scgwr {scgwr}

Scalable Geographically Weighted Regression

Description

This function estimates a scalable geographically weighted regression (GWR) model. See scgwr_p for parallel implementqtion of the model for very large samples.

Usage

scgwr( coords, y, x = NULL, knn = 100, kernel = "gau",
       p = 4, approach = "CV", nsamp = NULL)

Arguments

coords

Matrix of spatial point coordinates (N x 2)

y

Vector of explained variables (N x 1)

x

Matrix of explanatory variables (N x K). Default is NULL

knn

Number of nearest-neighbors being geographically weighted. Default is 100. Larger knn is better for larger samples (see Murakami er al., 2019)

kernel

Kernel to model spatial heterogeneity. Gaussian kernel ("gau") and exponential kernel ("exp") are available

p

Degree of the polynomial to approximate the kernel function. Default is 4

approach

If "CV", leave-one-out cross-validation is used for the model calibration. If "AICc", the corrected Akaike Information Criterion is minimized for the calibation. Default is "CV"

nsamp

Number of samples used to approximate the cross-validation. The samples are randomly selected. If the value is large enough (e.g., 10,000), error due to the random sampling is quite small owing to the central limit theorem. The value must be smaller than the sample size. Default is NULL

Value

b

Matrix of estimated coefficients (N x K)

bse

Matrix of the standard errors for the coefficients (N x k)

t

Matrix of the t-values for the coefficients (N x K)

p

Matrix of the p-values for the coefficients (N x K)

par

Estimated model parameters includeing a scale parameter and a shrinkage parameter if penalty = TRUE (see Murakami et al., 2018)

e

Error statistics. It includes sum of squared errors (SSE), residual standard error (resid_SE), R-squared (R2), adjusted R2 (adjR2), log-likelihood (logLik), corrected Akaike information criterion (AICc), and the cross-validation (CV) score measured by root mean squared error (RMSE) (CV_score(RMSE))

pred

Vector of predicted values (N x 1)

resid

Vector of residuals (N x 1)

other

Other objects internally used

References

Murakami, D., Tsutsumida, N., Yoshida, T., Nakaya, T., and Lu, B. (2019) Scalable GWR: A linear-time algorithm for large-scale geographically weighted regression with polynomial kernels. <arXiv:1905.00266>.

See Also

scgwr_p, predict0

Examples

require( spData )
data( boston )
coords <- boston.c[, c("LON", "LAT") ]
y      <- log(boston.c[,"MEDV"])
x      <- boston.c[, c("CRIM", "ZN", "INDUS", "CHAS", "AGE")]
res    <- scgwr( coords = coords, y = y, x)
res