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Nested LMM (Hiyerarşik Karma Model)

Fields → Sağlık Bilimleri → ⚡ Nested LMM (Hiyerarşik Karma Model)

Nested LMM (Hiyerarşik Karma Model)

⚡ Advanced · Mixed Models · Nested

v1.0.1

Health Sciences context — fixed effect (treatment) + nested random effects. HbA1c_pct ~ tedavi + (1|hastane/doktor/hasta). Difference from VARCOMP: a fixed effect (e.g. treatment/group comparison) is added.

hastane/doktor/hasta 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 Health Sciences, if the same patients 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: doctor within hospital, patient within doctor.
  3. Random effects ~ Normal(0, σ²).
  4. ≥1 observation in each treatment-patient 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): HbA1c
  • Replication (R): vizit
  • Upper-level group (P): klinik
  • Lower-level group (F): doktor_no
  • SS method: 1
4
Estimator: REML.
5
▶ Run. Fixed-effect β̂ + p + σ² for each random level.

🧪 Example Data — Health Sciences

📂 samples/Ileri_Duzey_v102/saglik-bilimleri/108_nested_lmm.xlsx · n = 216 · Treatment: Control/Treatment-A/Treatment-B · Hierarchy: hospital/doctor/patient

⬇ Download the example data set (.xlsx)

hastane doktor hasta tedavi HbA1c_pct
HASTANE_01 DOKTOR_01_01 HASTA_01_01_01 Kontrol 5.808
HASTANE_01 DOKTOR_01_01 HASTA_01_01_01 Tedavi-A 10.445
HASTANE_01 DOKTOR_01_01 HASTA_01_01_01 Tedavi-B 13.117
HASTANE_01 DOKTOR_01_01 HASTA_01_01_02 Kontrol 5.695
HASTANE_01 DOKTOR_01_01 HASTA_01_01_02 Tedavi-A 9.989
… … … … …

📊 MerQur Output (summary)

Nested LMM (HbA1c_pct ~ tedavi + (1|hastane/doktor/hasta)) 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 hastane 0.49 doktor 0.25 hasta 0.16 Residual 0.25

📄 APA 7 Yorumu

A nested LMM was fitted on 216 observations of nested data (hospital = 6) in the Health Sciences field. Relative to the control group, Treatment-A increased HbA1c_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 doctor-ids should not recur within each hospital.
  • Optimizer stalling (lbfgs llf=inf) — MerQur resolves this with a bfgs/cg cascade.
  • Treatment × hospital 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.