title: Generalized functional extended redundancy analysis.
abstract: Functional extended redundancy analysis (FERA) was recently developed to integrate data reduction into functional linear models. This technique extracts a component from each of multiple sets of predictor data in such a way that the component accounts for the maximum variance of response data. Moreover, it permits predictor and/or response data to be functional. FERA can be of use in describing overall characteristics of each set of predictor data and in summarizing the relationships between predictor and response data. In this paper, we extend FERA into the framework of generalized linear models (GLM), so that it can deal with response data generated from a variety of distributions. Specifically, the proposed method reduces each set of predictor functions to a component and uses the component for explaining exponential-family responses. As in GLM, we specify the random, systematic, and link function parts of the proposed method. We develop an iterative algorithm to maximize a penalized log-likelihood criterion that is derived in combination with a basis function expansion approach. We conduct two simulation studies to investigate the performance of the proposed method based on synthetic data. In addition, we apply the proposed method to two examples to demonstrate its empirical usefulness.
authors.affiliation: Department of Psychology, McGill University, 1205 Dr. Penfield Avenue, Montreal, Quebec, H3A 1B1, Canada, heungsun.hwang@mcgill.ca.
authors.forename: Heungsun
authors.initials: H
authors.lastname: Hwang
authors.forename: Hye Won
authors.initials: HW
authors.lastname: Suk
authors.forename: Yoshio
authors.initials: Y
authors.lastname: Takane
authors.forename: Jang-Han
authors.initials: JH
authors.lastname: Lee
authors.forename: Jooseop
authors.initials: J
authors.lastname: Lim
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006801:Humans; D016014:Linear Models; D011594:Psychometrics / Q000379:methods*