{"title":"贝叶斯联合相对量子回归潜序多元线性模型在多方一致分析中的应用","authors":"YuZhu Tian, ChunHo Wu, ManLai Tang, MaoZai Tian","doi":"10.1007/s10182-024-00509-y","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we propose a Bayesian quantile regression (QR) approach to jointly model multivariate ordinal data. Firstly, a multivariate latent variable model is used to link the multivariate ordinal data and latent continuous responses and the multivariate asymmetric Laplace (MAL) distribution is employed to construct the joint QR-based working likelihood for the considered model. Secondly, adaptive-<span>\\(L_{1/2}\\)</span> penalization priors of regression parameters are incorporated into the working likelihood to implement high-dimensional Bayesian joint QR inference. Markov Chain Monte Carlo (MCMC) algorithm is utilized to derive the fully conditional posterior distributions of all parameters. Thirdly, Bayesian joint relatively QR estimation approach is recommended to result in more efficient estimation results. Finally, Monte Carlo simulation studies and a real instance analysis of multirater agreement data are presented to illustrate the performance of the proposed Bayesian joint relatively QR approach.</p>","PeriodicalId":55446,"journal":{"name":"Asta-Advances in Statistical Analysis","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bayesian joint relatively quantile regression of latent ordinal multivariate linear models with application to multirater agreement analysis\",\"authors\":\"YuZhu Tian, ChunHo Wu, ManLai Tang, MaoZai Tian\",\"doi\":\"10.1007/s10182-024-00509-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we propose a Bayesian quantile regression (QR) approach to jointly model multivariate ordinal data. Firstly, a multivariate latent variable model is used to link the multivariate ordinal data and latent continuous responses and the multivariate asymmetric Laplace (MAL) distribution is employed to construct the joint QR-based working likelihood for the considered model. Secondly, adaptive-<span>\\\\(L_{1/2}\\\\)</span> penalization priors of regression parameters are incorporated into the working likelihood to implement high-dimensional Bayesian joint QR inference. Markov Chain Monte Carlo (MCMC) algorithm is utilized to derive the fully conditional posterior distributions of all parameters. Thirdly, Bayesian joint relatively QR estimation approach is recommended to result in more efficient estimation results. Finally, Monte Carlo simulation studies and a real instance analysis of multirater agreement data are presented to illustrate the performance of the proposed Bayesian joint relatively QR approach.</p>\",\"PeriodicalId\":55446,\"journal\":{\"name\":\"Asta-Advances in Statistical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-08-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asta-Advances in Statistical Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10182-024-00509-y\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asta-Advances in Statistical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10182-024-00509-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
摘要
本文提出了一种贝叶斯量化回归(QR)方法,用于对多元序数数据进行联合建模。首先,使用多变量潜变量模型将多变量序数数据和潜连续响应联系起来,并使用多变量非对称拉普拉斯(MAL)分布为所考虑的模型构建基于 QR 的联合工作似然。其次,将回归参数的自适应-(L_{1/2}\) 惩罚先验纳入工作似然,以实现高维贝叶斯联合 QR 推理。利用马尔可夫链蒙特卡罗(MCMC)算法得出所有参数的全条件后验分布。第三,建议采用贝叶斯联合相对 QR 估计方法,以获得更高效的估计结果。最后,介绍了蒙特卡罗模拟研究和多方一致数据的真实实例分析,以说明所建议的贝叶斯联合相对 QR 方法的性能。
Bayesian joint relatively quantile regression of latent ordinal multivariate linear models with application to multirater agreement analysis
In this paper, we propose a Bayesian quantile regression (QR) approach to jointly model multivariate ordinal data. Firstly, a multivariate latent variable model is used to link the multivariate ordinal data and latent continuous responses and the multivariate asymmetric Laplace (MAL) distribution is employed to construct the joint QR-based working likelihood for the considered model. Secondly, adaptive-\(L_{1/2}\) penalization priors of regression parameters are incorporated into the working likelihood to implement high-dimensional Bayesian joint QR inference. Markov Chain Monte Carlo (MCMC) algorithm is utilized to derive the fully conditional posterior distributions of all parameters. Thirdly, Bayesian joint relatively QR estimation approach is recommended to result in more efficient estimation results. Finally, Monte Carlo simulation studies and a real instance analysis of multirater agreement data are presented to illustrate the performance of the proposed Bayesian joint relatively QR approach.
期刊介绍:
AStA - Advances in Statistical Analysis, a journal of the German Statistical Society, is published quarterly and presents original contributions on statistical methods and applications and review articles.