IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v40y2025i4d10.1007_s00180-024-01591-1.html
   My bibliography  Save this article

Analysing kinematic data from recreational runners using functional data analysis

Author

Listed:
  • Edward Gunning

    (University of Limerick)

  • Steven Golovkine

    (University of Limerick)

  • Andrew J. Simpkin

    (University of Galway)

  • Aoife Burke

    (Dublin City University)

  • Sarah Dillon

    (Dublin City University
    University of Limerick)

  • Shane Gore

    (Dublin City University
    Dublin City University)

  • Kieran Moran

    (Dublin City University
    Dublin City University)

  • Siobhan O’Connor

    (Dublin City University)

  • Enda White

    (Dublin City University)

  • Norma Bargary

    (University of Limerick)

Abstract

We present a multivariate functional mixed effects model for kinematic data from a large number of recreational runners. The runners’ sagittal plane hip and knee angles are modelled jointly as a bivariate function with random effects functions accounting for the dependence among bilateral measurements. The model is fitted by applying multivariate functional principal component analysis (mv-FPCA) and modelling the mv-FPCA scores using scalar linear mixed effects models. Simulation and bootstrap approaches are introduced to construct simultaneous confidence bands for the fixed effects functions, and covariance functions are reconstructed to summarise the variability structure in the data and thoroughly investigate the suitability of the proposed model. In our scientific application, we observe a statistically significant effect of running speed on both joints. We observe strong within-subject correlations, reflecting the highly idiosyncratic nature of running technique. Our approach is applicable to modelling multiple streams of smooth biomechanical data collected in complex experimental designs.

Suggested Citation

  • Edward Gunning & Steven Golovkine & Andrew J. Simpkin & Aoife Burke & Sarah Dillon & Shane Gore & Kieran Moran & Siobhan O’Connor & Enda White & Norma Bargary, 2025. "Analysing kinematic data from recreational runners using functional data analysis," Computational Statistics, Springer, vol. 40(4), pages 1825-1847, April.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:4:d:10.1007_s00180-024-01591-1
    DOI: 10.1007/s00180-024-01591-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-024-01591-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-024-01591-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Bates, Douglas & Mächler, Martin & Bolker, Ben & Walker, Steve, 2015. "Fitting Linear Mixed-Effects Models Using lme4," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 67(i01).
    2. Simon N. Wood, 2011. "Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 3-36, January.
    3. Jiang, Jiakun & Lin, Huazhen & Zhong, Qingzhi & Li, Yi, 2022. "Analysis of multivariate non-gaussian functional data: A semiparametric latent process approach," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    4. Wonyul Lee & Michelle F. Miranda & Philip Rausch & Veerabhadran Baladandayuthapani & Massimo Fazio & J. Crawford Downs & Jeffrey S. Morris, 2019. "Bayesian Semiparametric Functional Mixed Models for Serially Correlated Functional Data, With Application to Glaucoma Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 495-513, April.
    5. Tomasz Górecki & Mirosław Krzyśko & Łukasz Waszak & Waldemar Wołyński, 2018. "Selected statistical methods of data analysis for multivariate functional data," Statistical Papers, Springer, vol. 59(1), pages 153-182, March.
    6. Paul Pao-Yen Wu & Nicholas Sterkenburg & Kirsten Everett & Dale W Chapman & Nicole White & Kerrie Mengersen, 2019. "Predicting fatigue using countermovement jump force-time signatures: PCA can distinguish neuromuscular versus metabolic fatigue," PLOS ONE, Public Library of Science, vol. 14(7), pages 1-16, July.
    7. Wensheng Guo, 2002. "Functional Mixed Effects Models," Biometrics, The International Biometric Society, vol. 58(1), pages 121-128, March.
    8. Diquigiovanni, Jacopo & Fontana, Matteo & Vantini, Simone, 2022. "Conformal prediction bands for multivariate functional data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    9. Jeffrey S. Morris & Raymond J. Carroll, 2006. "Wavelet‐based functional mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 179-199, April.
    10. Zhu, Tianming & Zhang, Jin-Ting & Cheng, Ming-Yen, 2022. "One-way MANOVA for functional data via Lawley–Hotelling trace test," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    11. John A. D. Aston & Jeng‐Min Chiou & Jonathan P. Evans, 2010. "Linguistic pitch analysis using functional principal component mixed effect models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 297-317, March.
    12. Steffen Fieuws & Geert Verbeke, 2006. "Pairwise Fitting of Mixed Models for the Joint Modeling of Multivariate Longitudinal Profiles," Biometrics, The International Biometric Society, vol. 62(2), pages 424-431, June.
    13. P. Z. Hadjipantelis & J. A. D. Aston & H. G. Müller & J. P. Evans, 2015. "Unifying Amplitude and Phase Analysis: A Compositional Data Approach to Functional Multivariate Mixed-Effects Modeling of Mandarin Chinese," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 545-559, June.
    14. Jeff Goldsmith & Tomoko Kitago, 2016. "Assessing systematic effects of stroke on motor control by using hierarchical function-on-scalar regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(2), pages 215-236, February.
    15. Marcos Matabuena & Marta Karas & Sherveen Riazati & Nick Caplan & Philip R. Hayes, 2023. "Estimating Knee Movement Patterns of Recreational Runners Across Training Sessions Using Multilevel Functional Regression Models," The American Statistician, Taylor & Francis Journals, vol. 77(2), pages 169-181, April.
    16. Ruonan Li & Luo Xiao, 2023. "Latent factor model for multivariate functional data," Biometrics, The International Biometric Society, vol. 79(4), pages 3307-3318, December.
    17. Zhu, Hongxiao & Morris, Jeffrey S. & Wei, Fengrong & Cox, Dennis D., 2017. "Multivariate functional response regression, with application to fluorescence spectroscopy in a cervical pre-cancer study," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 88-101.
    18. Golovkine, Steven & Klutchnikoff, Nicolas & Patilea, Valentin, 2022. "Clustering multivariate functional data using unsupervised binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    19. J. Fan & J.‐T. Zhang, 2000. "Two‐step estimation of functional linear models with applications to longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 303-322.
    20. Clara Happ & Sonja Greven, 2018. "Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 649-659, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pierpaolo D’Urso & Michele Gallo & Paola Zuccolotto, 2025. "Editorial: special issue on sports data science," Computational Statistics, Springer, vol. 40(4), pages 1683-1688, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Kan & Luo, Sheng, 2019. "Bayesian functional joint models for multivariate longitudinal and time-to-event data," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 14-29.
    2. Reiss Philip T. & Huang Lei & Mennes Maarten, 2010. "Fast Function-on-Scalar Regression with Penalized Basis Expansions," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-30, August.
    3. Øystein Sørensen & Anders M. Fjell & Kristine B. Walhovd, 2023. "Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 456-486, June.
    4. Qiu, Zhiping & Fan, Jiangyuan & Zhang, Jin-Ting & Chen, Jianwei, 2024. "Tests for equality of several covariance matrix functions for multivariate functional data," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    5. Chau, Van Vinh & von Sachs, Rainer, 2016. "Functional mixed effects wavelet estimation for spectra of replicated time series," LIDAM Discussion Papers ISBA 2016013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Lin Zhang & Veerabhadran Baladandayuthapani & Hongxiao Zhu & Keith A. Baggerly & Tadeusz Majewski & Bogdan A. Czerniak & Jeffrey S. Morris, 2016. "Functional CAR Models for Large Spatially Correlated Functional Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 772-786, April.
    7. Zhang, Xiaoke & Zhong, Qixian & Wang, Jane-Ling, 2020. "A new approach to varying-coefficient additive models with longitudinal covariates," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    8. Ana-Maria Staicu & Yingxing Li & Ciprian M. Crainiceanu & David Ruppert, 2014. "Likelihood Ratio Tests for Dependent Data with Applications to Longitudinal and Functional Data Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 932-949, December.
    9. John A. D. Aston & Jeng‐Min Chiou & Jonathan P. Evans, 2010. "Linguistic pitch analysis using functional principal component mixed effect models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 297-317, March.
    10. Hongxiao Zhu & Philip J. Brown & Jeffrey S. Morris, 2012. "Robust Classification of Functional and Quantitative Image Data Using Functional Mixed Models," Biometrics, The International Biometric Society, vol. 68(4), pages 1260-1268, December.
    11. Niels Lundtorp Olsen & Bo Markussen & Lars Lau Raket, 2018. "Simultaneous inference for misaligned multivariate functional data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1147-1176, November.
    12. Devin Kirk & Samantha Straus & Marissa L Childs & Mallory Harris & Lisa Couper & T Jonathan Davies & Coreen Forbes & Alyssa-Lois Gehman & Maya L Groner & Christopher Harley & Kevin D Lafferty & Van Sa, 2024. "Temperature impacts on dengue incidence are nonlinear and mediated by climatic and socioeconomic factors: A meta-analysis," PLOS Climate, Public Library of Science, vol. 3(3), pages 1-18, March.
    13. Philipp F. M. Baumann & Enzo Rossi & Alexander Volkmann, 2020. "What Drives Inflation and How: Evidence from Additive Mixed Models Selected by cAIC," Papers 2006.06274, arXiv.org, revised Aug 2022.
    14. Aranya Koshy & Shahin Tavakoli, 2022. "Exploring British accents: Modelling the trap–bath split with functional data analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(4), pages 773-805, August.
    15. Haixu Wang & Jiguo Cao, 2023. "Nonlinear prediction of functional time series," Environmetrics, John Wiley & Sons, Ltd., vol. 34(5), August.
    16. Tapabrata Maiti & Samiran Sinha & Ping-Shou Zhong, 2016. "Functional Mixed Effects Model for Small Area Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 886-903, September.
    17. Yiqiang Lu & Riquan Zhang, 2009. "Smoothing spline estimation of generalised varying-coefficient mixed model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(7), pages 815-825.
    18. Chen, Ziqi & Hu, Jianhua & Zhu, Hongtu, 2020. "Surface functional models," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    19. Matthew Reimherr & Dan Nicolae, 2016. "Estimating Variance Components in Functional Linear Models With Applications to Genetic Heritability," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 407-422, March.
    20. Nolan, Tui H. & Richardson, Sylvia & Ruffieux, Hélène, 2025. "Efficient Bayesian functional principal component analysis of irregularly-observed multivariate curves," Computational Statistics & Data Analysis, Elsevier, vol. 203(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:40:y:2025:i:4:d:10.1007_s00180-024-01591-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.