On a state-space modelling for functional data

The objective of this paper is to derive a state-space model for several continuous-time processes, by applying the Karhunen–Loève expansion, and then to apply the Kalman filter equations. The accuracy of the models on the basis of deterministic or random inputs is studied by means of simulation on two well-known processes.Project MTM2004-5992 of Dirección General de Investigación del Ministerio de Ciencia y Tecnología of Spain and the Research Group FQM307 financed by III-PAI of Conserjería de Educación y Ciencia de la Junta de Andalucí

Comparison of Positivity in Two EpidemicWaves of COVID-19 in Colombia with FDA

We use the functional data methodology to examine whether there are significant differences between two waves of contagion by COVID-19 in Colombia between 7 July 2020 and 20 July 2021. A pointwise functional t-test is initially used, then an alternative statistical test proposal for paired samples is presented, which has a theoretical distribution and performs well in small samples. Our statistical test generates a scalar p-value, which provides a global idea about the significance of the positivity curves, complementing the existing punctual tests, as an advantage.Government of Andalusia (Spain) PID2020-113961GB-I00Ministry of Science and Innovation, Spain (MICINN) Spanish GovernmentEuropean Commission CEX2020-001105-M/AEI/10.13039/501100011033.Junta de Andaluci

Functional PLS logit regression model

Functional logistic regression has been developed to forecast a binary response variable from a functional predictor. In order to fit this model, it is usual to assume that the functional observations and the parameter function of the model belong to a same finite space generated by a basis of functions. This consideration turns the functional model into a multiple logit model whose design matrix is the product of the matrix of sample paths basic coefficients and the matrix of the inner products between basic functions. The likelihood estimation of the parameter function of this model is very inaccurate due to the high dependence structure of the so obtained design matrix (multicollinearity). In order to solve this drawback several approaches have been proposed. These employ standard multivariate data analysis methods on the design matrix. This is the case of the functional principal component logistic regression model. As an alternative a functional partial least squares logit regression model is proposed, that has as covariates a set of partial least squares components of the design matrix of the multiple logit model associated to the functional one.Project MTM2004-5992 from Dirección General de Investigación, Ministerio de Ciencia y Tecnologí

Using basis expansions for estimating functional PLS regression. Applications with chemometric data

There are many chemometric applications, such as spectroscopy, where the objective is to explain a scalar response from a functional variable (the spectrum) whose observations are functions of wavelengths rather than vectors. In this paper, PLS regression is considered for estimating the linear model when the predictor is a functional random variable. Due to the infinite dimension of the space to which the predictor observations belong, they are usually approximated by curves/functions within a finite dimensional space spanned by a basis of functions. We show that PLS regression with a functional predictor is equivalent to finite multivariate PLS regression using expansion basis coefficients as the predictor, in the sense that, at each step of the PLS iteration, the same prediction is obtained. In addition, from the linear model estimated using the basis coefficients, we derive the expression of the PLS estimate of the regression coefficient function from the model with a functional predictor. The results provided by this functional PLS approach are compared with those given by functional PCR and discrete PLS and PCR using different sets of simulated and spectrometric data.Project P06-FQM-01470 from Consejería de Innovación, Ciencia y Empresa. Junta de Andalucía, SpainProject MTM2007-63793 from Dirección General de Investigación, Ministerio de Educación y Ciencia, Spai

Using principal components for estimating logistic regression with high-dimensional multicollinear data

The logistic regression model is used to predict a binary response variable in terms of a set of explicative ones. The estimation of the model parameters is not too accurate and their interpretation in terms of odds ratios may be erroneous, when there is multicollinearity (high dependence) among the predictors. Other important problem is the great number of explicative variables usually needed to explain the response. In order to improve the estimation of the logistic model parameters under multicollinearity and to reduce the dimension of the problem with continuous covariates, it is proposed to use as covariates of the logistic model a reduced set of optimum principal components of the original predictors. Finally, the performance of the proposed principal component logistic regression model is analyzed by developing a simulation study where different methods for selecting the optimum principal components are compared.Project MTM2004-5992 from Dirección General de Investigación, Ministerio de Ciencia y Tecnologí

Reviewers’ ratings and bibliometric indicators: hand in hand when assessing over research proposals?

The authors would like to thank Rodrigo Costas and Antonio Callaba de Roa for their helpful comments in previous version of this paper as well as the two anonymous reviewers for the constructive comments. We would also like to thank Bryan J. Robinson for revising the text. Nicolas Robinson-García is currently supported with a FPU grant from the Spanish government, Ministerio de Economía y Competitividad.Background: The 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. Objective: We 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 materials: We 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. Results: 63.4% 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. Discussion: Bibliometric 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 area

New Modeling Approaches Based on Varimax Rotation of Functional Principal Components

Functional Principal Component Analysis (FPCA) is an important dimension reduction technique to interpret themainmodes of functional data variation in terms of a small set of uncorrelated variables. The principal components can not always be simply interpreted and rotation is one of the main solutions to improve the interpretation. In this paper, two new functional Varimax rotation approaches are introduced. They are based on the equivalence between FPCA of basis expansion of the sample curves and Principal Component Analysis (PCA) of a transformation of thematrix of basis coefficients. The first approach consists of a rotation of the eigenvectors that preserves the orthogonality between the eigenfunctions but the rotated principal component scores are not uncorrelated. The second approach is based on rotation of the loadings of the standardized principal component scores that provides uncorrelated rotated scores but non-orthogonal eigenfunctions. A simulation study and an application with data from the curves of infections by COVID-19 pandemic in Spain are developed to study the performance of these methods by comparing the results with other existing approaches.Spanish Ministry of Science, Innovation and Universities (FEDER program) MTM2017-88708-PGovernment of Andalusia (Spain) FQM-307 FPU18/0177

Complementary Material to the study "Reviewers' ratings and bibliometric indicators: hand in hand when assessing over research proposals?

Complementary material of a study which analyzes the influence of bibliometric indicators.This work was supported by the National R&D Plan 2008 (research project Parameterization of citation indicators at a national level according with the ANEP categories [TIN2008-03180-E])

Discussion of different logistic models with functional data. Application to Systemic Lupus Erythematosus

The relationship between time evolution of stress and flares in Systemic Lupus Erythematosus patients has recently been studied. Daily stress data can be considered as observations of a single variable for a subject, carried out repeatedly at different time points (functional data). In this study, we propose a functional logistic regression model with the aim of predicting the probability of lupus flare (binary response variable) from a functional predictor variable (stress level). This method differs from the classical approach, in which longitudinal data are considered as observations of different correlated variables. The estimation of this functional model may be inaccurate due to multicollinearity, and so a principal component based solution is proposed. In addition, a new interpretation is made of the parameter function of the model, which enables the relationship between the response and the predictor variables to be evaluated. Finally, the results provided by different logit approaches (functional and longitudinal) are compared, using a sample of Lupus patients.Project P06-FQM-01470 from ’’Consejería de Innovación, Ciencia y Empresa. Junta de Andalucía, Spain’’Project MTM2007-63793 from Dirección General de Investigación, Ministerio de Educación y Ciencia, Spai

Functional PCA and Base-Line Logit Models

In many statistical applications data are curves measured as functions of a continuous parameter as time. Despite of their functional nature and due to discrete time observation, these type of data are usually analyzed with multivariate statistical methods that do not take into account the high correlation between observations of a single curve at nearby time points. Functional data analysis methodologies have been developed to solve these type of problems. In order to predict the class membership (multi-category response variable) associated to an observed curve (functional data), a functional generalized logit model is proposed. Base-line category logit formula- tions will be considered and their estimation based on basis expansions of the sample curves of the functional predictor and parameters. Functional principal component analysis will be used to get an accurate estimation of the functional parameters and to classify sample curves in the categories of the response variable. The good performance of the proposed methodology will be studied by developing an experimental study with simulated and real data.Projects MTM2010-20502 from Dirección General de Investigación del MEC SpainFQM-08068 from Consejería de Innovación, Ciencia y Empresa de la Junta de Andalucía Spai