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Nested LMM (Hiyerarşik Karma Model)

Fields → Sosyal, Beşeri ve İdari Bilimler → ⚡ Nested LMM (Hiyerarşik Karma Model)

Nested LMM (Hiyerarşik Karma Model)

⚡ Advanced · Mixed Models · Nested

v1.0.1

Social, Human and Administrative Sciences context — fixed effect (treatment) + nested random effects. is_tatmini_skoru ~ tedavi + (1|sektor/firma/calisan). Difference from VARCOMP: a fixed effect (e.g. treatment/group comparison) is added.

sektor/firma/calisan 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 Social, Humanities and Administrative Sciences, if the same employees 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: firma within sektor, calisan within firma.
  3. Random effects ~ Normal(0, σ²).
  4. ≥1 observation in each treatment-calisan 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 — Social, Human and Administrative Sciences

📂 samples/Ileri_Duzey_v102/sosyal-beseri-idari/108_nested_lmm.xlsx · n = 216 · Treatment: Control/Treatment-A/Treatment-B · Hierarchy: sector/company/employee

⬇ Download the example data set (.xlsx)

sektor firma calisan tedavi is_tatmini_skoru
SEKTOR_01 FIRMA_01_01 CALISAN_01_01_01 Kontrol 2.3
SEKTOR_01 FIRMA_01_01 CALISAN_01_01_01 Tedavi-A 5.857
SEKTOR_01 FIRMA_01_01 CALISAN_01_01_01 Tedavi-B 9.309
SEKTOR_01 FIRMA_01_01 CALISAN_01_01_02 Kontrol 3.107
SEKTOR_01 FIRMA_01_01 CALISAN_01_01_02 Tedavi-A 6.265
… … … … …

📊 MerQur Output (summary)

Nested LMM (is_tatmini_skoru ~ tedavi + (1|sektor/firma/calisan)) 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 sektor 0.16 firma 0.09 calisan 0.09 Residual 0.16

📄 APA 7 Yorumu

A Nested LMM was fitted on 216 nested observations (sector=6) in the field of Social, Humanities and Administrative Sciences. Relative to the control group, Treatment-A increased is_tatmini_skoru 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

  • Specifying “crossed” instead of “nested” — the firma-id values must not repeat across each sektor.
  • Optimizer failure (lbfgs llf=inf) — MerQur resolves this with a bfgs/cg cascade.
  • Treatment × sektor 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.