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Spatial Error Model

Research Disciplines → Agriculture, Forestry & Aquatic → ⚡ Spatial Error Model

Spatial Error Model

⚡ Advanced · Spatial Regression

v1.0.2

Agriculture, Forestry & Aquatic context — Spatial Error Model. Regression that accounts for the spatial neighborhood structure of agac_capi_cm. Spatial weight matrix: K-nearest neighbor (k=5), row-standardized.

Y = Xβ + λWu + εlibpysal KNN Wspreg MLλ ≈ 0.65

🎯 What is it for?

Classic OLS assumes the observations are independent — but in lat/lon data, nearby points take on similar values (spatial autocorrelation). The Spatial Error Model incorporates this structure into the model; otherwise the standard errors of the OLS β estimates come out too small (type-I error).

📌 When is it used?

  • Spatial data (with lat/lon) + continuous DV in Agriculture, Forestry & Aquatic
  • Moran’s I p < .05 — evidence of spatial autocorrelation
  • Spatial clustering in the OLS residuals (hotspot over DBSCAN)

⚙ Assumptions

  1. Lat/lon coordinates ({lat, lon}).
  2. Continuous DV (agac_capi_cm).
  3. Design of the spatial weight matrix (KNN k=5 — default, with a dist.band alternative).
  4. The λ parameter is stable between 0-1; there is a risk of fragility at the boundary.

📊 How to Run in MerQur

1
Load the data (lat, lon, DV, X1, X2 columns).
2
Analysis → ⚡ Advanced → Spatial Error Model.
3

Panel assignments (form fields in the program):

  • Columns: {'y': 'birim_id', 'x': ['X1', 'X2'], 'lat': 'lat', 'lon': 'lon'}
  • Parameters: {'weights': 'knn', 'k': 5}
4
Estimator: ML (default).
5
▶ Run. Coefficient forest plot + λ + map.

📊 Sample Dataset — Agriculture, Forestry & Aquatic

ℹ Note: The scenario, MerQur output and interpretation below were produced by actually running the real example dataset in MerQur. Numeric results on your own data will differ; the goal is to show how the analysis is set up and interpreted end-to-end.

🎬 Example File

This analysis is demonstrated on the following example dataset for Agriculture, Forestry & Aquatic:

Ziraat_Orman_Su/106_spatial_error_residual.xlsx

🎬 Scenario

Again across spatial units we model Y_value with X1, X2; but this time the spatial dependence is in the residuals (from
unobserved shared environmental factors). The spatial-error model (SEM) models the spatial structure of the error term to keep
the coefficients from becoming biased/inflated: what are the X effects once they are purified from the hidden spatial residual
arising from the neighborhood?

⚙️ Variable Selection

  • Dependent (outcome): Y_value
  • Predictors: X1, X2
  • Coordinates: lat, lon

Data Preview (First 5 Rows)

unit_id lat lon X1 X2 Y_value
1.0 40.729 36.2513 58.0 18.3 369.6
2.0 37.3016 39.779 60.9 46.8 460.7
3.0 38.3563 33.0728 73.2 48.6 495.5
4.0 41.2077 28.8098 82.7 15.0 199.5
5.0 40.7324 29.6924 48.9 32.5 410.3

n = 100 · Columns: unit_id, lat, lon, X1, X2, Y_value

📈 MerQur Output

SPATIAL ERROR MODEL RESULT
─────────────────────────────────────────────

λ (lambda) = 0.590 z = 6.38, p < .001 Pseudo R² = 0.84 AIC = 1037.4
Y_value ~ X1 + X2 (lat/lon)

💬 Interpretation

Again across spatial units we modeled Y with X1, X2; but this time the spatial dependence is in the residuals (from
unobserved shared environmental factors). The spatial-error model (SEM) models the spatial structure of the error
term to keep the coefficients from becoming biased/inflated. The result is significant: lambda = 0.59, z = 6.38, p <
.001 — a strong spatial autocorrelation in the residuals. This supports the “omitted spatial variables” hypothesis:
something spatially structured that we did not include is affecting the residuals. With pseudo R² = 0.84 the model is
still strong. Choosing between SAR and SEM means asking whether the spillover is in the outcome (SAR) or in the error
(SEM); here AIC finds SEM slightly better.

⚠ Common Mistakes

  • λ ≈ 1 → matrix singularity; try a looser W (k=10).
  • The choice of W matrix affects the results — compare KNN and DistanceBand.
  • Projected coordinates (UTM) instead of Lat/Lon may be preferable for accurate distance.

📚 MerQur’a Atıf

Örücü, Ö. K. (2026). MerQur: Integrated Academic Data Analysis & Reporting Platform [Computer software] (Version 1.0.0). https://doi.org/10.53463/merqur.2026001

Tüm atıf formatları →

📝 Üretim Notu — Bu sayfadaki örnek veri sentetik olarak üretilmiştir (sabit SEED=42, generator: samples/Ileri_Duzey_v102/_generate_v102_datasets.py). Sayfa içeriği Anthropic Claude desteği ile hazırlanmış, akademik doğruluk yazar tarafından kontrol edilmiştir.