An introduction to function-on-scalar regression

Function-on-scalar regression models feature a function over some do- main as the response while the regressors are scalars. Collections of time series as well as 2D or 3D images can be considered a functional response. We give a hands-on introduction into 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 con- siderations 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 basic understanding of generalized regression and spline-based estimation.

@article{id2310,
  author = {Bauer, Alexander and Scheipl, Fabian and K\"uchenhoff, Helmut and Gabriel, Alice-Agnes},
  doi = {10.1177/1471082X17748034},
  journal = {Statistical Modelling Journal},
  language = {en},
  number = {3-4},
  pages = {346{\textendash}364},
  title = {An introduction to function-on-scalar regression},
  url = {http://journals.sagepub.com/doi/abs/10.1177/1471082X17748034},
  volume = {18},
  year = {2018},
}

%O Journal Article
%A Bauer, Alexander
%A Scheipl, Fabian
%A Küchenhoff, Helmut
%A Gabriel, Alice-Agnes
%R 10.1177/1471082X17748034
%J Statistical Modelling Journal
%G en
%N 3-4
%P 346–364
%T An introduction to function-on-scalar regression
%U http://journals.sagepub.com/doi/abs/10.1177/1471082X17748034
%V 18
%D 2018