MGWFER: Causal Spatially Varying Coefficients via Panel Fixed Effects

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Each dataset is available as a labeled Stata .dta and its source file.

⇩ Download all data (ZIP)stata_codebook.do

Run stata_codebook.do in Stata once to attach long-form per-variable notes to the .dta files.

Load directly in code

Every file loads straight from GitHub (raw URLs). Swap the file name to load any dataset.

Stata

* Stata 14+ : `use` reads an https URL directly
global BASE "https://raw.githubusercontent.com/cmg777/starter-academic-v501/master/content/post/python_mgwrfer/data/"
use "${BASE}simulated_panel_data.dta", clear
describe
notes

Python

!pip install -q pyreadstat
import pandas as pd
BASE = "https://raw.githubusercontent.com/cmg777/starter-academic-v501/master/content/post/python_mgwrfer/data/"
df = pd.read_stata(BASE + "simulated_panel_data.dta")

# load every dataset at once
files = ["simulated_panel_data"]
data = {f: pd.read_stata(BASE + f + ".dta") for f in files}

# pyreadstat (richest metadata) reads LOCAL files -> download first
import pyreadstat, urllib.request
urllib.request.urlretrieve(BASE + "simulated_panel_data.dta", "simulated_panel_data.dta")
df, meta = pyreadstat.read_dta("simulated_panel_data.dta")

Copy and paste this snippet in Google Colab app. https://colab.research.google.com/notebooks/empty.ipynb

R

# R : haven::read_dta auto-downloads an https URL
library(haven)
BASE <- "https://raw.githubusercontent.com/cmg777/starter-academic-v501/master/content/post/python_mgwrfer/data/"
df <- read_dta(paste0(BASE, "simulated_panel_data.dta"))

Overview & sources

Companion data for a Python tutorial faithful to Li & Fotheringham (2026), which introduces Multiscale Geographically Weighted Fixed Effects Regression (MGWFER) — a local panel framework that removes time-invariant spatial confounders from Multiscale GWR. The dataset is a fully synthetic spatial panel generated verbatim from the paper’s data-generating process (Eqs. 39–45) on a 15×15 grid of 225 spatial units observed over 3 time periods (675 observations). Each covariate is coupled to a time-invariant spatial context sc_i (Cor(x_k, sc) ≈ 0.84), so the indirect contextual effect channel is active and Cor(x_4, y) ≈ 0.84 even though β_4 ≡ 0. Because the true coefficient surfaces (beta1_true–beta4_true) and the confounder (alpha_true) are carried as columns, the panel is ground truth against which OLS, pooled OLS, fixed effects, cross-sectional MGWR, pooled MGWR, and MGWFER can be benchmarked. The entire data-generating process is open and reproducible.

Data sources

Cite this data

Please cite this dataset as follows.

APA

Mendez, C. (2026). MGWFER: Causal Spatially Varying Coefficients via Panel Fixed Effects [Data set]. https://carlos-mendez.org/post/python_mgwrfer/

Li, Z., & Fotheringham, A. S. (2026). Spatial Context as a Time-Invariant Confounder: A Fixed-Effects Extension of MGWR. Annals of the American Association of Geographers. https://doi.org/10.1080/24694452.2026.2654481

BibTeX

@misc{mendez2026pythonmgwrfer,
  author       = {Mendez, Carlos},
  title        = {MGWFER: Causal Spatially Varying Coefficients via Panel Fixed Effects},
  year         = {2026},
  howpublished = {\url{https://carlos-mendez.org/post/python_mgwrfer/}},
  note         = {Data set}
}

@article{li2026spatial,
  author  = {Li, Zhipeng and Fotheringham, A. Stewart},
  title   = {Spatial Context as a Time-Invariant Confounder: A Fixed-Effects Extension of {MGWR}},
  journal = {Annals of the American Association of Geographers},
  year    = {2026},
  doi     = {10.1080/24694452.2026.2654481}
}

Variable explorer search & filter all 14 variables

Type to filter by name or label, or use the chips to filter by type. Each row shows a mini distribution. Click a header to sort.

Cross-file variable index

Which file each variable appears in (● = present).

Construction & formulas

The data are generated from a two-part data-generating process on a 15×15 grid of N = 225 units indexed by integer coordinates (i, j), each observed over T = 3 periods (paper Eqs. 39–45). The columns alpha_true and beta1_true–beta4_true are the known truth the estimators are scored against.

• Time-invariant spatial context / fixed effect (alpha_true, sc_i): sc_i = 30·(exp(j/15) − 1) — an exponential gradient in the column index j (range 2.07–51.55, mean 23.29). It enters the outcome directly and drives the covariate levels.
• True slope β₁ (beta1_true): a quadratic dome peaking at the grid centre, 1 + (q²−(q−i/2)²)(q²−(q−j/2)²)/q⁴ with q = ⌈15/4⌉ (range 1.06–2.00).
• True slope β₂ (beta2_true): a linear gradient, 1 + (i+j)/(2·15) (range 1.07–2.00).
• True slope β₃ (beta3_true): constant 1.5 everywhere (tests spatial homogeneity).
• True slope β₄ (beta4_true): identically 0 everywhere (a null effect — tests false-positive detection).
• Covariate equation (the indirect contextual channel, Eqs. 40–43): x_k,it = 0.05·sc_i + ν_k,it, ν ~ N(0, 0.5), for k = 1,2,3,4 — every covariate is a noisy linear function of spatial context, giving Cor(x_k, sc) ≈ 0.84.
• Outcome equation (Eqs. 44–45): y_it = sc_i + β₁(i,j)·x1 + β₂(i,j)·x2 + β₃(i,j)·x3 + ε_it, ε ~ N(0, 0.5) — note x4 is excluded from y (β₄ ≡ 0), so its 0.84 correlation with y is spurious, transmitted only through the shared parent sc.

The headline correction: pooled estimators recover β_k + δ_k (true slope plus the indirect contextual effect δ_k); the within-transformation ỹ_it = y_it − ȳ_i removes the time-invariant sc_i exactly, neutralising δ_k and restoring identification of the local slopes.

The datasets

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Known limitations & caveats

• Synthetic data. There is no real data behind this tutorial; values are simulated from the paper's DGP with a fixed seed. Results are internally consistent with the design but are not empirical evidence about real-world spatial processes.
• Truth columns are not observable in practice. alpha_true and beta1_true–beta4_true are carried only so estimators can be scored. In an applied setting these are exactly the unknowns the methods try to recover — do not feed them to the models as predictors.
• Indirect channel by construction. Every covariate is 84% correlated with spatial context, and x4 is 84% correlated with y despite β₄ = 0. Any model that fails to condition on sc (cross-sectional/pooled OLS, MGWR_cs, PMGWR) will misread this as a real local effect — that is the point of the simulation, not a data error.
• Reduced 15×15 grid. The paper uses a 30×30 grid; this panel uses 15×15 (225 units) so the multiscale bandwidth search completes in minutes. All qualitative conclusions are preserved, but exact RMSE/correlation magnitudes differ from the paper's.
• Balanced, short panel. Only T = 3 periods; the within estimator's degrees of freedom are NT − K − N = 446. Fixed-effects identification relies on strict exogeneity conditional on the fixed effects (no time-varying confounders).