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.
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Acknowledgements
The authors thank the Associate Editor and three anonymous reviewers for their constructive comments. The work reported in the paper was supported by the Natural Sciences and Engineering Research Council of Canada (No. 10630) to the third author, by the International Cooperation Program of the National Research Foundation of Korea (2012-K2A1A2033137) to the fourth 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., Takane, Y. et al. Generalized Functional Extended Redundancy Analysis. Psychometrika 80, 101–125 (2015). https://doi.org/10.1007/s11336-013-9373-x
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DOI: https://doi.org/10.1007/s11336-013-9373-x