Manuel Escabias

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.

Principal component estimation of functional logistic regression: discussion of two different approaches

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.

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.

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.

Reviewers’ Ratings and Bibliometric Indicators: Hand in Hand When Assessing Over Research Proposals?

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 areas.

Forecasting binary longitudinal data by a functional PC-ARIMA model

In order to forecast time evolution of a binary response variable from a related continuous time series a functional logit model is proposed. The estimation of this model from discrete time observations of the predictor is solved by using functional principal component analysis and ARIMA modelling of the associated discrete time series of principal components. The proposed model is applied to forecast the risk of drought from El Nino phenomenon.

Stepwise selection of functional covariates in forecasting peak levels of olive pollen

High levels of airborne olive pollen represent a problem for a large proportion of the population because of the many allergies it causes. Many attempts have been made to forecast the concentration of airborne olive pollen, using methods such as time series, linear regression, neural networks, a combination of fuzzy systems and neural networks, and functional models. This paper presents a functional logistic regression model used to study the relationship between olive pollen concentration and different climatic factors, and on this basis to predict the probability of high (and possibly extreme) levels of airborne pollen, selecting the best subset of functional climatic variables by means of a stepwise method based on the conditional likelihood ratio test.

Solving Multicollinearity in Functional Multinomial Logit Models for Nominal and Ordinal Responses

Di erent functional logit models to estimate a multicategory response variable from a functional predictor will be formulated in terms of di erent types of logit transformations as base-line category logits for nominal responses or cumulative, adjacent-categories or continuation-ratio logits for ordinal responses. Estimation procedures of functional logistic regression based on functional PCA of sample curves will be generalized to the case of a multicategory response. The true functional form of sample curves will be reconstructed in terms of basis expansions whose coe cients will be estimated from irregularly distributed discrete time observations.

Proposal of a stochastic model to determine the bibliometric variables influencing the quality of a journal: application to the field of Dentistry

On the basis of the Impact Factor of Journal Citation Reports developed by ISI as a journal quality indicator, this paper puts forth an ordinal regression model to estimate the journal’s position by terciles. The set of explanatory variables includes the H-index of its Editor-in-chief, percentage of papers published in the journal that received external funding, average number of papers published yearly, and two factors concerning the scope and structure of the journal. The proposed model was applied to the field of Dentistry, Oral Surgery and Medicine, and led us to the conclusion that the above mentioned covariables alone had a significant input in the model, but not the factors. The essay performed on a sample of 30 Dentistry journals included in JCR provided a confirmatory correct classification rate (CCR) of 80%, with a predictive CCR of 75% on a sample of eight new journals not previously considered in the phase of model estimation.

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 formulations 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.