gwl.est {gwrr}

Geographically weighted lasso

Description

This function fits a geographically weighted lasso (GWL) model

Usage

gwl.est(form, locs, data, kernel = "exp", cv.tol)

Arguments

form

A regression model forumula, as in the functions lm and glm

locs

A matrix of spatial coordinates of data points, where the x coordinate is first, then the y coordinate; coordinates are assumed to not be latitude and longitude, as Euclidean distance is calculated from coordinates

data

A data frame with data to fit model

kernel

A kernel weighting function, either exp or gauss, where exponential function is default

cv.tol

A stopping tolerance in terms of cross-validation error for the bi-section search routine to estimate the kernel bandwidth using cross-validation; if missing an internally calculated value is used

Details

This function estimates penalized spatially varying coefficients using the geographically weighed regression and lasso approaches. Spatial kernel weights are applied to observations using the estimated kernel bandwidth to estimate local models at each data point. The kernel bandwidth and lasso solutions are currently estimated using cross-validation with an exponential or Gaussian kernel function. Some regression coefficients may be penalized to zero. The function estimates regression coefficients, the outcome variable values, and the model fit.

Value

A list with the following items:

phi

Kernel bandwidth

RMSPE

Root mean squared prediction error from bandwidth estimation

beta

Matrix of estimated regression coefficients, where a row contains the coefficients for one regression term for all data points

yhat

Estimated outcome variable values

RMSE

Root mean squared error from estimation

rsquare

Approximate R-square for GWR model

Author(s)

David Wheeler

References

Wheeler DC (2009) Simultaneous coefficient penalization and model selection in geographically weighted regression: The geographically weighted lasso. Environment and Planning A, 41: 722-742

See Also

gwrr.est

Examples

data(columbus)
locs <- cbind(columbus$x, columbus$y)
col.gwl <- gwl.est(crime ~ income + houseval, locs, columbus, "exp")
plot(col.gwl$beta[2,], col.gwl$beta[3,])
plot(columbus$x, columbus$y, cex=col.gwl$beta[1,]/10)