# Geographically Weighted Summary Statistics

Video 1 : Geographically Weighted Summary Statistics

# Module Description

This function calculates basic and robust Geographically weighted summary statistics [1]. This includes geographically weighted means,standard deviations and skew. Robust alternatives include geographically weighted medians, interquartile ranges and quantile imbalances. This function also calculates basic geographically weighted covariances together with basic and robust geographically weighted correlations.

# Argument

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

`Variables` : a vector of variable names to be evaluated.

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

`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).

`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

`quantile` :if TRUE, median, interquartile range, quantile imbalance will be calculated

# Value

A SpatialPointsDataFrame (may be gridded) or SpatialPolygonsDataFrame object with local means,local standard deviations,local variance, local skew,local coefficients of variation, local covariances, local correlations (Pearson’s), local correlations (Spearman’s), local medians, local interquartile ranges, local quantile imbalances and coordinates. In the plot tab, the values obtained in the summary can be plotted, customized and downloaded in `.pdf` or `.png`.

# References

[1] 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

[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

[3] Fotheringham S, Brunsdon, C, and Charlton, M (2002), Geographically Weighted Regression: The Analysis of Spatially Varying Relationships, Chichester: Wiley.