Abstract
We propose a functional version of extended redundancy analysis that examines directional relationships among several sets of multivariate variables. As in extended redundancy analysis, the proposed method posits that a weighed composite of each set of exogenous variables influences a set of endogenous variables. It further considers endogenous and/or exogenous variables functional, varying over time, space, or other continua. Computationally, the method reduces to minimizing a penalized least-squares criterion through the adoption of a basis function expansion approach to approximating functions. We develop an alternating regularized least-squares algorithm to minimize this criterion. We apply the proposed method to real datasets to illustrate the empirical feasibility of the proposed method.
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We thank the Associate Editor and three anonymous reviewers for their constructive comments on an earlier version of the paper, which greatly improved the quality of the paper. The work reported in the paper was supported by the National Research Foundation of Korea Grant (No. 2011-0027731) funded by the Korean government (MEST) to the third author, and by the Social Science and Humanities Research Council of Canada and Fonds de Recherche sur la Société et la Culture to the fifth author.
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Hwang, H., Suk, H.W., Lee, JH. et al. Functional Extended Redundancy Analysis. Psychometrika 77, 524–542 (2012). https://doi.org/10.1007/s11336-012-9268-2
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DOI: https://doi.org/10.1007/s11336-012-9268-2