This function applies Geographically Weighted Regression (GWR) to a given formula and dataset. GWR is a local form of linear regression used to model spatially varying relationships.
Usage
applyGWR(
formula,
data,
longlat = TRUE,
cl = NULL,
fit.points = NULL,
showProgressSteps = FALSE
)Arguments
- formula
A formula object describing the model to be fitted, e.g.,
log(y) ~ x1 + x2.- data
A spatial data frame (
SpatialPointsDataFrameorSpatialPolygonsDataFrame) containing the variables in the formula.- longlat
Logical; if
TRUE, coordinates are treated as longitude/latitude. Default isTRUE.- cl
Optional. A cluster object for parallel processing created by
makeCluster. Default isNULL.- fit.points
Optional. A spatial data frame for making predictions at specified locations. If
NULL, no predictions are made.- showProgressSteps
Logical; if
TRUE, prints progress messages during the analysis. Default isFALSE.
Value
A list with the following components:
- inputs
A list containing the inputs used for the GWR analysis:
formula,data, andlonglat.- output
A list of class
gwrcontaining the following elements:
Details
This function is intended for use with spatial datasets where relationships between variables may vary across space. GWR fits a separate regression model at each location in the data, weighting nearby points more heavily based on a specified bandwidth.
References
Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. John Wiley & Sons. doi:10.1002/9780470999141
Brunsdon, C., Fotheringham, A. S., & Charlton, M. E. (1996). Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity. Geographical Analysis, 28(4), 281-298. doi:10.1111/j.1538-4632.1996.tb00936.x
Fotheringham, A. S., & O'Sullivan, D. (2004). Spatial Nonstationarity and Local Models. In Geographic Information Systems: Principles, Techniques, Management and Applications (2nd ed., pp. 239-255). Wiley.
Bivand, R. S., Pebesma, E., & Gómez-Rubio, V. (2013). Applied Spatial Data Analysis with R (2nd ed.). Springer. doi:10.1007/978-1-4614-7618-4
Examples
data(meuse.grid, package = "spEnviroDistr")
coordinates(meuse.grid) = ~x+y
proj4string(meuse.grid) <- CRS("+init=epsg:28992")
#> Warning: GDAL Message 1: +init=epsg:XXXX syntax is deprecated. It might return a CRS with a non-EPSG compliant axis order.
gridded(meuse.grid) <- TRUE
data(meuse, package = "spEnviroDistr")
coordinates(meuse) = ~x+y
proj4string(meuse) <- CRS("+init=epsg:28992")
cl <- createCluster(free = 2)
RESULT <- applyGWR(log(copper) ~ alt + dist, meuse, longlat = FALSE, cl = cl)
print(RESULT$output)
#> Call:
#> gwr(formula = formula, data = data, bandwidth = bwG, adapt = adG,
#> hatmatrix = TRUE, longlat = longlat, cl = cl, predictions = TRUE)
#> Kernel function: gwr.Gauss
#> Adaptive quantile: 0.01146238 (about 1 of 155 data points)
#> Summary of GWR coefficient estimates at data points:
#> Min. 1st Qu. Median 3rd Qu. Max.
#> X.Intercept. -17.0918413 3.7531281 9.3204449 13.0599683 40.5131677
#> alt -0.9623308 -0.2499946 -0.1443481 0.0032744 0.5419798
#> dist -9.2546319 -3.8881674 -1.9964676 -0.7525851 3.9001866
#> Global
#> X.Intercept. 6.7962
#> alt -0.0786
#> dist -1.5609
#> Number of data points: 155
#> Effective number of parameters (residual: 2traceS - traceS'S): 85.62554
#> Effective degrees of freedom (residual: 2traceS - traceS'S): 69.37446
#> Sigma (residual: 2traceS - traceS'S): 0.261182
#> Effective number of parameters (model: traceS): 66.28962
#> Effective degrees of freedom (model: traceS): 88.71038
#> Sigma (model: traceS): 0.2309702
#> Sigma (ML): 0.1747339
#> AICc (GWR p. 61, eq 2.33; p. 96, eq. 4.21): 139.6473
#> AIC (GWR p. 96, eq. 4.22): -34.63161
#> Residual sum of squares: 4.732451
#> Quasi-global R2: 0.8810787
RESULT <- applyGWR(log(copper) ~ alt + dist + elev, meuse, longlat = FALSE, cl = cl, fit.points = meuse.grid)