SAR (Spatial Autoregressive Lag)
v1.0.2
Architecture, Planning & Design context — Spatial Lag 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). SAR (Spatial Autoregressive Lag) 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 ρ parameter is stable within 0-1; risk of fragility near the boundary.
📊 How Is It Run 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/105_spatial_sar_park_value_spatial.xlsx
🎬 Scenario
We model park value with SAR, which includes the effect of neighbour values (spatial
lag, rho).
⚙️ 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 | 1089340.0 |
| 2.0 | 39.7804 | 31.3363 | 36869.0 | 0.525 | 2509011.0 |
| 3.0 | 40.6427 | 37.658 | 1816.0 | 0.137 | 50000.0 |
| 4.0 | 38.931 | 30.9028 | 21223.0 | 0.668 | 1767107.0 |
| 5.0 | 39.3061 | 32.7805 | 13899.0 | 0.491 | 764180.0 |
n = 100 · Columns: park_id, lat, lon, area_m2, green_ratio, park_value_TL
📈 MerQur Output
─────────────────────────────────────────────
rho (spatial lag) = 0.29 z = 3.19 p = 0.001 Pseudo R2 = 0.81
Park value ~ area + green ratio + neighbour park value
💬 Interpretation
Modelling park value, we accounted for spatial dependence — the tendency of nearby parks to be similar in value.
The SAR (spatial autoregressive) model links a park’s value to its neighbours’ value too (rho). Here rho = 0.29,
significantly positive (z = 3.19, p = 0.001): the neighbour effect is real and moderate — a park’s value is
influenced by neighbouring parks/surroundings (neighborhood prestige, access). The model explains 81% of the
variance. Using a spatial model is critical, because ordinary regression gives spurious significant results when
spatial autocorrelation is present. SAR is the right way to model urban park/real-estate values with spread and
neighbour effects.
⚠ Common Mistakes
- ρ ≈ 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.