Modeling environmental data by functional principal component logistic regression

Abstract

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.

A dynamic regression model for air pollen concentration

“…A second possible expansion would be the functional data approach by considering the continuous-time character of the process and its sample-paths. Some previous research on this way has been done by Valderrama et al (2002), and Escabias et al (2005). 1 ARIMA (0,0,1) · (0,1,1) 6 223.8561 2 ARIMA (0,0,1) · (0,1,1) 6 24.9598 3 ARIMA (0,0,1) · (0,1,1) 6 -44.1591 …”

Model-based clustering of time series in group-specific functional subspaces

“…The basis expansion of each observed curve x i (t) = p j=1 γ ij ψ j (t) can be estimated by an interpolation procedure (see Escabias et al (2005) for instance), if the curves are observed without noise, or by least square smoothing, if they are observed with error. In the present paper the second option will be used.…”

Automatic Variable Selection for Partially Linear Functional Additive Model and Its Application to the Tecator Data Set

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