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Spatial Error Model

Research Disciplines → Education Sciences → ⚡ Spatial Error Model

Spatial Error Model

⚡ Advanced · Spatial Regression

v1.0.2

Education Sciences context — Spatial Error Model. A regression that accounts for the spatial neighborhood structure of okul_basari_skoru. Spatial weight matrix: K-nearest neighbor (k=5), row standardized.

Y = Xβ + λWu + εlibpysal KNN Wspreg MLλ ≈ 0.45

🎯 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) + a continuous DV in Education Sciences
  • 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 (school_success_score).
  3. Spatial weight matrix design (KNN k=5 — default, with dist.band as an alternative).
  4. The λ parameter is stable between 0 and 1; there is a risk of fragility near 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 — Education Sciences

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 Education Sciences:

Egitim_Bilimleri/106_spatial_error_residual.xlsx

🎬 Scenario

Imagine the same kind of regional education data over 100 spatial units,
where the predictors X1 and X2 explain part of an outcome Y_value but the
leftover residuals are still spatially clustered, perhaps due to unmeasured
neighborhood factors. The coordinates are stored in lat and lon. Here a
Spatial Error model is the right tool because the spatial dependence lives
in the error term rather than in the outcome itself, so we model correlated
residuals to obtain unbiased standard errors and trustworthy predictor
estimates. This corrects inference when nearby areas share hidden
influences.

⚙️ Variable Selection

  • Coordinates: lat, lon
  • Predictors: X1, X2
  • Dependent variable: Y_value

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
─────────────────────────────────────────────

lambda (spatial error) = 0.59 z = 6.38 p < .001 Pseudo R2 = 0.84
Y ~ X1 + X2 + spatial error structure

💬 Interpretation

The spatial error model addresses a different kind of spatial dependence than SAR: not a direct effect of
neighbour values, but correlation induced through the residuals by unobserved (omitted) spatial factors. Lambda =
0.59 (z = 6.38, p < .001) shows this spatial error structure is strong — there are unmeasured common spatial
factors (regional policy, socio-economic background). Which spatial model is appropriate (SAR or SEM) depends on
whether the effect comes from neighbour values or from unmeasured factors. SEM cleans out these unmeasured
spatial confounders to estimate the true effect of the variables more accurately.

⚠ 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.