Geographically Weighted Discriminant Analysis

Module Description

This module performs Geographically Weighted Discriminant Analysis, which includes the calculation of location-wise probabilities and entropy.

Argument

Grouping factor: Variable used for grouping.

Discriminators:Variables used as discriminators.

Mean.gw: if true, localised mean is used for GW discriminant analysis; otherwise, global mean is used.

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.

longlat: if TRUE, great circle distances will be calculated.

wqda: if TRUE, a weighted quadratic discriminant analysis will be applied; otherwise a weighted linear discriminant analysis 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).

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 (Minkowski distance): the power of the Minkowski distance (p=1 is manhattan distance, p=2 is euclidean distance).

Figure 1. Minkowski distance

Figure 1. Minkowski distance

Kernel: A set of five commonly used kernel functions;

Figure 2.  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.

Figure 2. 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.

Theta (Angle in radians): an angle in radians to rotate the coordinate system, default is 0

Value

An object of class “gwda”. This includes a SpatialPointsDataFrame or SpatialPolygonsDataFrame object, SDF, (see package “sp”) with the probabilities for each level, the highest probabiliity and the entropy of the probabilities in its “data” slot.

Video

Video 1 : Geographically Weighted Discriminant Analysis

References

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

Brunsdon, C, Fotheringham S, and Charlton, M (2007), Geographically Weighted Discriminant Analysis, Geographical Analysis 39:376-396. https://doi.org/10.1111/j.1538-4632.2007.00709.x