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Functional Generalized Structured Component Analysis

Published online by Cambridge University Press:  01 January 2025

Hye Won Suk  and
Heungsun Hwang
Hye Won Suk*
Affiliation:
Arizona State University
Heungsun Hwang
Affiliation:
McGill University
*
Correspondence should be made to Hye Won Suk, Department of Psychology, Arizona State University, 950 S. McAllister, BOX 871104, Tempe, AZ 85287-1104 USA. Email: Hyewon.Suk@asu.edu
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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.

Keywords

generalized structured component analysisfunctional data analysisbasis function expansionsplinespenalized least squaresalternating least squares
Type
Article
Information
Psychometrika , Volume 81 , Issue 4 , December 2016 , pp. 940 - 968
Copyright
Copyright © 2016 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (doi:10.1007/s11336-016-9521-1) contains supplementary material, which is available to authorized users.

References

Abdi, H., Lewis-Beck, M., Bryman, A., Futing, T. (2003). Partial least squares (PLS) regression. Encyclopedia for research methods for the social sciences, Thousand Oaks, CA: Sage. 792–795.Google Scholar
Byrd, R., Bilbert, J. C., Nocedal, J. (2000). A Trust Region Method Based on Interior Point Techniques for Nonlinear Programming. Mathematical Programming A, 89, 149–185.CrossRefGoogle Scholar
Byrd, R. H., Hribar, M. E., Nocedal, J. (1999). An interior point algorithm for large scale nonlinear programming. SIAM Journal of Optimization, 9, 877–900.CrossRefGoogle Scholar
Craven, P., Wahba, G. (1979). (2001). Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation. Numerische Mathematik, 31, 377–403.CrossRefGoogle Scholar
De Boor, C. A practical guide to splines, New York: Springer.CrossRefGoogle Scholar
de De Leeuw, J., Young, F. W., Takane, Y. (1976). (1993). (1982). Additive structure in qualitative data: An alternating least squares method with optimal scaling features. Psychometrika, 41 (4), 471–503.CrossRefGoogle Scholar
Dierckx, P. Curve and surface fitting with splines, Oxford: Clarendon.CrossRefGoogle Scholar
Efron, B. The jackknife, the bootstrap, and other resampling plans, Philadelphia: Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
Eilers, PHC, Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11 (2), 89–102.CrossRefGoogle Scholar
Fahn, S., Elton, R. L., & Members of the UPDRS Development Committee Fahn, S., Marsden, D., Calne, D., Goldstein, M. (1987). (2006). Unified Parkinson’s disease rating scale. Recent development in Parkinson’s disease, MacMillan Healthcare Information: Florham Park, NJ.Google Scholar
Ferraty, F., Vieu, P. Nonparametric functional data analysis theory and practice, New York: Springer.Google Scholar
Frenkel-Toledo, S., Giladi, N., Peretz, C., Herman, T., Gruendlinger, L., Hausdorff, J. M. (2005). Treadmill walking as an external pacemaker to improve gait rhythm and stability in Parkinson’s disease. Movement Disorder, 20 (9), 1109–1114.CrossRefGoogle Scholar
Goldberger, A. L., Amaral, LAN, Glass, L., Hausdorff, J. M., Ivanov, P. C., Mark, R. G. et al. (2000). PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals. Circulation, 101, e215–e220.CrossRefGoogle ScholarPubMed
Hastie, T., Tibshirani, R. (1993). (2009). Varying-coefficient models. Journal of the Royal Statistical Society. Series B (Methodological), 55 (4), 757–796.CrossRefGoogle Scholar
Hastie, T., Tibshirani, R., Friedman, J. H. The elements of statistical learning data mining, inference, and prediction, New York: Springer.Google Scholar
Hausdorff, J. M., Lowenthal, J., Herman, T., Gruendlinger, L., Peretz, C., Giladi, N. (2005). Rhythmic auditory stimulation modulates gait variability in Parkinson’s disease. European Journal of Neuroscience, 26, 2369–2375.CrossRefGoogle Scholar
Hoehn, M. M., Yahr, M. D. (1967). Parkinsonism: Onset, progression and mortality. Neurology, 17 (5), 427–442.CrossRefGoogle Scholar
Hwang, H., DeSarbo, W. S., Takane, Y. (2007). Fuzzy Clusterwise Generalized Structured Component Analysis. Psychometrika, 72 (2), 181–198.CrossRefGoogle Scholar
Hwang, H., Jung, K., Takane, Y., Woodward, T. (2012). Functional multiple-set canonical correlation analysis. Psychometrika, 77, 48–64.CrossRefGoogle Scholar
Hwang, H., Suk, H. W., Lee, J.- H., Moskowitz, D. S., Lim, J. (2012). Functional extended redundancy analysis. Psychometrika, 77, 524–542.CrossRefGoogle ScholarPubMed
Hwang, H., Suk, H. W., Takane, Y., Lee, J.- H., Lim, J. (2015). Generalized functional extended redundancy analysis. Psychometrika, 80, 101–125.CrossRefGoogle ScholarPubMed
Hwang, H., Takane, Y. (2004). Generalized structured component analysis. Psychometrika, 69 (1), 81–99.CrossRefGoogle Scholar
Hwang, H., Takane, Y., Malhotra, N. (2007). Multilevel Generalized Structured Component Analysis. Behaviormetrika, 34 (2), 95–109.CrossRefGoogle Scholar
Jackson, I., Sirois, S. (2009). Infant cognition: Going full factorial with pupil dilation. Developmental science, 12 (4), 670–679.CrossRefGoogle ScholarPubMed
Li, R., Root, T. L., Shiffman, S., Walls, T. A., Schafer, J. L. (2006). A local linear estimation procedure for functional multilevel modeling. Models for intensive longitudinal data, New York: Oxford University Press. 63–83.CrossRefGoogle Scholar
Lindquist, M. A. (2012). Functional causal mediation analysis with an application to brain connectivity. Journal of the American Statistical Association, 107 (500), 1297–1309.CrossRefGoogle ScholarPubMed
Mattar, AAG, Ostry, D. J. (2010). (1971). Generalization of dynamics learning across changes in movement amplitude. Journal of Neurophysiology, 104 (1), 426–438.CrossRefGoogle ScholarPubMed
Mulaik, S. A. The foundations of factor analysis, New York: McGraw-Hill.CrossRefGoogle Scholar
Ormoneit, D., Black, M. J., Hastie, T., Kjellström, H. (2005). Representing cyclic human motion using functional analysis. Image and Vision Computing, 23 (14), 1264–1276.CrossRefGoogle Scholar
Park, K. K., Suk, H. W., Hwang, H., Lee, J.- H. (2013). A functional analysis of deception detection of a mock crime using infrared thermal imaging and the Concealed Information Test. Frontiers in Human Neuroscience, 7, 70CrossRefGoogle ScholarPubMed
Podsiadlo, D., Richardson, S. (1991). The timed up & go: A test of basic functional mobility for frail elderly persons. Journal of the American Geriatrics Society, 39 (2), 142–148.CrossRefGoogle Scholar
Ramsay, J. O., Dalzell, C. J. (1991). (2009). (2005). Some tools for functional data analysis. Journal of the Royal Statistical Society: Series B (Methodological), 53 (3), 539–572.CrossRefGoogle Scholar
Ramsay, J. O., Hooker, G., Graves, S. Functional data analysis with R and MATLAB, New York: Springer.CrossRefGoogle Scholar
Ramsay, J. O., Silverman, B. W. Functional data analysis, New York: Springer.Google Scholar
Tan, X., Shiyko, M. P., Li, R., Li, Y., Dierker, L. (2012). A time-varying effect model for intensive longitudinal data. Psychological Methods, 17 (1), 61–77.CrossRefGoogle ScholarPubMed
Tian, T. S. (2010). Functional data analysis in brain imaging studies. Frontiers in Psychology, 1, 35CrossRefGoogle ScholarPubMed
Tucker, L. R. (1951). A method for synthesis of factor analysis studies (Personnel Research Section Report No. 984). Washington: Department of the Army.CrossRefGoogle Scholar
Vines, B. W., Krumhansl, C. L., Wanderley, M. M., Levitin, D. J. (2006). Cross-modal interactions in the perception of musical performance. Cognition, 101 (1), 80–113.CrossRefGoogle ScholarPubMed
Wiesner, M., Windle, M. (2004). Assessing covariates of adolescent delinquency trajectories: A latent growth mixture modeling approach. Journal of Youth and Adolescence, 33, 431–442.CrossRefGoogle Scholar
Yogev, G., Giladi, N., Peretz, C., Springer, S., Simon, E. S., Hausdorff, J. M. (2005). (2013). (1996). Dual tasking, gait rhythmicity, and Parkinson’s disease: which aspects of gait are attention demanding?. The European journal of neuroscience, 22 (5), 1248–1256.CrossRefGoogle ScholarPubMed
Zhang, J.- T. Analysis of variance for functional data, Boca Raton, FL: CRC Press.CrossRefGoogle Scholar
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