Given a base X/Y dataset, calculates bisquare weighted sums of points from feature dataset
bisq_xy(base, feat, bandwidth, weight = 1)A vector of bi-square weighted sums
base dataset (eg gridcells), needs to be SpatialPolygonsDataFrame
feature dataset (eg another crime generator), needs to be SpatialPointsDataFrame
distances above this value do not contribute to the bi-square weight
if 1 (default), does not use attribute weights, else pass in string that is the variable name for weights in feat
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).
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.
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
# \donttest{
data(nyc_cafe); data(nyc_bor)
gr_nyc <- prep_grid(nyc_bor,15000)
gr_nyc$bscafe <- bisq_xy(gr_nyc,nyc_cafe,12000)
# }
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