# Geographically Weighted Discriminant Analysis

Video 1 : Geographically Weighted Discriminant Analysis

# Module Description

This module performs Geographically Weighted Discriminant Analysis [1], which includes the probabilities for each level, the highest probability and the entropy of the probabilities.

# Argument

The arguments were taken from Gollini et al.[2]

`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).

`Kernel`: A set of five commonly used kernel functions;

`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.

# References

[1] 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

[2] 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