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1 Type Package Package gwrr February 20, 2015 Title Fits geographically weighted regression models with diagnostic tools Version Date Author David Wheeler Maintainer David Wheeler Depends fields, lars Fits geographically weighted regression (GWR) models and has tools to diagnose and remediate collinearity in the GWR models. Also fits geographically weighted ridge regression (GWRR) and geographically weighted lasso (GWL) models. License GPL (>= 2) LazyLoad yes NeedsCompilation no Repository CRAN Date/Publication :13:24 R topics documented: gwrr-package columbus gwl.est gwr.bw.est gwr.est gwr.vdp gwrr.est Index 12 1
2 2 gwrr-package gwrr-package Geographically weighted regression models with penalties and diagnostic tools Fits geographically weighted regression (GWR) models and has tools to diagnose collinearity in the GWR models. Also fits geographically weighted ridge regression (GWRR) and geographically weighted lasso (GWL) models. Package: gwrr Type: Package Version: Date: License: GPL (>=2) LazyLoad: yes Author(s) David Wheeler Maintainer: David Wheeler Wheeler DC (2007) Diagnostic tools and a remedial method for collinearity in geographically weighted regression. Environment and Planning A, 39: Wheeler DC (2009) Simultaneous coefficient penalization and model selection in geographically weighted regression: The geographically weighted lasso. Environment and Planning A, 41: locs <- cbind(columbus$x, columbus$y) col.gwr <- gwr.est(crime ~ income + houseval, locs, columbus, "exp") plot(col.gwr$beta[2,], col.gwr$beta[3,]) col.vdp <- gwr.vdp(crime ~ income + houseval, locs, columbus, col.gwr$phi, "exp") hist(col.vdp$condition)
3 columbus 3 columbus Columbus crime Crime rate in planning neighborhoods in Columbus, Ohio in 1980 Usage Format A data frame with 49 observations on the following 6 variables. houseval a numeric vector income a numeric vector crime a numeric vector distcbd a numeric vector x a numeric vector y a numeric vector The data consist of variables for mean housing value, mean household income, residential and vehicle thefts combined per thousand people for 1980, distance to the central business district (CBD), and x and y spatial coordinates of neighborhood centroids. Source Anselin L (1988) Spatial Econometrics: Methods and Models. Kluwer, Dordrecht Wheeler DC (2007) Diagnostic tools and a remedial method for collinearity in geographically weighted regression. Environment and Planning A, 39: plot(columbus$x, columbus$y)
4 4 gwl.est gwl.est Geographically weighted lasso This function fits a geographically weighted lasso (GWL) model Usage gwl.est(form, locs, data, kernel = "exp", cv.tol) Arguments form locs data kernel cv.tol A regression model forumula, as in the functions lm and glm 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 A data frame with data to fit model A kernel weighting function, either exp or gauss, where exponential function is default 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 Value 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. A list with the following items: phi RMSPE beta yhat RMSE rsquare Kernel bandwidth Root mean squared prediction error from bandwidth estimation Matrix of estimated regression coefficients, where a row contains the coefficients for one regression term for all data points Estimated outcome variable values Root mean squared error from estimation Approximate R-square for GWR model
5 gwr.bw.est 5 Author(s) David Wheeler Wheeler DC (2009) Simultaneous coefficient penalization and model selection in geographically weighted regression: The geographically weighted lasso. Environment and Planning A, 41: See Also gwrr.est 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$beta[1,]/10) gwr.bw.est Cross-validation estimation of kernel bandwidth Estimate the kernel function bandwidth with cross-validation Usage gwr.bw.est(form, locs, data, kernel = "exp", cv.tol) Arguments form locs data kernel cv.tol A regression model forumula, as in the functions lm and glm A matrix of spatial coordinates of data points, where the x coordinate is first, then the y coordinate; coordinates are assumed to not be latitude and longitude, as Euclidean distance is calculated from coordinates A data frame with data to fit model A kernel weighting function, either exp or gauss, where exponential function is default A stopping tolerance in terms of cross-validation error for the bi-section search routine to estimate the kernel bandwidth using cross-validation; if missing an internally calculated value is used
6 6 gwr.est This function estimates the kernel bandwidth in a GWR model with leave-one-out cross-validation. It does not estimate the final regression coefficients or outcome variable. Value A list with the following items: phi RMSPE cv.score Kernel bandwidth Root mean squared prediction error from bandwidth estimation Sum of squared prediction errors from bandwidth estimation Author(s) David Wheeler Wheeler DC (2007) Diagnostic tools and a remedial method for collinearity in geographically weighted regression. Environment and Planning A, 39: See Also gwr.est locs <- cbind(columbus$x, columbus$y) col.bw <- gwr.bw.est(crime ~ income + houseval, locs, columbus, "exp") col.gwr <- gwr.est(crime ~ income + houseval, locs, columbus, "exp", bw=col.bw$phi) gwr.est Geographically weighted regression This function fits a geographically weighted regression (GWR) model Usage gwr.est(form, locs, data, kernel = "exp", bw = TRUE, cv.tol)
7 gwr.est 7 Arguments form locs data kernel bw cv.tol A regression model forumula, as in the functions lm and glm 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 A data frame with data to fit model A kernel weighting function, either exp or gauss, where exponential function is default Either TRUE to estimate a bandwidth for the kernel function, or the bandwidth to use to fit the model; bandwidth is estimated by default 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 Value This function estimates spatially varying coefficients using the GWR approach. Spatial kernel weights are applied to observations using the estimated or supplied kernel bandwidth to estimate local models at each data point. The bandwidth is currently estimated with cross-validation with an exponential or Gaussian kernel function. The function estimates regression coefficients, the outcome variable values, and the model fit. A list with the following items: phi RMSPE beta yhat RMSE rsquare Kernel bandwidth Root mean squared prediction error from bandwidth estimation Matrix of estimated regression coefficients, where a row contains the coefficients for one regression term for all data points Estimated outcome variable values Root mean squared error from estimation Approximate R-square for GWR model Author(s) David Wheeler Wheeler DC (2007) Diagnostic tools and a remedial method for collinearity in geographically weighted regression. Environment and Planning A, 39: See Also gwr.bw.est
8 8 gwr.vdp locs <- cbind(columbus$x, columbus$y) col.gwr <- gwr.est(crime ~ income + houseval, locs, columbus, "exp") plot(col.gwr$beta[2,], col.gwr$beta[3,]) plot(columbus$x, columbus$y, cex=col.gwr$beta[1,]/10) gwr.vdp Collinearity diagnostics for geographically weighted regression Uses the collinearity diagnostic tools of variance-decomposition proportions and condition indexes for geographically weighted regression (GWR) models. Usage gwr.vdp(form, locs, data, phi, kernel = "exp", sel.ci = 30, sel.vdp = 0.5) Arguments form locs data phi kernel sel.ci sel.vdp A regression model forumula, as in the functions lm and glm 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 A data frame with data to fit model The kernel bandwidth used in the GWR model The kernel weighting function used in the GWR model, either exp or gauss; exp is the default The threshold value to use for the condition index to indicate observations with a collinearity issue; indexes above this value will be flagged; the default is 30 The threshold value to use for the variance-decomposition proportion to indicate observations with a collinearity issue; proportions above this value will be flagged; the default is 0.5 This function calculates the variance-decomposition proportions and the condition indexes for the weighted design matrix used in a GWR model. The kernel function and bandwidth used to estimate the GWR model must be input to this function. Observations with a large condition index and relatively large variance-decomposition proportions for more than one regression term indicate an issue with collinearity.
9 gwrr.est 9 Value A list with the following items: condition vdp flag.cond flag.vdp flag.cond.vdp Largest condition index for each observation Variance-decomposition proportions for the largest variance component for each observation True if largest condition index exceeds threshold True if variance-decomposition proportions for more than one term exceed threshold True if condition index and variance-decompostion proportions exceed thresholds Author(s) David Wheeler Wheeler DC (2007) Diagnostic tools and a remedial method for collinearity in geographically weighted regression. Environment and Planning A, 39: See Also gwr.bw.est locs <- cbind(columbus$x, columbus$y) col.bw <- gwr.bw.est(crime ~ income + houseval, locs, columbus, "exp") col.vdp <- gwr.vdp(crime ~ income + houseval, locs, columbus, col.bw$phi, "exp") hist(col.vdp$condition) gwrr.est Geographically weighted ridge regression This function fits a geographically weighted ridge regression (GWRR) model Usage gwrr.est(form, locs, data, kernel = "exp", bw = TRUE, rd = TRUE, cv.tol)
10 10 gwrr.est Arguments form locs data kernel bw rd cv.tol A regression model forumula, as in the functions lm and glm 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 A data frame with data to fit model A kernel weighting function, either exp or gauss, where exponential function is default Either TRUE to estimate a bandwidth for the kernel function, or the bandwidth to use to fit the model; bandwidth is estimated by default Either TRUE to estimate a ridge shrinkage parameter, or the ridge parameter to use to fit the model; ridge parameter is estimated by default 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 Value This function estimates penalized spatially varying coefficients using the GWR and ridge regression approaches. Spatial kernel weights are applied to observations using the estimated or supplied kernel bandwidth to estimate local models at each data point. The bandwidth is estimated with cross-validation with an exponential or Gaussian kernel function. The regression coefficients are penalized with a ridge parameter that is estimated with cross-validation. The function estimates regression coefficients, the outcome variable values, and the model fit. A list with the following items: phi lambda RMSPE beta yhat RMSE rsquare Kernel bandwidth Ridge shrinkage parameter Root mean squared prediction error from bandwidth estimation Matrix of estimated regression coefficients, where a row contains the coefficients for one regression term for all data points Estimated outcome variable values Root mean squared error from estimation Approximate R-square for GWR model Author(s) David Wheeler Wheeler DC (2007) Diagnostic tools and a remedial method for collinearity in geographically weighted regression. Environment and Planning A, 39:
11 gwrr.est 11 See Also gwr.est locs <- cbind(columbus$x, columbus$y) col.gwrr <- gwrr.est(crime ~ income + houseval, locs, columbus, "exp", bw=2.00, rd=0.03) plot(col.gwrr$beta[2,], col.gwrr$beta[3,]) plot(columbus$x, columbus$y, cex=col.gwrr$beta[1,]/10) col.gwr <- gwrr.est(crime ~ income + houseval, locs, columbus, "exp", bw=col.gwrr$phi, rd=0)
12 Index Topic datasets columbus, 3 Topic models gwl.est, 4 gwr.bw.est, 5 gwr.est, 6 gwrr.est, 9 Topic multivariate gwr.vdp, 8 Topic package gwrr-package, 2 columbus, 3 gwl.est, 4 gwr.bw.est, 5, 7, 9 gwr.est, 6, 6, 11 gwr.vdp, 8 gwrr (gwrr-package), 2 gwrr-package, 2 gwrr.est, 5, 9 12
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DS Machine Learning and Data Mining I. Alina Oprea Associate Professor, CCIS Northeastern University
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