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Nested LMM (Hiyerarşik Karma Model)

Fields → Ziraat, Orman ve Su Ürünleri → ⚡ Nested LMM (Hiyerarşik Karma Model)

Nested LMM (Hiyerarşik Karma Model)

⚡ Advanced · Mixed Models · Nested

v1.0.1

Agriculture, Forestry and Fisheries context — fixed effect (treatment) + nested random effects. boy_artisi_m ~ tedavi + (1|saha/populasyon/aile). Difference from VARCOMP: a fixed effect (e.g. treatment/group comparison) is added.

saha/populasyon/aile 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 Agriculture, Forestry and Aquaculture, if different treatments are applied within the same families, a classical 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

  1. Continuous DV, categorical fixed effect.
  2. Nested structure: population within site, family within population.
  3. Random effects ~ Normal(0, σ²).
  4. ≥1 observation in each treatment-family 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: deger
  • Replication Variable: blok
  • Upper Group: ust_grup
  • Inner (Nested) Group: alt_grup_no
  • SS Type: 1
4
Estimator: REML.
5
▶ Run. Fixed-effect β̂ + p + σ² for each random level.

🧪 Example Data — Agriculture, Forestry and Fisheries

📂 samples/Ileri_Duzey_v102/ziraat-orman-su-urunleri/108_nested_lmm.xlsx · n = 216 · Treatment: Control/Treatment-A/Treatment-B · Hierarchy: site/population/family

⬇ Download the example data set (.xlsx)

saha populasyon aile tedavi boy_artisi_m
SAHA_01 POPULASYON_01_01 AILE_01_01_01 Kontrol 3.489
SAHA_01 POPULASYON_01_01 AILE_01_01_01 Tedavi-A 7.926
SAHA_01 POPULASYON_01_01 AILE_01_01_01 Tedavi-B 10.586
SAHA_01 POPULASYON_01_01 AILE_01_01_02 Kontrol 3.285
SAHA_01 POPULASYON_01_01 AILE_01_01_02 Tedavi-A 7.427
… … … … …

📊 MerQur Output (summary)

Nested LMM (boy_artisi_m ~ tedavi + (1|saha/populasyon/aile)) 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 saha 0.20 populasyon 0.09 aile 0.05 Residual 0.06

📄 APA 7 Yorumu

A Nested LMM was fitted on 216 nested observations (site=6) in the field of Agriculture, Forestry and Aquaculture. Relative to the control group, Treatment-A increased boy_artisi_m by 4.0 units and Treatment-B by 7.0 units (both p < .001). The random components are of the expected σ² magnitudes, and the ICC is moderate.

⚠ Common Mistakes

  • Defining “crossed” instead of “nested” — the population IDs should not recur across each site.
  • Optimizer crashing (lbfgs llf=inf) — MerQur resolves this with a bfgs/cg cascade.
  • Treatment × site 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.