian L.","family":"Bayes","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jorge L.","family":"Baz\u00e1n","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,11,1]]},"reference":[{"issue":"13\u201315","key":"1297_CR1","doi-asserted-by":"publisher","first-page":"2389","DOI":"10.1080\/02664763.2020.1823946","volume":"48","author":"HTK Akdur","year":"2021","unstructured":"Akdur HTK (2021) Unit-Lindley mixed-effect model for proportion data. J Appl Stat 48(13\u201315):2389\u20132405","journal-title":"J Appl Stat"},{"key":"1297_CR2","volume-title":"Plots, transformation and regression: an introduction to graphical methods of diagnostic regression analysis","author":"AC Atkinson","year":"1985","unstructured":"Atkinson AC (1985) Plots, transformation and regression: an introduction to graphical methods of diagnostic regression analysis. New York, NY, Oxford"},{"issue":"3","key":"1297_CR3","doi-asserted-by":"publisher","first-page":"483","DOI":"10.4310\/SII.2017.v10.n3.a11","volume":"10","author":"CL Bayes","year":"2017","unstructured":"Bayes CL, Baz\u00e1n JL, de Castro M (2017) A quantile parametric mixed regression model for bounded response variables. Stat Interface 10(3):483\u2013493","journal-title":"Stat Interface"},{"issue":"4","key":"1297_CR4","doi-asserted-by":"publisher","first-page":"841","DOI":"10.1214\/12-BA728","volume":"7","author":"CL Bayes","year":"2012","unstructured":"Bayes CL, Baz\u00e1n JL, Garcia C (2012) A new robust regression model for proportions. Bayesian Anal 7(4):841\u2013866","journal-title":"Bayesian Anal"},{"issue":"4","key":"1297_CR5","first-page":"810","volume":"35","author":"JL Baz\u00e1n","year":"2017","unstructured":"Baz\u00e1n JL, Valdivieso L, Branco MD (2017) Measurement of the nonsense word fluency: bayesian approach to a item response model with speededness. Rev Bras Biom 35(4):810\u2013833","journal-title":"Rev Bras Biom"},{"issue":"1","key":"1297_CR6","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/s00180-020-01002-1","volume":"36","author":"J Biswas","year":"2021","unstructured":"Biswas J, Das K (2021) A Bayesian quantile regression approach to multivariate semi-continuous longitudinal data. Comput Stat 36(1):241\u2013260","journal-title":"Comput Stat"},{"issue":"1","key":"1297_CR7","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1111\/anzs.12106","volume":"57","author":"Y Cai","year":"2015","unstructured":"Cai Y, Jiang T (2015) Estimation of non-crossing quantile regression curves. Aust N Z J Stat 57(1):139\u2013162","journal-title":"Aust N Z J Stat"},{"issue":"1\u20132","key":"1297_CR8","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/S0378-3758(01)00277-4","volume":"110","author":"B Chakraborty","year":"2003","unstructured":"Chakraborty B (2003) On multivariate quantile regression. J Stat Plan Inference 110(1\u20132):109\u2013132","journal-title":"J Stat Plan Inference"},{"issue":"2","key":"1297_CR9","doi-asserted-by":"publisher","first-page":"352","DOI":"10.1002\/bimj.201600225","volume":"60","author":"MA da Silva","year":"2018","unstructured":"da Silva MA, de Oliveira ES, von Davier AA, Baz\u00e1n JL (2018) Estimating the DINA model parameters using the No-U-Turn Sampler. Biom J 60(2):352\u2013368","journal-title":"Biom J"},{"issue":"9","key":"1297_CR10","doi-asserted-by":"publisher","first-page":"1694","DOI":"10.1080\/00949655.2019.1593984","volume":"89","author":"A de la Cruz Huayanay","year":"2019","unstructured":"de la Cruz Huayanay A, Baz\u00e1n JL, Cancho VG, Dey DK (2019) Performance of asymmetric links and correction methods for imbalanced data in binary regression. J Stat Comput Simul 89(9):1694\u20131714","journal-title":"J Stat Comput Simul"},{"issue":"3","key":"1297_CR11","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1080\/10618600.1996.10474708","volume":"5","author":"PK Dunn","year":"1996","unstructured":"Dunn PK, Smyth GK (1996) Randomized quantile residuals. J Comput Graph Stat 5(3):236\u2013244","journal-title":"J Comput Graph Stat"},{"issue":"10","key":"1297_CR12","doi-asserted-by":"publisher","first-page":"1936","DOI":"10.1080\/00949655.2018.1430801","volume":"88","author":"R Fern\u00e1ndez","year":"2018","unstructured":"Fern\u00e1ndez R, Bayes CL, Valdivieso L (2018) A beta-inflated mean regression model with mixed effects for fractional response variables. J Stat Comput Simul 88(10):1936\u20131957","journal-title":"J Stat Comput Simul"},{"issue":"7","key":"1297_CR13","doi-asserted-by":"publisher","first-page":"799","DOI":"10.1080\/0266476042000214501","volume":"31","author":"SLP Ferrari","year":"2004","unstructured":"Ferrari SLP, Cribari-Neto F (2004) Beta regression for modelling rates and proportions. J Appl Stat 31(7):799\u2013815","journal-title":"J Appl Stat"},{"key":"1297_CR14","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1016\/j.csda.2012.12.002","volume":"61","author":"JI Figueroa-Zu\u00f1iga","year":"2013","unstructured":"Figueroa-Zu\u00f1iga JI, Arellano-Valle RB, Ferrari SLP (2013) Mixed beta regression: a Bayesian perspective. Comput Stat Data Anal 61:137\u2013147","journal-title":"Comput Stat Data Anal"},{"issue":"6","key":"1297_CR15","doi-asserted-by":"publisher","first-page":"997","DOI":"10.1007\/s11222-013-9416-2","volume":"24","author":"A Gelman","year":"2014","unstructured":"Gelman A, Hwang J, Vehtari A (2014) Understanding predictive information criteria for Bayesian models. Stat Comput 24(6):997\u20131016","journal-title":"Stat Comput"},{"issue":"4","key":"1297_CR16","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1214\/ss\/1177011136","volume":"7","author":"A Gelman","year":"1992","unstructured":"Gelman A, Rubin DB (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7(4):457\u2013472","journal-title":"Stat Sci"},{"issue":"3","key":"1297_CR17","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1007\/s11222-013-9381-9","volume":"24","author":"M Geraci","year":"2014","unstructured":"Geraci M, Bottai M (2014) Linear quantile mixed models. Stat Comput 24(3):461\u2013479","journal-title":"Stat Comput"},{"issue":"14","key":"1297_CR18","doi-asserted-by":"publisher","first-page":"3423","DOI":"10.1080\/03610926.2018.1476717","volume":"48","author":"ME Ghitany","year":"2019","unstructured":"Ghitany ME, Mazucheli J, Menezes AFB, Alqallaf F (2019) The unit-inverse Gaussian distribution: a new alternative to two-parameter distributions on the unit interval. Commun Stat-Theory Methods 48(14):3423\u20133438","journal-title":"Commun Stat-Theory Methods"},{"issue":"2","key":"1297_CR19","doi-asserted-by":"publisher","first-page":"1073","DOI":"10.1016\/j.jeconom.2007.01.002","volume":"141","author":"MN Harris","year":"2007","unstructured":"Harris MN, Zhao X (2007) A zero-inflated ordered probit model, with an application to modelling tobacco consumption. J Econ 141(2):1073\u20131099","journal-title":"J Econ"},{"key":"1297_CR20","first-page":"1593","volume":"15","author":"MD Hoffman","year":"2014","unstructured":"Hoffman MD, Gelman A (2014) The no-u-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. J Mach Learn Res 15:1593\u20131623","journal-title":"J Mach Learn Res"},{"key":"1297_CR21","unstructured":"INEI (2009) Mapa de pobreza provincial y distrital 2009. El enfoque de la pobreza monetaria. Direcci\u00f3n T\u00e9cnica de Demograf\u00eda e Indicadores Sociales. Instituto Nacional de Estad\u00edstica e Inform\u00e1tica (INEI). Lima, Peru"},{"issue":"1","key":"1297_CR22","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1016\/j.jksus.2018.08.001","volume":"32","author":"P Jodr\u00e1","year":"2018","unstructured":"Jodr\u00e1 P (2018) A bounded distribution derived from the shifted Gompertz law. J King Saud Univ-Sci 32(1):523\u2013536","journal-title":"J King Saud Univ-Sci"},{"issue":"4","key":"1297_CR23","doi-asserted-by":"publisher","first-page":"727","DOI":"10.1002\/bimj.201500030","volume":"58","author":"A Lemonte","year":"2016","unstructured":"Lemonte A, Bazan JL (2016) New class of Johnson SB distributions and its associated regression model for rates and proportions. Biom J 58(4):727\u2013746","journal-title":"Biom J"},{"issue":"1","key":"1297_CR24","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/s00180-019-00898-8","volume":"35","author":"AG Lemonte","year":"2020","unstructured":"Lemonte AG, Moreno-Arenas G (2020) On a heavy-tailed parametric quantile regression model for limited range response variables. Comput Stat 35(1):379\u2013398","journal-title":"Comput Stat"},{"issue":"3","key":"1297_CR25","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1080\/03461238.2012.687697","volume":"2014","author":"A Lenart","year":"2014","unstructured":"Lenart A (2014) The moments of the Gompertz distribution and maximum likelihood estimation of its parameters. Scand Actuar J 2014(3):255\u2013277","journal-title":"Scand Actuar J"},{"issue":"1","key":"1297_CR26","first-page":"25","volume":"79","author":"J Mazucheli","year":"2019","unstructured":"Mazucheli J, Menezes AF, Dey S (2019) Unit-Gompertz distribution with applications. Statistica (Bologna) 79(1):25\u201343","journal-title":"Statistica (Bologna)"},{"key":"1297_CR27","unstructured":"Merkle EC, Furr D, Rabe-Hesketh S (2018) Bayesian model assessment: use of conditional vs marginal likelihoods. arXiv preprint arXiv:1802.04452"},{"issue":"3","key":"1297_CR28","doi-asserted-by":"publisher","first-page":"845","DOI":"10.1214\/17-BA1079","volume":"13","author":"S Migliorati","year":"2018","unstructured":"Migliorati S, Di Brisco AM, Ongaro A (2018) A new regression model for bounded responses. Bayesian Anal 13(3):845\u2013872","journal-title":"Bayesian Anal"},{"issue":"1","key":"1297_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s12711-019-0515-1","volume":"51","author":"M Nishio","year":"2019","unstructured":"Nishio M, Arakawa A (2019) Performance of Hamiltonian Monte Carlo and No-U-Turn Sampler for estimating genetic parameters and breeding values. Genet Sel Evol 51(1):1\u201312","journal-title":"Genet Sel Evol"},{"key":"1297_CR30","unstructured":"Oliveira ESB, Andrade Filho MC, Bayes CL, Baz\u00e1n JL (2018) New Gompertz based distributions to skewed bounded responses [abstract]. In: VI workshop on probabilistic and statistical methods - PROGRAM, S\u00e3o Carlos, SP, Brazil. pp 18\u201319. http:\/\/wpsm.icmc.usp.br\/6WPSM\/program_6WPSM.pdf"},{"issue":"6","key":"1297_CR31","doi-asserted-by":"publisher","first-page":"1609","DOI":"10.1016\/j.csda.2011.10.005","volume":"56","author":"R Ospina","year":"2012","unstructured":"Ospina R, Ferrari SL (2012) A general class of zero-or-one inflated beta regression models. Comput Stat Data Anal 56(6):1609\u20131623","journal-title":"Comput Stat Data Anal"},{"issue":"2","key":"1297_CR32","doi-asserted-by":"publisher","first-page":"199","DOI":"10.2307\/3315445","volume":"23","author":"F Peng","year":"1995","unstructured":"Peng F, Dey DK (1995) Bayesian analysis of outlier problems using divergence measures. Can J Stat 23(2):199\u2013213","journal-title":"Can J Stat"},{"issue":"1","key":"1297_CR33","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1080\/03610918.2017.1381740","volume":"48","author":"GHA Pereira","year":"2019","unstructured":"Pereira GHA (2019) On quantile residuals in beta regression. Commun Stat-Simul Comput 48(1):302\u2013316","journal-title":"Commun Stat-Simul Comput"},{"key":"1297_CR34","unstructured":"PNUD (2009) Informe sobre desarrollo humano Per\u00fa 2009: por una densidad del Estado al servicio de la gente. Parte II: Una visi\u00f3n desde las cuencas. Programa de las Naciones Unidas para el Desarrollo. Lima, Peru"},{"issue":"4","key":"1297_CR35","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1111\/j.1467-9469.2008.00603.x","volume":"35","author":"Z Qiu","year":"2008","unstructured":"Qiu Z, Song PXG, Tan M (2008) Simplex mixed-effects models for longitudinal proportional data. Scand J Stat 35(4):577\u2013596","journal-title":"Scand J Stat"},{"key":"1297_CR36","unstructured":"R Core Team (2018) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria URL http:\/\/www.R-project.org\/"},{"issue":"3","key":"1297_CR37","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1207\/S15327906MBR3903_1","volume":"39","author":"WM Rogers","year":"2004","unstructured":"Rogers WM, Schmitt N (2004) Parameter recovery and model fit using multidimensional composites: A comparison of four empirical parceling algorithms. Multivar Behav Res 39(3):379\u2013412","journal-title":"Multivar Behav Res"},{"key":"1297_CR38","unstructured":"Stan Development Team (2014) RStan: the R interface to Stan, version 2.5.0 URL http:\/\/mc-stan.org\/rstan.html"},{"key":"1297_CR39","unstructured":"Stan Development Team (2021) Stan modeling language user\u2019s guide and reference manual, version 2.28 URL https:\/\/mc-stan.org\/docs\/2_28\/reference-manual\/index.html"},{"issue":"464","key":"1297_CR40","doi-asserted-by":"publisher","first-page":"1063","DOI":"10.1198\/01622145030000001007","volume":"98","author":"A Tsodikov","year":"2003","unstructured":"Tsodikov A, Ibrahim J, Yakovlev A (2003) Estimating cure rates from survival data: an alternative to two-component mixture models. J Am Stat Assoc 98(464):1063\u20131078","journal-title":"J Am Stat Assoc"},{"issue":"5","key":"1297_CR41","doi-asserted-by":"publisher","first-page":"1413","DOI":"10.1007\/s11222-016-9696-4","volume":"27","author":"A Vehtari","year":"2017","unstructured":"Vehtari A, Gelman A, Gabry J (2017) Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27(5):1413\u20131432","journal-title":"Stat Comput"},{"issue":"12","key":"1297_CR42","first-page":"3571","volume":"11","author":"S Watanabe","year":"2010","unstructured":"Watanabe S (2010) Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. J Mach Learn Res 11(12):3571\u20133594","journal-title":"J Mach Learn Res"},{"key":"1297_CR43","doi-asserted-by":"publisher","DOI":"10.1201\/9781420074086","volume-title":"Mixed effects models for complex data","author":"L Wu","year":"2009","unstructured":"Wu L (2009) Mixed effects models for complex data. Chapman and Hall\/CRC, Boca Raton, FL"},{"issue":"3","key":"1297_CR44","first-page":"331","volume":"52","author":"K Yu","year":"2003","unstructured":"Yu K, Lu Z, Stander J (2003) Quantile regression: applications and current research areas. J R Stat Soc Ser D (The Statistician) 52(3):331\u2013350","journal-title":"J R Stat Soc Ser D (The Statistician)"}],"container-title":["Computational Statistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-022-01297-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00180-022-01297-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-022-01297-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T12:44:25Z","timestamp":1751633065000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00180-022-01297-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,1]]},"references-count":44,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["1297"],"URL":"https:\/\/doi.org\/10.1007\/s00180-022-01297-2","relation":{},"ISSN":["0943-4062","1613-9658"],"issn-type":[{"value":"0943-4062","type":"print"},{"value":"1613-9658","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,1]]},"assertion":[{"value":"25 July 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 October 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 November 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}