Abstract
The problem of multicollinearity associated with the estimation of a functional logit model can be solved by using as predictor variables a set of functional principal components. The functional parameter estimated by functional principal component logit regression is often nonsmooth and then difficult to interpret. To solve this problem, different penalized spline estimations of the functional logit model are proposed in this paper. All of them are based on smoothed functional PCA and/or a discrete penalty in the log-likelihood criterion in terms of B-spline expansions of the sample curves and the functional parameter. The ability of these smoothing approaches to provide an accurate estimation of the functional parameter and their classification performance with respect to unpenalized functional PCA and LDA-PLS are evaluated via simulation and application to real data. Leave-one-out cross-validation and generalized cross-validation are adapted to select the smoothing parameter and the number of principal components or basis functions associated with the considered approaches.
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Acknowledgements
This research has been funded by project P11-FQM-8068 from Consejería de Innovación, Ciencia y Empresa. Junta de Andalucía, Spain and project MTM2010-20502 from Dirección General de Investigación, Ministerio de Educación y Ciencia, Spain. The authors would like to thank Caroline Lévéder for providing us with the data from Danone.
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Aguilera-Morillo, M.C., Aguilera, A.M., Escabias, M. et al. Penalized spline approaches for functional logit regression. TEST 22, 251–277 (2013). https://doi.org/10.1007/s11749-012-0307-1
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DOI: https://doi.org/10.1007/s11749-012-0307-1