Functional Concurrent Regression Mixture Models Using Spiked Ewens-Pitman Attraction Priors.

IF 4.9 2区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Bayesian Analysis Pub Date : 2024-12-01 Epub Date: 2023-05-02 DOI:10.1214/23-ba1380
Mingrui Liang, Matthew D Koslovsky, Emily T Hébert, Michael S Businelle, Marina Vannucci
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引用次数: 0

Abstract

Functional concurrent, or varying-coefficient, regression models are a form of functional data analysis methods in which functional covariates and outcomes are collected concurrently. Two active areas of research for this class of models are identifying influential functional covariates and clustering their relations across observations. In various applications, researchers have applied and developed methods to address these objectives separately. However, no approach currently performs both tasks simultaneously. In this paper, we propose a fully Bayesian functional concurrent regression mixture model that simultaneously performs functional variable selection and clustering for subject-specific trajectories. Our approach introduces a novel spiked Ewens-Pitman attraction prior that identifies and clusters subjects' trajectories marginally for each functional covariate while using similarities in subjects' auxiliary covariate patterns to inform clustering allocation. Using simulated data, we evaluate the clustering, variable selection, and parameter estimation performance of our approach and compare its performance with alternative spiked processes. We then apply our method to functional data collected in a novel, smartphone-based smoking cessation intervention study to investigate individual-level dynamic relations between smoking behaviors and potential risk factors.

使用尖刺Ewens-Pitman吸引先验的功能并发回归混合模型
功能并发或变化系数回归模型是功能数据分析方法的一种形式,其中功能协变量和结果是同时收集的。这类模型的两个活跃研究领域是识别有影响的功能协变量和聚类它们在各观测值之间的关系。在各种应用中,研究人员已经应用和开发了一些方法来分别实现这些目标。然而,目前还没有一种方法能同时完成这两项任务。在本文中,我们提出了一种完全贝叶斯的功能并发回归混合模型,该模型可同时对特定受试者的轨迹进行功能变量选择和聚类。我们的方法引入了一种新颖的穗状 Ewens-Pitman 吸引先验,可识别和聚类每个功能协变量的受试者轨迹,同时利用受试者辅助协变量模式的相似性为聚类分配提供信息。通过模拟数据,我们评估了我们的方法在聚类、变量选择和参数估计方面的性能,并将其与其他尖峰过程进行了比较。然后,我们将我们的方法应用于一项基于智能手机的新型戒烟干预研究中收集的功能数据,以调查吸烟行为与潜在风险因素之间的个体水平动态关系。
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来源期刊
Bayesian Analysis
Bayesian Analysis 数学-数学跨学科应用
CiteScore
6.50
自引率
13.60%
发文量
59
审稿时长
>12 weeks
期刊介绍: Bayesian Analysis is an electronic journal of the International Society for Bayesian Analysis. It seeks to publish a wide range of articles that demonstrate or discuss Bayesian methods in some theoretical or applied context. The journal welcomes submissions involving presentation of new computational and statistical methods; critical reviews and discussions of existing approaches; historical perspectives; description of important scientific or policy application areas; case studies; and methods for experimental design, data collection, data sharing, or data mining. Evaluation of submissions is based on importance of content and effectiveness of communication. Discussion papers are typically chosen by the Editor in Chief, or suggested by an Editor, among the regular submissions. In addition, the Journal encourages individual authors to submit manuscripts for consideration as discussion papers.
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