Geographically and Temporally Weighted Regression (GTWR)¶

Model Overview¶

Geographically and Temporally Weighted Regression (GTWR) extends GWR by incorporating temporal information via a spatio-temporal distance metric. GTWR assigns a spatio-temporal ratio parameter \(\lambda \in [0, 1]\) that balances the influence of spatial proximity versus temporal proximity on the weighting scheme.

Key features:

Supports automatic bandwidth selection via CV or AIC criteria.
Supports OpenMP parallel computation.
Provides standard errors and diagnostic statistics.

Constructor¶

from pygwmodel import GTWR, BandwidthWeight
from pygwmodel.spatial_weight import CRSSTDistance

algorithm = GTWR(
    data,                   # GeoDataFrame
    'PURCHASE',             # dependent variable
    ['FLOORSZ', 'UNEMPLOY', 'PROF'],  # independent variables
    times='TIME',           # temporal column
    weight=BandwidthWeight(36.0, adaptive=True),
    distance=CRSSTDistance(lambda_=0.5)
)

Parameters:

Parameter	Type	Description
`sdf`	`GeoDataFrame`	Input data with geometry
`depen_var`	`str`	Dependent variable column name
`indep_vars`	`List[str]`	Independent variable column names
`times`	`str`	Column for temporal stamps
`weight`	`BandwidthWeight`	Bandwidth configuration
`distance`	`CRSSTDistance`	Spatio-temporal distance (default CRSSTDistance)
`has_intercept`	`bool`	Include intercept term (default True)

Code Examples¶

Basic Fit¶

from pygwmodel import GTWR, BandwidthWeight
from pygwmodel.spatial_weight import CRSSTDistance

algorithm = GTWR(
    data, 'PURCHASE', ['FLOORSZ', 'UNEMPLOY', 'PROF'],
    times='TIME',
    weight=BandwidthWeight(36.0, adaptive=True),
    distance=CRSSTDistance(lambda_=0.5)
).fit()

print(algorithm.diagnostic)
# {'RSS': ..., 'AIC': ..., 'AICc': ..., 'RSquare': ...}

print(algorithm.result_layer.columns)
# Index(['Intercept', 'FLOORSZ', 'UNEMPLOY', 'PROF',
#        'Intercept_SE', 'FLOORSZ_SE', 'UNEMPLOY_SE', 'PROF_SE',
#        'fitted'])

Bandwidth Auto-Selection¶

algorithm = GTWR(
    data, 'PURCHASE', ['FLOORSZ', 'UNEMPLOY', 'PROF'],
    times='TIME',
    weight=BandwidthWeight(36.0, adaptive=True),
    distance=CRSSTDistance(lambda_=0.5)
).fit(optimize_bandwidth=GTWR.BandwidthSelectionCriterionType.CV)

print(f"Optimal bandwidth: {algorithm.weight.bandwidth}")

Prediction¶

prediction = algorithm.predict(data)
print(prediction.columns)
# Index(['Intercept', 'FLOORSZ', 'UNEMPLOY', 'PROF',
#        'y_hat', 'residual'])

Parallel Execution¶

from pygwmodel import GTWR, ParallelType

algorithm = GTWR(..., weight=...)
algorithm.enable_parallel(ParallelType.OpenMP, threads=4).fit()