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

Ji Yeh Choi (), Heungsun Hwang and Marieke E. Timmerman
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Ji Yeh Choi: McGill University
Heungsun Hwang: McGill University
Marieke E. Timmerman: University of Groningen

Psychometrika, 2018, vol. 83, issue 1, No 1, 20 pages

Abstract: 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.

Keywords: three-way data; parallel factor analysis; functional data analysis; spatial and temporal variation (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11336-017-9558-9

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