This module contain functions for basic and Robust GWR, generalised GWR, Heterocedastic GWR, Mixed GWR, Scalable GWR and Local collinearity diagnostics for basic GWR.
Argument | Basic | Robust | Generalized | Heterocedastic | Mixed | Scalable |
---|---|---|---|---|---|---|
Dependient |
✔ | ✔ | ✔ | ✔ | ✔ | ✔ |
Independient |
✔ | ✔ | ✔ | ✔ | ✔ | ✔ |
Family |
x | x | ✔ | x | x | x |
Cv |
✔ | x | ✔ | x | x | x |
Kernel |
✔ | ✔ | ✔ | ✔ | ✔ | ✔ |
Power |
✔ | ✔ | ✔ | ✔ | ✔ | ✔ |
Theta |
✔ | ✔ | ✔ | ✔ | ✔ | ✔ |
Longlat |
✔ | ✔ | ✔ | ✔ | ✔ | ✔ |
Adaptive |
✔ | ✔ | ✔ | ✔ | ✔ | x |
Distance bandwidth |
✔ | ✔ | ✔ | ✔ | ✔ | x |
Max iter |
x | ✔ | x | ✔ | x | x |
Fixed |
x | x | x | x | ✔ | x |
Intercep fixed |
x | x | x | x | ✔ | x |
Diagnostic |
x | x | x | x | ✔ | x |
F123 |
x | ✔ | x | x | x | x |
Filtered |
x | ✔ | x | x | x | x |
bw.adapt |
x | x | x | x | x | ✔ |
Polynomial |
x | x | x | x | x | ✔ |
The same arguments are used in the Local collinearity diagnostics module as in the GWR Basic module, except for CV.
Dependient
: Dependent variable of the regression
model.
Independient
: Independent(s) variable(s) of the
regression model.
Family
: a description of the model’s error distribution
and link function, which can be “poisson” or “binomial”.
Cv
: if TRUE, cross-validation data will be
calculated
Kernel
: A set of five commonly used kernel
functions;
Power (Minkowski distance)
: the power of the Minkowski
distance (p=1 is manhattan distance, p=2 is euclidean distance).
Theta (Angle in radians)
: an angle in radians to rotate
the coordinate system, default is 0
longlat
: if TRUE, great circle distances will be
calculated
Adaptive
:if TRUE calculate an adaptive kernel where the
bandwidth (bw) corresponds to the number of nearest neighbours
(i.e. adaptive distance); default is FALSE, where a fixed kernel is
found (bandwidth is a fixed distance)
Distance bandwidth
: bandwidth used in the weighting
function. It has two options, automatic
which is calculated
in the Bandwidth selection module and manual
in which the
user enter the value.
Max iter
: maximum number of iterations for the automatic
approach
Fixed
: independent variables that appeared in the
formula that are to be treated as global
Intercep fixed
: logical, if TRUE the intercept will be
treated as global
Diagnostic
: logical, if TRUE the diagnostics will be
calculated
F123
:default FALSE, otherwise calculate F-test
results
Filtered
: default FALSE, the automatic approach is used,
if TRUE the filtered data approach is employed, as that described in
Fotheringham et al [1]
bw.adapt
: adaptive bandwidth (i.e. number of nearest
neighbours) used for geographically weighting
Polynomial
: degree of the polyunomial to approximate the
kernel function
SDF a SpatialPointsDataFrame (may be gridded) or SpatialPolygonsDataFrame object (see package “sp”) integrated with fit.points,GWR coefficient estimates, predicted values, coefficient standard errors and t-values in its “data” slot.
In the plot tab, the values obtained in the summary can be plotted,
customized and downloaded in .pdf
or .png
.
[1] Fotheringham S, Brunsdon, C, and Charlton, M (2002), Geographically Weighted Regression: The Analysis of Spatially Varying Relationships, John Wiley & Sons,Chichester.
[2] Belsley, D. A., Kuh, E., & Welsch, R. E. (2005). Regression diagnostics: Identifying influential data and sources of collinearity. John Wiley & Sons.
[3] Wheeler, D., & Tiefelsdorf, M. (2005). Multicollinearity and correlation among local regression coefficients in geographically weighted regression. Journal of Geographical Systems, 7(2), 161-187.
[4] Wheeler, D.C., Diagnostic tools and a remedial method for collinearity in geographically weighted regression. Environment and Planning A 2007, 39, (10), 2464-2481.
[5] Griffith, D.A., Spatial-filtering-based contributions to a critique of geographically weighted regression (GWR). Environment and Planning A 2008, 40, (11), 2751-2769.
[6] Wheeler, D.; Waller, L., Comparing spatially varying coefficient models: a case study examining violent crime rates and their relationships to alcohol outlets and illegal drug arrests. Journal of Geographical Systems 2009, 11, (1), 1-22.
[7] Wheeler, D.C., Simultaneous coefficient penalization and model selection in geographically weighted regression: the geographically weighted lasso. Environment and Planning A 2009, 41, (3), 722-742.
[8] Gollini, I., Lu, B., Charlton, M., Brunsdon, C., & Harris, P. (2015). GWmodel: An R Package for Exploring Spatial Heterogeneity Using Geographically Weighted Models. Journal of Statistical Software, 63(17), 1–50. https://doi.org/10.18637/jss.v063.i17
[9] Oshan, T. M., Li, Z., Kang, W., Wolf, L. J., & Fotheringham, A. S. (2019). mgwr: A Python implementation of multiscale geographically weighted regression for investigating process spatial heterogeneity and scale. ISPRS International Journal of Geo-Information, 8(6), 269.
[10] Zou, H. and Hastie, T. 2005. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B, 672., pp.301-320.
[11] Friedman J, Hastie T, Tibshirani R 2010. Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software 331:1–22
[12] Dormann, C.F., J. Elith, S. Bacher, et al. 2013. Collinearity: a review of methods to deal with it and a simulation study evaluating their performance. Ecography 36: 27-46.
[13] Comber, A., Brunsdon, C., Charlton, M., Dong, G., Harris, R., Lu, B., … & Harris, P. (2020). The GWR route map: a guide to the informed application of Geographically Weighted Regression. arXiv preprint arXiv:2004.06070.
[14] Mei L-M, He S-Y, Fang K-T (2004) A note on the mixed geographically weighted regression model. Journal of regional science 44(1):143-157
[15] Murakami, D., N. Tsutsumida, T. Yoshida, T. Nakaya & B. Lu (2019) Scalable GWR: A linear-time algorithm for large-scale geographically weighted regression with polynomial kernels. arXiv:1905.00266