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).
Figure 2. Minkowski 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
(Leung et al. 2000)
Filtered
: default FALSE, the automatic approach is used,
if TRUE the filtered data approach is employed, as that described in
Fotheringham et al. (2002 p.73-80)
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, y value,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
format (see video)
Brunsdon C, Fotheringham AS, Charlton ME (2002) Geographically weighted summary statistics -a framework for localised exploratory data analysis. Computers, Environment and Urban Systems 26:501-524. https://doi.org/10.1016/S0198-9715(01)00009-6
Fotheringham S, Brunsdon, C, and Charlton, M (2002), Geographically Weighted Regression: The Analysis of Spatially Varying Relationships, Chichester: Wiley.
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
Harris P, Clarke A, Juggins S, Brunsdon C, Charlton M (2014) Geographically weighted methods and their use in network re-designs for environmental monitoring. Stochastic Environmental Research and Risk Assessment 28: 1869-1887. https://doi.org/10.1007/s00477-014-0851-1
Nakaya, T., M. Charlton, S. Fotheringham & C. Brunsdon. 2009. How to use SGWRWIN (GWR4.0).Maynooth, Ireland: National Centre for Geocomputation.
Harris P, Fotheringham AS, Juggins S (2010) Robust geographically weighed regression: a technique for quantifying spatial relationships between freshwater acidification critical loads and catchment attributes. Annals of the Association of American Geographers 100(2): 286-306
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
Nakaya T, Fotheringham AS, Brunsdon C, Charlton M (2005) Geographically Weighted Poisson Regression for Disease Association Mapping, Statistics in Medicine 24: 2695-2717
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