SAR (Spatial Autoregressive Lag)
v1.0.2
Natural Sciences & Mathematics context — Spatial Lag Model. A regression that accounts for the spatial neighborhood structure of hava_kalitesi_indeksi. 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) + continuous DV in Natural Sciences & Mathematics
- Moran’s I p < .05 — evidence of spatial autocorrelation
- Spatial clustering in OLS residuals (hotspot over DBSCAN)
⚙ Assumptions
- Lat/lon coordinates ({lat, lon}).
- Continuous DV (hava_kalitesi_indeksi).
- Spatial weight matrix design (KNN k=5 — default, with a dist.band alternative).
- The ρ parameter is stable between 0 and 1; there is a fragility risk at the boundary.
📊 How to Run in MerQur
Panel assignments (form fields in the program):
- Columns:
{'y': 'birim_id', 'x': ['X1', 'X2'], 'lat': 'lat', 'lon': 'lon'} - Parameters:
{'weights': 'knn', 'k': 5}
📊 Sample Dataset — Natural Sciences & Mathematics
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 Natural Sciences & Mathematics:
Fen_Matematik/105_spatial_sar_spatial.xlsx
🎬 Scenario
When modeling a measurement we handle spatial spillover with SAR. For
neighborhood effects, SAR is appropriate.
⚙️ Variable Selection
- Dependent variable: Y_value
- Predictor(s): X1
- Predictor(s): X2
- Latitude: lat
- Longitude: lon
Data Preview (First 5 Rows)
| unit_id | lat | lon | X1 | X2 | Y_value |
|---|---|---|---|---|---|
| 1.0 | 40.729 | 36.2513 | 58.0 | 18.3 | 375.9 |
| 2.0 | 37.3016 | 39.779 | 60.9 | 46.8 | 464.0 |
| 3.0 | 38.3563 | 33.0728 | 73.2 | 48.6 | 530.5 |
| 4.0 | 41.2077 | 28.8098 | 82.7 | 15.0 | 197.6 |
| 5.0 | 40.7324 | 29.6924 | 48.9 | 32.5 | 385.3 |
n = 100 · Columns: unit_id, lat, lon, X1, X2, Y_value
📈 MerQur Output
─────────────────────────────────────────────
rho = 0.336 z = 4.94 p < .001 *** Pseudo R^2 = 0.87 (N = 100, k-NN W, k = 5)
outcome: Y_value, predictors: X1, X2
💬 Interpretation
When modeling a measurement (Y_value), we handled spatial spillover (the effect of neighboring units) with SAR: the
spatial lag parameter is significant and positive (rho = 0.34, p < .001) — a unit’s value is related to its
neighbors’ value, a “cluster/spillover” pattern. SAR incorporates spatial dependency into the model; if ignored,
standard errors are biased. In the lab/environmental studies it is the right method for modeling the geographic
spread of measurements (neighborhood effect).
⚠ 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.