Spatial Error Model
v1.0.2
Architecture, Planning & Design context — Spatial Error Model. Regression that accounts for the spatial neighborhood structure of emlak_fiyati_TL_m2. Spatial weight matrix: K-nearest neighbor (k=5), row standardized.
🎯 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 Architecture, Planning & Design
- Moran’s I p < .05 — evidence of spatial autocorrelation
- Spatial clustering in the OLS residuals (hotspots on DBSCAN)
⚙ Assumptions
- Lat/lon coordinates ({lat, lon}).
- Continuous DV (emlak_fiyati_TL_m2).
- Spatial weight matrix design (KNN k=5 — default, with a dist.band alternative).
- The λ parameter is stable between 0 and 1; there is a fragility risk at the boundary.
📊 How to Run It in MerQur?
Panel assignments (form fields in the program):
- Columns:
{'y': 'park_deger_TL', 'x': ['alan_m2', 'yesil_orani'], 'lat': 'lat', 'lon': 'lon'} - Parameters:
{'weights': 'knn', 'k': 5}
📊 Sample Dataset — Architecture, Planning & Design
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 Architecture, Planning & Design:
Peyzaj_Mimarligi/106_spatial_error_use_residual.xlsx
🎬 Scenario
We examine park value with the spatial error model, which captures the correlation
induced by unmeasured spatial factors through the residuals (lambda).
⚙️ Variable Selection
- Dependent: park_value_TL | Predictors: area_m2, green_ratio | Coordinates: lat, lon
Data Preview (First 5 Rows)
| park_id | lat | lon | area_m2 | green_ratio | park_value_TL |
|---|---|---|---|---|---|
| 1.0 | 40.8754 | 41.6339 | 43707.0 | 0.244 | 1127526.0 |
| 2.0 | 39.7804 | 31.3363 | 36869.0 | 0.525 | 2525100.0 |
| 3.0 | 40.6427 | 37.658 | 1816.0 | 0.137 | 38431.0 |
| 4.0 | 38.931 | 30.9028 | 21223.0 | 0.668 | 1760014.0 |
| 5.0 | 39.3061 | 32.7805 | 13899.0 | 0.491 | 717165.0 |
n = 100 · Columns: park_id, lat, lon, area_m2, green_ratio, park_value_TL
📈 MerQur Output
─────────────────────────────────────────────
lambda (spatial error) = 0.41 z = 3.40 p = 0.001 Pseudo R2 = 0.79
Park value ~ variables + 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 = 0.41 (z =
3.40, p = 0.001) shows this spatial error structure is significant — there are unmeasured common spatial factors
(neighborhood infrastructure, socio-economic context, transport). 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 on park value 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
📝 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.