# 2d and 3d Space-Varying Coefficient Models

### Description

2d and 3d space-varying coefficient models are fitted to regular grid data using either a full B-spline tensor product approach or a sequential approximation. The latter one is computationally more efficient. Resolution increment is enabled.

### Details

Package: | svcm |

Type: | Package |

Version: | 0.1.2 |

Date: | 2007-04-19 |

License: | GPL version 2 or newer |

Depends: | R (>= 2.4.0), Matrix, splines |

LazyLoad: | yes |

LazyData: | yes |

URL: | http://www.statistik.lmu.de/~heim |

Originally, VCMs have been suggested by Hastie and Tibshirani (1993) for regressions with coefficients varying smoothly over a one-dimensional continuous variable such as time-varying effects. This package provides extensions to two- and three-dimensional space-varying coefficients surfaces for regularly gridded data without missings. Such a SVCM takes into account spatial correlation. The use of spline-basis functions serves to model the spatial coefficient field. As a consequence, estimates are accessible at any arbitrary position, not only on the original grid of voxels. Resolution can be easily increased and moreover penalized for possible initial anisotropy of the voxel size.

Two techniques are implemented. The multidimensional smoothing approach takes advantage of the sparsity of the spatial arrays involved. The second sequential one basically adapts the 'new smoothing spline' in Dierckx (1982), thus reducing the 3d (or higher-dimensional) problem to a sequence of one-dimensional smoothers.

The 2d and 3d examples have been chosen from the field of human brain imaging.

### Author(s)

Susanne Heim, with support from Paul Eilers, Thomas Kneib, and Michael Kobl

Maintainer: Susanne Heim <susanneheim@gmx.net>

### References

Dierckx P. (1982) A fast algorithm for smoothing data on a rectangular
grid while using spline functions. *SIAM Journal on Numerical
Analysis* **19(6)**, 1286-1304.

Hastie T. and Tibshirani R. (1993) Varying-Coefficient Models (with
discussion). *Journal of the Royal Statistical Society* B
**55**, 757-796.

Heim S., Fahrmeir L., Eilers P. H. C. and Marx B. D. (2006)
Space-Varying Coefficient Models for Brain
Imaging. *Ludwig-Maximilians-University, SFB 386*, Discussion
Paper **455**.