This module implements basic or robust Geographically Weighted Principal Components Analysis (GWPCA)
Variables
: a vector of variable names to be evaluated
k
: the number of retained components; k must be less than the number of variable
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.
Robust
: if TRUE, robust GWPCA will be applied; otherwise basic GWPCA will be applied.
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).
longlat
: if TRUE, great circle distances will be calculated.
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.
Power
: the power of the Minkowski distance,default is 2, i.e. the Euclidean distance.
Figure 2. Minkowski distance
Theta (Angle in radians)
: an angle in radians to rotate the coordinate system, default is 0
Returns a list of class “gwpca” as Gwmodel Package:
a list class object including the model fitting parameters for generating the report file
the localised loadings
a SpatialPointsDataFrame or SpatialPolygonsDataFrame object (see package “sp”) integrated with local proportions of variance for each principle components, cumulative proportion and winning variable for the 1st principle component in its “data” slot
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, Brunsdon C, Charlton M (2011) Geographically weighted principal components analysis. International Journal of Geographical Information Science 25:1717-1736. https://doi.org/10.1080/13658816.2011.554838
Harris P, Brunsdon C, Charlton M, Juggins S, Clarke A (2014) Multivariate spatial outlier detection using robust geographically weighted methods. Mathematical Geosciences 46(1) 1-31. https://doi.org/10.1007/s11004-013-9491-0
Harris P, Clarke A, Juggins S, Brunsdon C, Charlton M (2015) Enhancements to a geographically weighted 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