Over the last few years many methods have been developed for analyzing functional data with different objectives. The purpose of this paper is to predict a binary response variable in terms of a functional variable whose sample information is given by a set of curves measured without error. In order to solve this problem we formulate a functional logistic regression model and propose its estimation by approximating the sample paths in a finite dimensional space generated by a basis. Then, the problem is reduced to a multiple logistic regression model with highly correlated covariates. In order to reduce dimension and to avoid multicollinearity, two different approaches of functional principal component analysis of the sample paths are proposed. Finally, a simulation study for evaluating the estimating performance of the proposed principal component approaches is developed.

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SUMMARYIn recent years, many studies have dealt with predicting a response variable based on the information provided by a functional variable. When the response variable is binary, different problems arise, such as multicollinearity and high dimensionality, which prejudice the estimation of the model and the interpretation of its parameters. In this article we address these problems by using functional logistic regression and principal component analysis. In order to obtain a unique solution for the maximum likelihood estimation of the parameter function, quasi-natural cubic spline interpolation of sample paths on their discrete time observations is proposed. We also introduce a new interpretation of the relationship between the response variable and the functional predictor where the change in the odds of success is evaluated from the estimated parameter function. An analysis of climatological data is finally presented to illustrate the practical performance of the proposed methodologies.

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BackgroundThe peer review system has been traditionally challenged due to its many limitations especially for allocating funding. Bibliometric indicators may well present themselves as a complement.ObjectiveWe analyze the relationship between peers’ ratings and bibliometric indicators for Spanish researchers in the 2007 National R&D Plan for 23 research fields.Methods and MaterialsWe analyze peers’ ratings for 2333 applications. We also gathered principal investigators’ research output and impact and studied the differences between accepted and rejected applications. We used the Web of Science database and focused on the 2002-2006 period. First, we analyzed the distribution of granted and rejected proposals considering a given set of bibliometric indicators to test if there are significant differences. Then, we applied a multiple logistic regression analysis to determine if bibliometric indicators can explain by themselves the concession of grant proposals.Results63.4% of the applications were funded. Bibliometric indicators for accepted proposals showed a better previous performance than for those rejected; however the correlation between peer review and bibliometric indicators is very heterogeneous among most areas. The logistic regression analysis showed that the main bibliometric indicators that explain the granting of research proposals in most cases are the output (number of published articles) and the number of papers published in journals that belong to the first quartile ranking of the Journal Citations Report.DiscussionBibliometric indicators predict the concession of grant proposals at least as well as peer ratings. Social Sciences and Education are the only areas where no relation was found, although this may be due to the limitations of the Web of Science’s coverage. These findings encourage the use of bibliometric indicators as a complement to peer review in most of the analyzed areas.

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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.