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Nested LMM (Hiyerarşik Karma Model)

Fields → Fen Bilimleri ve Matematik → ⚡ Nested LMM (Hiyerarşik Karma Model)

Nested LMM (Hiyerarşik Karma Model)

⚡ Advanced · Mixed Models · Nested

v1.0.1

Natural Sciences and Mathematics context — fixed effect (treatment) + nested random effects. reaksiyon_verimi_pct ~ tedavi + (1|laboratuvar/tezgah/tekrar). Difference from VARCOMP: a fixed effect (e.g. treatment/group comparison) is added.

laboratuvar/tezgah/tekrar 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 the Natural Sciences and Mathematics, if the same replicates 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: bench within laboratory, replicate within bench.
  3. Random effects ~ Normal(0, σ²).
  4. ≥1 observation in each treatment-replicate 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 — Natural Sciences and Mathematics

📂 samples/Ileri_Duzey_v102/fen-bilimleri-matematik/108_nested_lmm.xlsx · n = 216 · Treatment: Control/Treatment-A/Treatment-B · Hierarchy: laboratuvar/tezgah/tekrar

⬇ Download sample data set (.xlsx)

laboratuvar tezgah tekrar tedavi reaksiyon_verimi_pct
LABORATUVAR_01 TEZGAH_01_01 TEKRAR_01_01_01 Kontrol 87.887
LABORATUVAR_01 TEZGAH_01_01 TEKRAR_01_01_01 Tedavi-A 87.062
LABORATUVAR_01 TEZGAH_01_01 TEKRAR_01_01_01 Tedavi-B 87.689
LABORATUVAR_01 TEZGAH_01_01 TEKRAR_01_01_02 Kontrol 87.448
LABORATUVAR_01 TEZGAH_01_01 TEKRAR_01_01_02 Tedavi-A 90.572
… … … … …

📊 MerQur Output (summary)

Nested LMM (reaksiyon_verimi_pct ~ tedavi + (1|laboratuvar/tezgah/tekrar)) 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 laboratuvar 12.25 tezgah 4.00 tekrar 2.25 Residual 4.00

📄 APA 7 Yorumu

A nested LMM was fitted on 216 observations of nested data (laboratory = 6) in the Natural Sciences and Mathematics field. Relative to the control group, Treatment-A increased reaksiyon_verimi_pct 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 bench-ids must not repeat across each laboratuvar.
  • Optimizer stalling (lbfgs llf=inf) — MerQur resolves it with a bfgs/cg cascade.
  • Treatment × laboratuvar 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.