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Functional Generalized Structured Component Analysis

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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.

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Notes

  1. This means that the chosen smoothing parameter values might have been suboptimal for the other 99 data sets. Therefore, the simulation results may be a bit conservative in the sense that the results would be better if the smoothing parameters have been chosen for every data set optimally.

  2. This is the ID of the patient used in the PhysioNet website.

  3. The original GSCA broke down when we used more than 15 equally spaced percentage occasions due to the high correlations between the responses evaluated at adjacent percentage occasions. Therefore, we ended up evaluating the mean curves at 14 percentage occasions.

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Acknowledgments

The authors are very grateful for the insightful and constructive comments made by the associate editor and three anonymous reviewers that have greatly improved the paper. The work of the first author was supported by the National Institute On Drug Abuse of the National Institutes of Health under Award Number R01DA009757.

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Authors and Affiliations

  1. Department of Psychology, Arizona State University, 950 S. McAllister, BOX 871104, Tempe, AZ, 85287-1104 , USA

    Hye Won Suk

  2. McGill University, Montreal, QC, Canada

    Heungsun Hwang

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  1. Hye Won Suk
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  2. Heungsun Hwang
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Correspondence to Hye Won Suk.

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Suk, H.W., Hwang, H. Functional Generalized Structured Component Analysis. Psychometrika 81, 940–968 (2016). https://doi.org/10.1007/s11336-016-9521-1

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