SGWR 0.5

The package contains serial SGWR, MPI-enabled FastSGWR, and multiscale SGWR (MSGWR).

MSGWR usage

from sgwr import MSGWR, Sel_BW

# coords: (n, 2) projected coordinates; y: (n, 1) Gaussian response
# X: (n, p) numeric predictors; data: (n, p) similarity attributes
# Keep data columns aligned with the corresponding predictors in X.
# Supply X and data without an intercept; constant=True adds it.
selector = Sel_BW(coords, y, X, data, multi=True)
selector.search(multi_bw_min=[20])  # choose bounds suitable for your sample
results = MSGWR(coords, y, X, data, selector).fit(n_chunks=1)
print(results.summary())
# results.summary(as_str=False) prints directly and returns None.
# results.summary(as_str=True) returns text (the default).

Use identical coordinates, response, predictors, similarity data, and model settings for selection and fitting. For fixed Gaussian weights, pass fixed=True to both classes. Defaults select adaptive bisquare weights. Explicit mismatched kernel options and spherical distances raise an error. MSGWR currently supports Gaussian responses and projected coordinates only. The existing serial SGWR and FastSGWR APIs remain available.

The MSGWR summary includes per-variable bandwidths, spatial mixing alphas, effective parameter counts, adjusted 95% significance levels and critical t values, global OLS results, model diagnostics, and coefficient statistics. alpha=1 means purely geographic weighting; this mixing parameter is distinct from the adjusted significance alpha. The intercept uses spatial weights only.

Standard errors and diagnostics replay the complete selection history, including initialization. They condition on the selected bandwidths and alphas; they do not account for uncertainty from selecting these quantities. sigma2_v1=True divides RSS by n - trace(S); False uses n - 2*trace(S) + trace(S.T @ S). Both work without retaining the full hat matrix. hat_matrix=True retains results.S and results.R for inspection. Chunking reduces inference memory, and fit(pool=pool) supports a multiprocessing.Pool (use an if __name__ == '__main__': guard on Windows).

exact_fit() solves the converged equations at the final selected weights. It can differ from fit() when selection has not converged and uses much more memory. Increase max_iter_multi or tighten tol_multi as appropriate and inspect selector.bw[2] for convergence scores.

Install from the project folder with python -m pip install .. Run the numerical checks with python -m pytest -q tests. See MSGWR_REVIEW.md for the changes and validation scope.

FastSGWR: "Enhancing the Computational Efficiency of the SGWR Model and Introducing Its Software Implementation." This article along the python packages (parallel & sequential), and a Graphic User Interface (GUI) tool named 'SGWR Model' is developed based on this article :SGWR: similarity and geographically weighted regression (https://doi.org/10.1080/13658816.2024.2342319).

Author info

• Code Author: M. Naser Lessani (GIBD)
• Realeased Year: 2026
• Affiliation: Geoinformation and Big Data Research Laboratory (GIBD), Department of Geography, The Pennsylvania State University, University Park, PA, USA

Overview

The SGWR (Similarity and Geographically Weighted Regression) model is a novel local spatial regression model that extends the conventional GWR by incorporating both geographical proximity and attribute similarity into a composite spatial weight matrix. The combination of spatial and attribute-based weights is governed by a parameter alpha, which is optimized based on AICc measure.

This Python package includes:

• MPI-enabled parallel implementations of the SGWR
• Serial version of the SGWR model
• Support for Gaussian and bi-square kernels
• Also, supports a combination of adaptive bisquare and gaussian

Key Features

• Parallel Computation with MPI: Achieve substantial runtime reductions using multiple CPU cores.
• Alpha Optimization: Automatically tune the contribution of similarity and spatial proximity.
• Kernel Flexibility: Choose between Gaussian (default) and bi-square kernels.
• Also, users have the ability to either chose standardize or don't standardize their data
• Evaluation Metrics: Outputs include R², adjusted R², AICc, and other metrics
• Also, users can run the GWR model in both parallel and serial version of this library

Installation Requirements

Ensure the following dependencies are installed:

Standard Python Libraries:

• os
• argparse
• datetime
• math
• copy
• typing (Optional)
• itertools (combinations)

MPI and CLI:

• mpi4py
• click

Numerical and Data Handling:

• numpy
• pandas
• scipy (stats, linalg, spatial.distance)

Machine Learning and Metrics:

• scikit-learn (metrics)

Specialized Geospatial Modeling:

• spglm (family, glm, iwls, utils)

Data Format

Input data must be a CSV file with the following column order:

longitude, latitude, dependent_variable, independent_variable_1, ..., independent_variable_n

Categorical variables must be pre-processed into dummy variables. Example: For a 3-class variable ("urban", "peri-urban", "rural"), create:

• urban_dummy: 1 if urban, else 0
• peri_urban_dummy: 1 if peri-urban, else 0
• Rural becomes the reference class (excluded)

Usage

After preparing your dataset and ensuring all dependencies are installed, the model can be run via the command line:

MPI Commands (parallel):

• fastsgwr run -np x -data path_to_data (by default the kernel is Gaussian function, and doesn't standardize the data)
• fastsgwr run -np x -data path_to_data -standardize (using Gaussian function and standardize the input data)
• fastsgwr run -np x -data path_to_data -bisquare
• fastsgwr run -np x -data path_to_data -bisquare -standardize
• fastsgwr run -np x -data path_to_data -biga (adaptive bisquare and gaussian)
• fastsgwr run -np x -data path__to_data -gwr (run gwr as well in parallel)
• x: Number of cores
• path_to_data: Path to the CSV dataset

The output will be a CSV file saved in the same input directory, and containing local coefficients and performance metrics. PI Commands (parallel):

Serial commands:

• selector = ALPHA(g_coords, g_y, g_x, data, fixed=True, kernel='gaussian') ## for fixed bandwidth and gaussian kernel
• bw, alpha = selector.fit()
• sgwr_model = SGWR(g_coords, g_y, g_x, bw, data, alpha, fixed=True, kernel='gaussian') ## after bandwidth and alpha optimizationi
• result = sgwr_model.fit()
• selector = ALPHA(g_coords, g_y, g_x, data) ## for adaptive bandwidth and bisquare kernel
• bw, alpha = selector.fit()
• sgwr_model = SGWR(g_coords, g_y, g_x, bw, data, alpha)
• result = sgwr_model.fit()

Parameter extraction when running in serial mode:

• result.R2
• result.adj_R2
• result.aicc
• result.aic
• result.params
• result.bse
• result.localR2
• result.filter_tvals()
• result.filter_tvals(alpha=0.05) ### t values with 95% confidence interval
• result.summary()

Citation

If you use this package in your work, please cite the following articles:

1. Lessani, M.N. and Li, Z., 2024. SGWR: similarity and geographically weighted regression. International Journal of Geographical Information Science, 38(7), pp.1232-1255.
2. Lessani, M.N. and Li, Z., 2025. Enhancing the computational efficiency of the SGWR model and introducing its software implementation. Annals of GIS, 31(4), pp.635-650.
3. Lessani, M.N., Li, Z., Yu, M., Greatrex, H. and Shen, C., 2026. M-SGWR: Multiscale Attribute-Similarity and Geographically Weighted Regression. Geographical Analysis.