IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v81y2016i4d10.1007_s11336-016-9521-1.html
   My bibliography  Save this article

Functional Generalized Structured Component Analysis

Author

Listed:
  • Hye Won Suk

    (Arizona State University)

  • Heungsun Hwang

    (McGill University)

Abstract

An extension of Generalized Structured Component Analysis (GSCA), called Functional GSCA, is proposed to analyze functional data that are considered to arise from an underlying smooth curve varying over time or other continua. GSCA has been geared for the analysis of multivariate data. Accordingly, it cannot deal with functional data that often involve different measurement occasions across participants and a large number of measurement occasions that exceed the number of participants. Functional GSCA addresses these issues by integrating GSCA with spline basis function expansions that represent infinite-dimensional curves onto a finite-dimensional space. For parameter estimation, functional GSCA minimizes a penalized least squares criterion by using an alternating penalized least squares estimation algorithm. The usefulness of functional GSCA is illustrated with gait data.

Suggested Citation

  • Hye Won Suk & Heungsun Hwang, 2016. "Functional Generalized Structured Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 940-968, December.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:4:d:10.1007_s11336-016-9521-1
    DOI: 10.1007/s11336-016-9521-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-016-9521-1
    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/s11336-016-9521-1?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Forrest Young & Jan Leeuw & Yoshio Takane, 1976. "Regression with qualitative and quantitative variables: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 505-529, December.
    2. Heungsun Hwang & Wayne Desarbo & Yoshio Takane, 2007. "Fuzzy Clusterwise Generalized Structured Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 181-198, June.
    3. Heungsun Hwang & Hye Suk & Yoshio Takane & Jang-Han Lee & Jooseop Lim, 2015. "Generalized Functional Extended Redundancy Analysis," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 101-125, March.
    4. Heungsun Hwang & Kwanghee Jung & Yoshio Takane & Todd Woodward, 2012. "Functional Multiple-Set Canonical Correlation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 77(1), pages 48-64, January.
    5. Heungsun Hwang & Hye Suk & Jang-Han Lee & D. Moskowitz & Jooseop Lim, 2012. "Functional Extended Redundancy Analysis," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 524-542, July.
    6. Heungsun Hwang & Yoshio Takane, 2004. "Generalized structured component analysis," Psychometrika, Springer;The Psychometric Society, vol. 69(1), pages 81-99, March.
    7. Jan Leeuw & Forrest Young & Yoshio Takane, 1976. "Additive structure in qualitative data: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 471-503, December.
    8. Martin A. Lindquist, 2012. "Functional Causal Mediation Analysis With an Application to Brain Connectivity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1297-1309, December.
    Full references (including those not matched with items on IDEAS)

    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. Zhou, Lixing & Takane, Yoshio & Hwang, Heungsun, 2016. "Dynamic GSCANO (Generalized Structured Canonical Correlation Analysis) with applications to the analysis of effective connectivity in functional neuroimaging data," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 93-109.
    2. Seohee Park & Seongeun Kim & Ji Hoon Ryoo, 2020. "Latent Class Regression Utilizing Fuzzy Clusterwise Generalized Structured Component Analysis," Mathematics, MDPI, vol. 8(11), pages 1-16, November.
    3. Heungsun Hwang & Moon-Ho Ho & Jonathan Lee, 2010. "Generalized Structured Component Analysis with Latent Interactions," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 228-242, June.
    4. Kwanghee Jung & Yoshio Takane & Heungsun Hwang & Todd Woodward, 2012. "Dynamic GSCA (Generalized Structured Component Analysis) with Applications to the Analysis of Effective Connectivity in Functional Neuroimaging Data," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 827-848, October.
    5. Minjung Kyung & Ju-Hyun Park & Ji Yeh Choi, 2022. "Bayesian Mixture Model of Extended Redundancy Analysis," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 946-966, September.
    6. Gyeongcheol Cho & Heungsun Hwang & Marko Sarstedt & Christian M. Ringle, 2020. "Cutoff criteria for overall model fit indexes in generalized structured component analysis," Journal of Marketing Analytics, Palgrave Macmillan, vol. 8(4), pages 189-202, December.
    7. Heungsun Hwang & Gyeongcheol Cho, 2020. "Global Least Squares Path Modeling: A Full-Information Alternative to Partial Least Squares Path Modeling," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 947-972, December.
    8. Tianyu Tan & Hye Suk & Heungsun Hwang & Jooseop Lim, 2013. "Functional fuzzy clusterwise regression analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(1), pages 57-82, March.
    9. Kadziński, MiŁosz & Greco, Salvatore & SŁowiński, Roman, 2012. "Extreme ranking analysis in robust ordinal regression," Omega, Elsevier, vol. 40(4), pages 488-501.
    10. van Rosmalen, J.M. & Koning, A.J. & Groenen, P.J.F., 2007. "Optimal Scaling of Interaction Effects in Generalized Linear Models," Econometric Institute Research Papers EI 2007-44, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Michio Yamamoto, 2012. "Clustering of functional data in a low-dimensional subspace," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 6(3), pages 219-247, October.
    12. Stéphanie Bougeard & Hervé Abdi & Gilbert Saporta & Ndèye Niang, 2018. "Clusterwise analysis for multiblock component methods," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(2), pages 285-313, June.
    13. Takane, Yoshio, 2016. "My Early Interactions with Jan and Some of His Lost Papers," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 73(i07).
    14. John C. Gower & Sugnet Gardner-Lubbe & Niel J. Le Roux, 2018. "Interaction: Fisher’s Optimal Scores Revisited," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(1), pages 92-112, March.
    15. Maria Giovanna Onorati & Francesco D. d’Ovidio & Laura Antonucci, 2017. "Cultural displacement as a lever to global-ready student profiles: results from a longitudinal study on International Lifelong Learning Programs (LLP)," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 545-563, March.
    16. Bolton, Patrick & Li, Tao & Ravina, Enrichetta & Rosenthal, Howard, 2020. "Investor ideology," Journal of Financial Economics, Elsevier, vol. 137(2), pages 320-352.
    17. Lukáš Sobíšek & Hana Řezanková, 2011. "Comparison of Dimensionality Reduction Methods Applied to Ordinal Variables [Srovnání metod pro redukci dimenzionality aplikovaných na ordinální proměnné]," Acta Oeconomica Pragensia, Prague University of Economics and Business, vol. 2011(1), pages 3-19.
    18. Florian Pargent & Florian Pfisterer & Janek Thomas & Bernd Bischl, 2022. "Regularized target encoding outperforms traditional methods in supervised machine learning with high cardinality features," Computational Statistics, Springer, vol. 37(5), pages 2671-2692, November.
    19. John C. Gower & Niël J. Le Roux & Sugnet Gardner-Lubbe, 2022. "Properties of individual differences scaling and its interpretation," Statistical Papers, Springer, vol. 63(4), pages 1221-1245, August.
    20. Berry, Michael W. & Browne, Murray & Langville, Amy N. & Pauca, V. Paul & Plemmons, Robert J., 2007. "Algorithms and applications for approximate nonnegative matrix factorization," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 155-173, September.

    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:psycho:v:81:y:2016:i:4:d:10.1007_s11336-016-9521-1. 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.