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Bauer, Alexander; Scheipl, Fabian; Kuechenhoff, Helmut; Gabriel, Alice-Agnes (2018): An introduction to semiparametric function-on-scalar regression. In: Statistical Modelling, Vol. 18, No. 3-4: pp. 346-364
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Abstract

Function-on-scalar regression models feature a function over some domain as the response while the regressors are scalars. Collections of time series as well as 2D or 3D images can be considered as functional responses. We provide a hands-on introduction for a flexible semiparametric approach for function-on-scalar regression, using spatially referenced time series of ground velocity measurements from large-scale simulated earthquake data as a running example. We discuss important practical considerations and challenges in the modelling process and outline best practices. The outline of our approach is complemented by comprehensive R code, freely available in the online appendix. This text is aimed at analysts with a working knowledge of generalized regression models and penalized splines.