Statistical Modelling 15 (3) (2015), 279–300

The functional linear array model

Sarah Brockhaus
Institut für Statistik,
Ludwig-Maximilians-Universität München,
Germany
e-mail: sarah.brockhaus@stat.uni-muenchen.de

Fabian Scheipl
Institut für Statistik,
Ludwig-Maximilians-Universität München,
Germany


Torsten Hothorn
Institut für Epidemiologie,
Biostatistik und Prävention,
Abteilung Biostatistik Universität Zürich,
Switzerland


Sonja Greven
Institut für Statistik,
Ludwig-Maximilians-Universität München,
Germany


Abstract:

The functional linear array model (FLAM) is a unified model class for functional regression models including function-on-scalar, scalar-on-function and function-on-function regression. Mean, median, quantile as well as generalized additive regression models for functional or scalar responses are contained as special cases in this general framework. Our implementation features a broad variety of covariate effects, such as, linear, smooth and interaction effects of grouping variables, scalar and functional covariates. Computational efficiency is achieved by representing the model as a generalized linear array model. While the array structure requires a common grid for functional responses, missing values are allowed. Estimation is conducted using a boosting algorithm, which allows for numerous covariates and automatic, data-driven model selection. To illustrate the flexibility of the model class we use three applications on curing of resin for car production, heat values of fossil fuels and Canadian climate data (the last one in the electronic supplement). These require function-on-scalar, scalar-on-function and function-on-function regression models, respectively, as well as additional capabilities such as robust regression, spatial functional regression, model selection and accommodation of missings. An implementation of our methods is provided in the R add-on package FDboost.

Keywords:

boosting; functional data analysis; smoothing; structured additive regression; varying coefficient models.

Downloads:

Example data and code in zipped archive
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