This module contain functions for automatic bandwidth selection to calibrate basic GW regresion (bw.gwr
) , generalised GWR model (bw.ggwr
), GW Principal Components Analysis (bw.gwpca
), and GW Discriminant Analysis (bw.gwda
)
Argument | bw.gwr | bw.ggwr | bw.gwda | bw.gwpca |
---|---|---|---|---|
Dependient |
✔ | ✔ | ✔ | x |
Independient |
✔ | ✔ | ✔ | x |
Family |
x | ✔ | x | x |
Approach |
✔ | ✔ | x | x |
Kernel |
✔ | ✔ | ✔ | ✔ |
Power |
✔ | ✔ | ✔ | ✔ |
Theta |
✔ | ✔ | ✔ | ✔ |
Longlat |
✔ | ✔ | ✔ | ✔ |
Adaptative |
✔ | ✔ | ✔ | ✔ |
Cov.gw |
x | x | ✔ | x |
Prior.gw |
x | x | ✔ | x |
Mean.gw |
x | x | ✔ | x |
wqda |
x | x | ✔ | x |
Variables |
x | x | x | ✔ |
Robust |
x | x | x | ✔ |
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”.
Approach
: specified by CV for cross-validation approach or by Akaike Information Criterion corrected (AICc) approach
Kernel
: A set of five commonly used kernel functions;
Figure 1. Five kernel functions \(w_{ij}\) is the j-th element of the diagonal of the matrix of geographical weights W(\(u_i\),\(v_i\)), and \(d_{ij}\) is the distance between observations i and j, and b is the bandwidth.
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, find an adaptive kernel with a bandwidth proportional to the number of nearest neighbors (i.e. adaptive distance); otherwise, find a fixed kernel (bandwidth is a fixed distance)
Cov.gw
:if TRUE, localised variance-covariance matrix is used for GW discriminant analysis; otherwise, global variance-covariance matrix is used
Prior.gw
: if TRUE, localised prior probability is used for GW discriminant analysis; otherwise, fixed prior probability is used
Mean.gw
: if true, localised mean is used for GW discriminant analysis; otherwise, global mean is used
wqda
: if TRUE, a weighted quadratic discriminant analysis will be applied; otherwise a weighted linear discriminant analysis will be applied
Variables
: a vector of variable names to be evaluated
Robust
: if TRUE, robust GWPCA will be applied; otherwise basic GWPCA will be applied
Returns the adaptive or fixed distance bandwidth.
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 (2015) Enhancements to a geographicallyweighted principal components analysis in the context of an application to an environmental data set. Geographical Analysis 47: 146-172. https://doi.org/10.1111/gean.12048