eigen_grid: Eigenvalues of a spatial weights matrix: for spatial...

In geostan: Bayesian Spatial Analysis

Eigenvalues of a spatial weights matrix: for spatial regression with raster data

Description

Approximate eigenvalues for the row-standardized spatial connectivity matrix W of a regular tessellation, e.g., remotely sensed imagery.

Usage

eigen_grid(row = 5, col = 5)

Arguments

row	Number of rows in the raster dataset
col	Number of columns in the raster dataset

Details

Uses Equation 5 from Griffith (2000) to calculate the eigenvalues for a row-standardized spatial weights matrix; this is valid for a regular tessellation (rectangular grid or raster). The rook criteria is used to define adjacency.

The purpose is to calculate eigenvalues of the spatial weights matrix for the CAR and SAR models, enabling spatial regression with large raster data sets. This function is used internally by prep_sar_data2 and prep_car_data2. For more details, see: vignette("raster-regression", package = "geostan").

Value

Returns the eigenvalues of the row-standardized spatial weights matrix (a numeric vector length row * col).

Source

Griffith, Daniel A. (2000). Eigenfunction properties and approximations of selected incidence matrices employed in spatial analyses. Linear Algebra and its Applications 321 (1-3): 95-112. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/S0024-3795(00)00031-8")}.

See Also

prep_sar_data2, prep_car_data2

Examples

e <- eigen_grid(row = 50, col = 95)
print(head(e, 25))

geostan documentation built on April 3, 2025, 10:04 p.m.