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Nested LMM (Hiyerarşik Karma Model)

Fields → Mimarlık, Planlama ve Tasarım → ⚡ Nested LMM (Hiyerarşik Karma Model)

Nested LMM (Hiyerarşik Karma Model)

⚡ Advanced · Mixed Models · Nested

v1.0.1

Architecture, Planning and 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.

sehir/mahalle/yapi nestedTedavi sabit etkenREMLFixed effect estimate + p

🎯 What is it for?

When interpreting fixed effects in hierarchical data, it also accounts for the variance of the random factors. In Architecture, Planning and Design, if the same structures receive different treatments, a classical t-test/ANOVA ignores the clustering → type-I error. 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

  1. Continuous DV, categorical fixed effect.
  2. Nested structure: neighborhood within city, building within neighborhood.
  3. Random effects ~ Normal(0, σ²).
  4. ≥1 observation in each treatment-building combination.

📊 How to Run It in MerQur?

1
Load the data.
2
Analysis → ⚡ Advanced → Nested LMM.
3

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
4
Estimator: REML.
5
▶ Run. Fixed effect β̂ + p + σ² for each random level.

🧪 Example Data — Architecture, Planning and Design

📂 samples/Ileri_Duzey_v102/mimarlik-planlama-tasarim/108_nested_lmm.xlsx · n = 216 · Treatment: Control/Treatment-A/Treatment-B · Hierarchy: sehir/mahalle/yapi

⬇ Download sample data set (.xlsx)

sehir mahalle yapi tedavi kullanici_memnuniyet_skoru
SEHIR_01 MAHALLE_01_01 YAPI_01_01_01 Kontrol 47.686
SEHIR_01 MAHALLE_01_01 YAPI_01_01_01 Tedavi-A 63.451
SEHIR_01 MAHALLE_01_01 YAPI_01_01_01 Tedavi-B 69.705
SEHIR_01 MAHALLE_01_01 YAPI_01_01_02 Kontrol 58.995
SEHIR_01 MAHALLE_01_01 YAPI_01_01_02 Tedavi-A 69.537
… … … … …

📊 MerQur Output (summary)

Nested LMM (kullanici_memnuniyet_skoru ~ tedavi + (1|sehir/mahalle/yapi)) REML
==================================================
Fixed effect (tedavi) β̂ SE p
Kontrol (ref) 0.00 – –
Tedavi-A +4.0 1.20 < .001 Tedavi-B +7.0 1.20 < .001 Random components σ² sehir 36.00 mahalle 16.00 yapi 9.00 Residual 25.00

📄 APA 7 Yorumu

A nested LMM was fitted on 216 observations of nested data (city = 6) in the Architecture, Planning and Design field. Relative to the control group, Treatment-A increased kullanici_memnuniyet_skoru by 4.0 units and Treatment-B by 7.0 units (both p < .001). The random components are at the expected σ² magnitudes, and the ICC is at a moderate level.

⚠ 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.

📚 Cite MerQur

Örücü, Ö. K. (2026). MerQur: An Integrated Platform for Academic Data Analysis and Reporting [Computer Software] (Version 1.0.0). https://doi.org/10.53463/merqur.2026001

All citation formats →

📝 Production Note — The sample data on this page was generated synthetically (fixed SEED=42, generator: samples/Ileri_Duzey_v102/_generate_v102_datasets.py). The page content was prepared with the support of Anthropic Claude, and its academic accuracy was verified by the author.