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Nested LMM (Hiyerarşik Karma Model)

Fields → Mühendislik → ⚡ Nested LMM (Hiyerarşik Karma Model)

Nested LMM (Hiyerarşik Karma Model)

⚡ Advanced · Mixed Models · Nested

v1.0.1

Engineering context — fixed effect (treatment) + nested random effects. urun_dayanim_MPa ~ tedavi + (1|fabrika/uretim_hatti/parti). Difference from VARCOMP: a fixed effect (e.g. treatment/group comparison) is added.

fabrika/uretim_hatti/parti 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 Engineering, if the same batches 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: uretim_hatti within fabrika, parti within uretim_hatti.
  3. Random effects ~ Normal(0, σ²).
  4. ≥1 observation in each treatment-parti 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 — Engineering

📂 samples/Ileri_Duzey_v102/muhendislik/108_nested_lmm.xlsx · n = 216 · Treatment: Control/Treatment-A/Treatment-B · Hierarchy: fabrika/uretim_hatti/parti

⬇ Download sample data set (.xlsx)

fabrika uretim_hatti parti tedavi urun_dayanim_MPa
FABRIKA_01 URETIM_HATTI_01_01 PARTI_01_01_01 Kontrol 355.218
FABRIKA_01 URETIM_HATTI_01_01 PARTI_01_01_01 Tedavi-A 376.136
FABRIKA_01 URETIM_HATTI_01_01 PARTI_01_01_01 Tedavi-B 374.672
FABRIKA_01 URETIM_HATTI_01_01 PARTI_01_01_02 Kontrol 364.527
FABRIKA_01 URETIM_HATTI_01_01 PARTI_01_01_02 Tedavi-A 353.466
… … … … …

📊 MerQur Output (summary)

Nested LMM (urun_dayanim_MPa ~ tedavi + (1|fabrika/uretim_hatti/parti)) 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 fabrika 324.00 uretim_hatti 144.00 parti 64.00 Residual 100.00

📄 APA 7 Yorumu

A nested LMM was fitted on 216 observations of nested data (plant = 6) in the Engineering field. Relative to the control group, Treatment-A increased urun_dayanim_MPa 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 uretim_hatti ids must not repeat across each fabrika.
  • Optimizer stalling (lbfgs llf=inf) — MerQur resolves it with a bfgs/cg cascade.
  • Treatment × fabrika 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.