Nested LMM (Hierarchical Mixed Model)
v1.0.1
Architecture, Planning & Design context — fixed effect (treatment) + nested random effects. kullanici_memnuniyet_skoru ~ tedavi + (1|sehir/mahalle/yapi). Difference from VARCOMP: a fixed effect (e.g. treatment/group comparison) is added.
🎯 What is it for?
When interpreting fixed effects in hierarchical data, it also accounts for the variance of the random factors. In Architecture, Planning & Design, if the same buildings receive different treatments, a classic t-test/ANOVA ignores the clustering → Type-I error. A nested LMM computes this correctly.
📌 When is it used?
- Comparison of a fixed effect (treatment, intervention, condition) + hierarchical sampling
- Multi-site clinical research, multi-center field trial
- Adjusting site/group-level variance in RCTs
⚙ Assumptions
- Continuous DV, categorical fixed effect.
- Nested structure: neighborhood within city, building within neighborhood.
- Random effects ~ Normal(0, σ²).
- ≥1 observation in each treatment-building combination.
📊 How to Run It in MerQur?
Panel assignments (form fields in the program):
- Dependent variable (DV):
memnuniyet - Replication (R):
vizit - Upper-level group (P):
sehir - Lower-level group (F):
park_no - SS method:
1
📊 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/108_nested_lmm_city_park_visit.xlsx
🎬 Scenario
In a nested design (city > park > visit) we test each level’s contribution separately;
nested LMM is appropriate.
⚙️ Variable Selection
- Dependent: satisfaction | Replication: visit | Upper group: city | Lower group: park_no
Data Preview (First 5 Rows)
| participant_id | visit | city | park_no | satisfaction |
|---|---|---|---|---|
| K0001 | V1 | Ankara | P01 | 2.73 |
| K0002 | V1 | Ankara | P01 | 2.17 |
| K0003 | V1 | Ankara | P01 | 2.87 |
| K0004 | V2 | Ankara | P01 | 3.08 |
| K0005 | V2 | Ankara | P01 | 3.81 |
n = 288 · Columns: participant_id, visit, city, park_no, satisfaction
📈 MerQur Output
─────────────────────────────────────────────
city (P): F = 9.06, p < .001 *** | park_no [within city] (F): F = 8.30, p < .001 ***
visit (R): F = 2.98, p = 0.038 *
💬 Interpretation
In this design the measurements are nested: city > park > visit. The nested mixed model tests each level’s
contribution to the variance separately. The results are significant at all levels: there are real differences
between cities (F = 9.06), between parks within a city (F = 8.30), and between visits (F = 2.98). Mixing up the
levels in nested data (e.g. ignoring the city) produces spurious significance or wrong standard errors. Nested LMM
is the correct framework for hierarchical urban designs (city/park/visit, region/neighborhood/unit), separating
the genuine contribution of each scale; it is the basis of multi-level urban green-space analysis.
⚠ Common Mistakes
- Specifying “crossed” instead of “nested” — the neighborhood-ids must not repeat across each sehir.
- Optimizer stalling (lbfgs llf=inf) — MerQur resolves it with a bfgs/cg cascade.
- Treatment × sehir imbalance — the fixed-effect coefficient may be biased.
📚 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.