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Yan X, Yu J, Ding W, Wang H, Zhao P. A novel two-way functional linear model with applications in human mortality data analysis. J Appl Stat 2023; 51:2025-2038. [PMID: 39071246 PMCID: PMC11271083 DOI: 10.1080/02664763.2023.2253379] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2023] [Accepted: 08/15/2023] [Indexed: 07/30/2024]
Abstract
Recently, two-way or longitudinal functional data analysis has attracted much attention in many fields. However, little is known on how to appropriately characterize the association between two-way functional predictor and scalar response. Motivated by a mortality study, in this paper, we propose a novel two-way functional linear model, where the response is a scalar and functional predictor is two-way trajectory. The model is intuitive, interpretable and naturally captures relationship between each way of two-way functional predictor and scalar-type response. Further, we develop a new estimation method to estimate the regression functions in the framework of weak separability. The main technical tools for the construction of the regression functions are product functional principal component analysis and iterative least square procedure. The solid performance of our method is demonstrated in extensive simulation studies. We also analyze the mortality dataset to illustrate the usefulness of the proposed procedure.
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Affiliation(s)
- Xingyu Yan
- School of Mathematics and Statistics and RIMS, Jiangsu Provincial Key Laboratory of Educational Big Data Science and Engineering, Jiangsu Normal University, Xuzhou, Jiangsu, People's Republic of China
| | - Jiaqian Yu
- School of Mathematics and Statistics and RIMS, Jiangsu Provincial Key Laboratory of Educational Big Data Science and Engineering, Jiangsu Normal University, Xuzhou, Jiangsu, People's Republic of China
| | - Weiyong Ding
- School of Mathematics and Statistics and RIMS, Jiangsu Provincial Key Laboratory of Educational Big Data Science and Engineering, Jiangsu Normal University, Xuzhou, Jiangsu, People's Republic of China
| | - Hao Wang
- School of Mathematics and Statistics, Anhui Normal University, Wuhu, People's Republic of China
| | - Peng Zhao
- School of Mathematics and Statistics and RIMS, Jiangsu Provincial Key Laboratory of Educational Big Data Science and Engineering, Jiangsu Normal University, Xuzhou, Jiangsu, People's Republic of China
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Metcalf O, Finlayson-Short L, Lamb KE, Zaloumis S, O’Donnell ML, Qian T, Varker T, Cowlishaw S, Brotman M, Forbes D. Ambulatory assessment to predict problem anger in trauma-affected adults: Study protocol. PLoS One 2022; 17:e0278926. [PMID: 36548307 PMCID: PMC9778625 DOI: 10.1371/journal.pone.0278926] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2022] [Accepted: 11/23/2022] [Indexed: 12/24/2022] Open
Abstract
BACKGROUND Problem anger is common after experiencing a traumatic event. Current evidence-driven treatment options are limited, and problem anger negatively affects an individual's capacity to engage with traditional psychological treatments. Smartphone interventions hold significant potential in mental health because of their ability to deliver low-intensity, precision support for individuals at the time and place they need it most. While wearable technology has the capacity to augment smartphone-delivered interventions, there is a dearth of evidence relating to several key areas, including feasibility of compliance in mental health populations; validity of in vivo anger assessment; ability to predict future mood states; and delivery of timely and appropriate interventions. METHODS This protocol describes a cohort study that leverages 10 days of ambulatory assessment in the form of ecological momentary assessment and a wearable. Approximately 100 adults with problem anger will complete four-hourly in vivo mobile application-delivered micro-surveys on anger intensity, frequency, and verbal and physical aggression, as well as other self-reported mental health and wellbeing measures. Concurrently, a commercial wearable device will continuously record indicators of physiological arousal. The aims are to test the feasibility and acceptability of ambulatory assessment in a trauma-affected population, and determine whether a continuously measured physiological indicator of stress predicts self-reported anger intensity. DISCUSSION This study will contribute new data around the ability of physiological indicators to predict mood state in individuals with psychopathology. This will have important implications for the design of smartphone-delivered interventions for trauma-affected individuals, as well as for the digital mental health field more broadly.
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Affiliation(s)
- Olivia Metcalf
- Department of Psychiatry, Phoenix Australia, University of Melbourne, Carlton, Victoria, Australia
| | - Laura Finlayson-Short
- Department of Psychiatry, Phoenix Australia, University of Melbourne, Carlton, Victoria, Australia
| | - Karen E. Lamb
- Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, University of Melbourne, Carlton, Victoria, Australia
| | - Sophie Zaloumis
- Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, University of Melbourne, Carlton, Victoria, Australia
| | - Meaghan L. O’Donnell
- Department of Psychiatry, Phoenix Australia, University of Melbourne, Carlton, Victoria, Australia
| | - Tianchen Qian
- Department of Statistics, University of California, Irvine, Irvine, California, United States of America
| | - Tracey Varker
- Department of Psychiatry, Phoenix Australia, University of Melbourne, Carlton, Victoria, Australia
| | - Sean Cowlishaw
- Department of Psychiatry, Phoenix Australia, University of Melbourne, Carlton, Victoria, Australia
| | - Melissa Brotman
- Neuroscience and Novel Therapeutics Unit, Emotion and Development Branch, National Institute of Mental Health, National Institutes of Health, Bethesda, Maryland, United States of America
| | - David Forbes
- Department of Psychiatry, Phoenix Australia, University of Melbourne, Carlton, Victoria, Australia
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Sun L, Wang K, Xu L, Zhang C, Balezentis T. A time-varying distance based interval-valued functional principal component analysis method – A case study of consumer price index. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2021.12.113] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Li T, Li T, Zhu Z, Zhu H. Regression Analysis of Asynchronous Longitudinal Functional and Scalar Data. J Am Stat Assoc 2020. [DOI: 10.1080/01621459.2020.1844211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Ting Li
- School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China
| | - Tengfei Li
- Department of Radiology and Biomedical Research Imaging Center (BRIC), University of North Carolina at Chapel Hill, Chapel Hill, NC
| | - Zhongyi Zhu
- Department of Statistics, Fudan University, Shanghai, China
| | - Hongtu Zhu
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC
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