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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Heungsun Hwang & Yoshio Takane, 2004. "Generalized structured component analysis," Psychometrika, Springer;The Psychometric Society, vol. 69(1), pages 81-99, March.
    8. 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.
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