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The Application of Partially Functional Linear Regression Model in Health Science

Received: 30 September 2020     Published: 4 November 2020
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Abstract

With the rapid development of information technology, data information also presents the Characteristics of diversity. Meanwhile more and more datum are presented in the form of functions. Therefore, functional data has become the focus of researchers. Functional data analysis has also proved to be of great value in the fields of biology, medicine and metrology. A partially functional linear regression model is proposed for the regression cases in which the response variables are scalar types and the predictive variables are both variable types and functional types. For the functional predictive variables, we use the functional principal component analysis method to reduce the dimension of the functional data.The least square method is used to calculate the estimate of parameters.With the improvement of people's living standard, people pay more and more attention to health. And an increasing number of people are eager to live a healthy life and keep healthy. Healthy and comfortable sleep has become a topic of increasing concern to researchers. Using data from PhysioNet Databases on activity and sleep in healthy people for this study, we found that the predicted variables in the model could well explain the response variables. The application of partially functional linear model is further extended.

Published in Science Discovery (Volume 8, Issue 6)
DOI 10.11648/j.sd.20200806.13
Page(s) 134-138
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Functional Data, Partially Functional Linear Regression, Functional Principal Component Analysis, Health Science

References
[1] RAMSAY J O, When the data are functions [J]. Psychometriha, 1982, 47(4):379-396.
[2] Ramsay J O, Dalzell C J. Some tools for functional data analysis [J]. J Roy Statist Soc Ser B, 1991,53(3): 539-572.
[3] ZHANG D W, LIN X H, SOWERS M. Two-stage functional mixed models for evaluating the effect of longitudinal covariate profiles on a scalar outcome [J].Biometrics, 2007, 63(2):351-362.
[4] SHIN H. Partial functional linear regression [J].Journal of Statistical Planning and inference, 2009, 139(10):3405-3418.
[5] SHIN H, LEE M H. On prediction rate in partial functional linear regression [J]. J Multivariate Anal, 2012, 103(1):93-106.
[6] YU P, ZHANG Z Z, DU J. A test of linearity in partial functional linear regression[J].Metriha, 2016, 79(8):953-969.
[7] FAN J Q, ZHANG C M, ZHANG, J. Generalized likelihood ratio statistics and wilkes phenomenon [J].The Aririals of Statistics, 2001, 29(1):153-193.
[8] LU Y, DU J, SUN 2 M. Functional partially linear quantile regression model [J].Metriha, 2014, 77(2):317-332.
[9] LI T F, XIE F C, FEND X N, et al. Functional linear regression model for nonig-norable missing scalar responses[J].Statistics Sinica, 2018, 28(4):1867-1886.
[10] HSING T, EUBANK R L. Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators [M].John Wiley & Sons, 2015.
[11] H.-G. MÜLLER, U. STADTMÜLLER. Generalized Functional Linear Models [J]. The Annals of Statistics, 2005, 33(2):774–805.
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[14] Carver CS, White TL. "Behavioural inhibition, behavioural activation, and affective responses to impending reward and punishment: The BIS/BAS Scales". J Pers Soc Psychol. 1994,67: 319–333.
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    Weiwei Xiao, Yixuan Wang. (2020). The Application of Partially Functional Linear Regression Model in Health Science. Science Discovery, 8(6), 134-138. https://doi.org/10.11648/j.sd.20200806.13

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    ACS Style

    Weiwei Xiao; Yixuan Wang. The Application of Partially Functional Linear Regression Model in Health Science. Sci. Discov. 2020, 8(6), 134-138. doi: 10.11648/j.sd.20200806.13

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    AMA Style

    Weiwei Xiao, Yixuan Wang. The Application of Partially Functional Linear Regression Model in Health Science. Sci Discov. 2020;8(6):134-138. doi: 10.11648/j.sd.20200806.13

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  • @article{10.11648/j.sd.20200806.13,
      author = {Weiwei Xiao and Yixuan Wang},
      title = {The Application of Partially Functional Linear Regression Model in Health Science},
      journal = {Science Discovery},
      volume = {8},
      number = {6},
      pages = {134-138},
      doi = {10.11648/j.sd.20200806.13},
      url = {https://doi.org/10.11648/j.sd.20200806.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sd.20200806.13},
      abstract = {With the rapid development of information technology, data information also presents the Characteristics of diversity. Meanwhile more and more datum are presented in the form of functions. Therefore, functional data has become the focus of researchers. Functional data analysis has also proved to be of great value in the fields of biology, medicine and metrology. A partially functional linear regression model is proposed for the regression cases in which the response variables are scalar types and the predictive variables are both variable types and functional types. For the functional predictive variables, we use the functional principal component analysis method to reduce the dimension of the functional data.The least square method is used to calculate the estimate of parameters.With the improvement of people's living standard, people pay more and more attention to health. And an increasing number of people are eager to live a healthy life and keep healthy. Healthy and comfortable sleep has become a topic of increasing concern to researchers. Using data from PhysioNet Databases on activity and sleep in healthy people for this study, we found that the predicted variables in the model could well explain the response variables. The application of partially functional linear model is further extended.},
     year = {2020}
    }
    

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    T1  - The Application of Partially Functional Linear Regression Model in Health Science
    AU  - Weiwei Xiao
    AU  - Yixuan Wang
    Y1  - 2020/11/04
    PY  - 2020
    N1  - https://doi.org/10.11648/j.sd.20200806.13
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    JO  - Science Discovery
    SP  - 134
    EP  - 138
    PB  - Science Publishing Group
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    AB  - With the rapid development of information technology, data information also presents the Characteristics of diversity. Meanwhile more and more datum are presented in the form of functions. Therefore, functional data has become the focus of researchers. Functional data analysis has also proved to be of great value in the fields of biology, medicine and metrology. A partially functional linear regression model is proposed for the regression cases in which the response variables are scalar types and the predictive variables are both variable types and functional types. For the functional predictive variables, we use the functional principal component analysis method to reduce the dimension of the functional data.The least square method is used to calculate the estimate of parameters.With the improvement of people's living standard, people pay more and more attention to health. And an increasing number of people are eager to live a healthy life and keep healthy. Healthy and comfortable sleep has become a topic of increasing concern to researchers. Using data from PhysioNet Databases on activity and sleep in healthy people for this study, we found that the predicted variables in the model could well explain the response variables. The application of partially functional linear model is further extended.
    VL  - 8
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Author Information
  • School of Science, North China University of Technology, Beijing, China

  • School of Science, North China University of Technology, Beijing, China

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