Geographically Weighted Summary Statistics (GWAverage / GWCorrelation)¶

Model Overview¶

Geographically Weighted Summary Statistics performs locally weighted descriptive statistics on multivariate data, revealing spatial heterogeneity in the statistical characteristics of variables.

Two classes are provided:

GWAverage — computes local mean, standard deviation, variance, skewness, coefficient of variation, and optionally local median, interquartile range, and quantile imbalance.
GWCorrelation — computes local Pearson correlation coefficients and Spearman rank correlation coefficients for every pair of variables.

GWAverage¶

For each variable, the following local statistics are computed:

Statistic	Attribute	Column Name
Local Mean	`local_mean`	`{variable}_Mean`
Local Std Dev	`local_sdev`	`{variable}_SDev`
Local Skewness	`local_skewness`	`{variable}_Skew`
Local CV	`local_cv`	`{variable}_CV`

When quantile=True:

Statistic	Attribute	Column Name
Local Median	`local_median`	`{variable}_Median`
IQR	`iqr`	`{variable}_IQR`
Quantile Imbalance	`qi`	`{variable}_QI`

GWCorrelation¶

For each pair of variables \((X_i, X_j)\), the following are computed:

Local Pearson correlation coefficient — via locally weighted covariance
Local Spearman rank correlation coefficient — via locally weighted correlation on ranked data

Column name format: {var1}.{var2}_Corr and {var1}.{var2}_SCorr.

Code Examples¶

GWAverage¶

from pygwmodel import GWAverage, BandwidthWeight

vars = ["PURCHASE", "FLOORSZ", "UNEMPLOY", "PROF"]

gwa = GWAverage(
    data, vars,
    weight=BandwidthWeight(36.0, adaptive=True),
    quantile=False
).run()

result = gwa.result_layer
print(result.columns)
# PURCHASE_Mean, PURCHASE_SDev, PURCHASE_Skew, PURCHASE_CV,
# FLOORSZ_Mean, ...

GWCorrelation¶

from pygwmodel import GWCorrelation, BandwidthWeight

gwc = GWCorrelation(data, vars, weight=BandwidthWeight(36.0, adaptive=True))
result = gwc.run().result_layer

print(result.columns)
# PURCHASE.FLOORSZ_Corr, PURCHASE.FLOORSZ_SCorr,
# PURCHASE.UNEMPLOY_Corr, ...

Parallel Execution¶

Both classes support OpenMP multi-threading:

from pygwmodel import GWAverage, GWCorrelation, ParallelType

gwa = GWAverage(data, vars, weight=...)
gwa.enable_parallel(ParallelType.OpenMP, threads=4).run()

gwc = GWCorrelation(data, vars, weight=...)
gwc.enable_parallel(ParallelType.OpenMP, threads=4).run()