An improvement of the invIrM Routine of the geostatistical R-package spdep by Cholesky inversion
Sprache des Vortragstitels:
Statistiktage 2007 - Kongress der Österreichischen Statistischen Gesellschaft ÖSG
Sprache des Tagungstitel:
The article is about an improvement of the invIrM Routine of the geostatistical R-package spdep authored by Roger Bivand. The task was to compute the term for the correlated error of an autoregressive spatial process by Cholesky Decomposition.
The Cholesky decomposition can only be used for symmetric, positive definite matrices. To handle the heterogeneity in the linkage degrees of spatial objects different coding schemes are available for the spatial weights matrix V. The R-package spdep is able to manage the B, W, C and S-coding scheme. By using the W and S-coding scheme the spatial weights matrix is not symmetric anymore so the Cholesky decomposition can not be performed.
For this special cases by using an algebraic transformation it is still possible to perform a Cholesky decomposition to derive the inverse matrix. The article shows how to perform this transformation and the implementation in R. The main improvement is the reduction of computing iterations up to 50% for large spatial link matrices by using the Cholesky decomposition instead of the triangular decomposition with the Gauss algorithm.
The article consists of the following sections:
Short introduction in spatial weights matrices, coding schemes and the simul¬ta¬neous autoregressive process
Inversion of a matrix by Cholesky decomposition an performance improvement
Solving the special case for the W and S-coding scheme
Implementation in R
Examples: Simulated area and Upper Austria