M. Naser Lessani
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Python Package Guidance

M-SGWR Code Implementation

Run the serial M-SGWR model, optimize predictor-specific bandwidths and alpha values with AICc or cross-validation, and extract model results.

Install the packagepip install sgwr
01

Prepare the data

Arrange the CSV columns as x-coordinate, y-coordinate, dependent variable, and then the predictor variables. The code below reads those fields, constructs coordinate pairs, and uses the predictors to build the attribute-similarity weights.

Python · Imports and data preparation
from sgwr import MSGWR, Sel_BW
import pandas as pd
import numpy as np

df = pd.read_csv(r"Data.csv")

columns = df.columns[3:]
print("Predictors:", columns)

g_y = df[df.columns[2]].values.reshape(-1, 1)
g_x = df[columns].values

u = df[df.columns[0]].values
v = df[df.columns[1]].values
g_coords = list(zip(u, v))

# Predictors used to construct attribute weights
data = g_x

If standardization is appropriate for the analysis, import StandardScaler from sklearn.preprocessing and transform both g_x and g_y before creating the selector.

02

Optimize with AICc

Create a multiscale selector and run the default AICc-based search. The notebook uses the greedy hill-climbing approach with fixed alpha step sizes; the commented alternative activates divide-and-conquer alpha optimization.

Python · AICc optimization and model fitting
# Divide-and-conquer alpha optimization
# selector = Sel_BW(
#     g_coords, g_y, g_x, data,
#     multi=True, alphacurve=True
# )

# Greedy hill-climbing alpha optimization
selector = Sel_BW(
    g_coords,
    g_y,
    g_x,
    data,
    columns,
    multi=True
)

msgwr_bw = selector.search()

print("Optimal bandwidths:", msgwr_bw)
print(
    "Optimal alphas:",
    np.array([value[-1] for value in selector.bw[-1].values()])
)

msgwr_fit = MSGWR(
    g_coords,
    g_y,
    g_x,
    data,
    selector
).fit()
03

Optimize with cross-validation

To use cross-validation instead of AICc, retain the same data preparation and selector configuration, then set the search criterion to CV before fitting the model.

Python · Cross-validation optimization
selector = Sel_BW(
    g_coords,
    g_y,
    g_x,
    data,
    columns,
    multi=True
)

msgwr_bw = selector.search(criterion="CV")

print("Optimal bandwidths:", msgwr_bw)
print(
    "Optimal alphas:",
    np.array([value[-1] for value in selector.bw[-1].values()])
)

msgwr_fit = MSGWR(
    g_coords,
    g_y,
    g_x,
    data,
    selector
).fit()
04

Review diagnostics and the model summary

Use the fitted model object to retrieve the principal goodness-of-fit statistics and print the full M-SGWR summary table.

Python · Diagnostics and summary
print("R2:", msgwr_fit.R2)
print("Adjusted R2:", msgwr_fit.adj_R2)
print("AIC:", msgwr_fit.aic)
print("AICc:", msgwr_fit.aicc)
print("BIC:", msgwr_fit.bic)
print("RSS:", np.sum(msgwr_fit.resid_response ** 2))

print(msgwr_fit.summary())
05

Extract coefficients and test significance

Extract the local coefficient matrix from params. The filtered t-value methods set non-significant values to zero, either with the model-adjusted threshold or a specified confidence level.

Python · Coefficients and filtered t-values
# Local coefficient estimates
local_coefficients = msgwr_fit.params

# Model-adjusted significance threshold
filtered_tvalues = msgwr_fit.filter_tvals()

# Filter using a 95% confidence level
filtered_tvalues_95 = msgwr_fit.filter_tvals(alpha=0.05)
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