Statistical Modelling 20 (4) (2020), 386–409
Spatio-temporal expectile regression models
Elmar Spiegel,
Chair of Statistics,
University of Göttingen,
Göttingen,
Germany
and
Institute of Computational Biology,
Helmholtz Zentrum München,
German Research Center for Environmental Health,
Neuherberg,
Germany.
e-mail: gianluca.sottile@unipa.it
Institute of Environmental Medicine,
Unit of Biostatistics,
Karolinska Institutet,
Stockholm,
Sweden.
e-mail: espiege@uni-goettingen.de
Thomas Kneib,
Chair of Statistics,
University of Göttingen,
Göttingen,
Germany
Fabian Otto-Sobotka,
Department of Health Services Research,
Carl von Ossietzky University Oldenburg,
Oldenburg,
Germany.
Abstract:
Spatio-temporal models are becoming increasingly popular in recent regression research. However, they usually rely on the assumption of a specific parametric distribution for the response and/or homoscedastic error terms. In this article, we propose to apply semiparametric expectile regression to model spatio-temporal effects beyond the mean. Besides the removal of the assumption of a specific distribution and homoscedasticity, with expectile regression the whole distribution of the response can be estimated. For the use of expectiles, we interpret them as weighted means and estimate them by established tools of (penalized) least squares regression. The spatio-temporal effect is set up as an interaction between time and space either based on trivariate tensor product P-splines or the tensor product of a Gaussian Markov random field and a univariate P-spline. Importantly, the model can easily be split up into main effects and interactions to facilitate interpretation. The method is presented along the analysis of spatio-temporal variation of temperatures in Germany from 1980 to 2014.
Keywords:
expectile regression, interaction terms, main effects, tensor product, P-spline, spatio- temporal model.
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