bisq_xy {ptools}

Bisquare weighted sum

Description

Given a base X/Y dataset, calculates bisquare weighted sums of points from feature dataset

Usage

bisq_xy(base, feat, bandwidth, weight = 1)

Arguments

base

base dataset (eg gridcells), needs to be SpatialPolygonsDataFrame

feat

feature dataset (eg another crime generator), needs to be SpatialPointsDataFrame

bandwidth

distances above this value do not contribute to the bi-square weight

weight

if 1 (default), does not use attribute weights, else pass in string that is the variable name for weights in feat

Details

This generates bi-square distance weighted sums of features within specified distance of the base centroid. Bisquare weights are calculated as:

w_{ij} = [ 1 - (d_{ij}/b)^2 ]^2

where d_ij is the Euclidean distance between the base point and and the feature point. If d < b, then w_ij equals 0. These are then multiplied and summed so each base point gets a cumulative weighted sum. See the GWR book for a reference. Uses loops and calculates all pairwise distances, so can be slow for large base and feature datasets. Consider aggregating/weighting feature dataset if it is too slow. Useful for quantifying features nearby (Groff, 2014), or for egohoods (e.g. spatial smoothing of demographic info, Hipp & Boessen, 2013).

Value

A vector of bi-square weighted sums

References

Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2003). Geographically weighted regression: the analysis of spatially varying relationships. John Wiley & Sons.

Groff, E. R. (2014). Quantifying the exposure of street segments to drinking places nearby. Journal of Quantitative Criminology, 30(3), 527-548.

Hipp, J. R., & Boessen, A. (2013). Egohoods as waves washing across the city: A new measure of “neighborhoods”. Criminology, 51(2), 287-327.

See Also

dist_xy() for calculating distance to nearest

count_xy() for counting points inside polygon

kern_xy() for estimating gaussian density of points for features at base polygon xy coords

bisq_xy() to estimate bi-square kernel weights of points for features at base polygon xy coords

idw_xy() to estimate inverse distance weights of points for features at base polygon xy coords

Examples

data(nyc_cafe); data(nyc_bor)
gr_nyc <- prep_grid(nyc_bor,15000)
gr_nyc$bscafe <- bisq_xy(gr_nyc,nyc_cafe,12000)