Description Usage Arguments Details Value Author(s) References See Also Examples

This function extracts eigenvectors and eigenvalues from a spatial weight matrix.

1 |

`x` |
Matrix of spatial point coordinates (N x 2), ShapePolygons object (N spatial units), or an user-specified spatial weight matrix (N x N) (see Details) |

`type` |
Type of spatial weights. The currently available options are "knn" for the k-nearest neighbor-based weights, and "tri" for the Delaunay triangulation-based weights. If ShapePolygons are provided for x, type is ignored, and the rook-type neighborhood matrix is created |

`k` |
Number of nearest neighbors. It is used if type ="knn" |

`threshold` |
Threshold for the eigenvalues (scalar). Suppose that lambda_1 is the maximum eigenvalue. Then, this fucntion extracts eigenvectors whose corresponding eigenvalues are equal or greater than [threshold x lambda_1]. It must be a value between 0 and 1. Default is 0.25 (see Details) |

`enum` |
Optional. The muximum acceptable mumber of eigenvectors to be used for spatial modeling (scalar) |

If user-specified spatial weight matrix is provided for x, this function returns the eigen-pairs of the matrix. Otherwise, if a SpatialPolygons object is provided to x, the rook-type neighborhood matrix is created using this polygon, and eigen-decomposed. Otherwise, if point coordinats are provided to x, a spatial weight matrix is created according to type, and eigen-decomposed.

By default, the ARPACK routine is implemented for fast eigen-decomposition.

threshold = 0.25 (default) is a standard setting for topology-based ESF (see Tiefelsdorf and Griffith, 2007) while threshold = 0.00 is a usual setting for distance-based ESF.

`sf` |
Matrix of the first L eigenvectors (N x L) |

`ev` |
Vector of the first L eigenvalues (L x 1) |

`other` |
List of other outcomes, which are internally used |

Daisuke Murakami

Tiefelsdorf, M. and Griffith, D.A. (2007) Semiparametric filtering of spatial autocorrelation: the eigenvector approach. Environment and Planning A, 39 (5), 1193-1221.

Murakami, D. and Griffith, D.A. (2018) Low rank spatial econometric models. Arxiv, 1810.02956.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
require(spdep);library(rgdal)
data(boston)
########## Rook adjacency-based W
poly <- readOGR(system.file("shapes/boston_tracts.shp",package="spData")[1])
weig1 <- weigen( poly )
########## knn-based W
coords <- boston.c[,c("LON", "LAT")]
weig2 <- weigen( coords, type = "knn" )
########## Delaunay triangulation-based W
coords <- boston.c[,c("LON", "LAT")]
weig3 <- weigen( coords, type = "tri")
########## User-specified W
dmat <- as.matrix(dist(coords))
cmat <- exp(-dmat)
diag(cmat)<- 0
weig4 <- weigen( cmat, threshold = 0 )
``` |

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