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Functional Parallel Factor Analysis for Functions of One- and Two-dimensional Arguments

Author

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  • Ji Yeh Choi

    (McGill University)

  • Heungsun Hwang

    (McGill University)

  • Marieke E. Timmerman

    (University of Groningen)

Abstract

Parallel factor analysis (PARAFAC) is a useful multivariate method for decomposing three-way data that consist of three different types of entities simultaneously. This method estimates trilinear components, each of which is a low-dimensional representation of a set of entities, often called a mode, to explain the maximum variance of the data. Functional PARAFAC permits the entities in different modes to be smooth functions or curves, varying over a continuum, rather than a collection of unconnected responses. The existing functional PARAFAC methods handle functions of a one-dimensional argument (e.g., time) only. In this paper, we propose a new extension of functional PARAFAC for handling three-way data whose responses are sequenced along both a two-dimensional domain (e.g., a plane with x- and y-axis coordinates) and a one-dimensional argument. Technically, the proposed method combines PARAFAC with basis function expansion approximations, using a set of piecewise quadratic finite element basis functions for estimating two-dimensional smooth functions and a set of one-dimensional basis functions for estimating one-dimensional smooth functions. In a simulation study, the proposed method appeared to outperform the conventional PARAFAC. We apply the method to EEG data to demonstrate its empirical usefulness.

Suggested Citation

  • Ji Yeh Choi & Heungsun Hwang & Marieke E. Timmerman, 2018. "Functional Parallel Factor Analysis for Functions of One- and Two-dimensional Arguments," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 1-20, March.
    • Handle: RePEc:spr:psycho:v:83:y:2018:i:1:d:10.1007_s11336-017-9558-9
    DOI: 10.1007/s11336-017-9558-9
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    References listed on IDEAS

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