Geographically Weighted Summary Statistics

Module Description

This function calculates basic and robust Geographically weighted summary statistics (GWSS). 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

Variables : a vector of variable names to be evaluated.

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.

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 2. Minkowski 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

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 format (see video)

Video

Video 1 : Geographically Weighted Summary Statistics

References

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

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

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 (2014) Geographically weighted methods and their use in network re-designs for environmental monitoring. Stochastic Environmental Research and Risk Assessment 28: 1869-1887. https://doi.org/10.1007/s00477-014-0851-1