Nested LMM (Hierarchical Mixed Model)
v1.0.1
Health Sciences context — fixed effect (treatment) + nested random effects. HbA1c_pct ~ tedavi + (1|hastane/doktor/hasta). The difference from VARCOMP: a fixed effect (e.g., treatment/group comparison) is added.
🎯 What is it for?
When interpreting fixed effects in hierarchical data, it also accounts for the variance of the random factors. In Health Sciences, if the same patients receive different treatments, 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
- Continuous DV, categorical fixed effect.
- Nested structure: doctor within hospital, patient within doctor.
- Random effects ~ Normal(0, σ²).
- ≥1 observation in each treatment-patient combination.
📊 How is it run in MerQur?
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
📊 Sample Dataset — Health Sciences
ℹ Note: The scenario, MerQur output and interpretation below were produced by actually running the real example dataset in MerQur. Numeric results on your own data will differ; the goal is to show how the analysis is set up and interpreted end-to-end.
🎬 Example File
This analysis is demonstrated on the following example dataset for Health Sciences:
Tip/108_nested_lmm_clinical_doctor_visit_HbA1c.xlsx
🎬 Scenario
We model HbA1c in a nested design (clinic>doctor>visit). For nested hierarchies,
nested LMM is appropriate.
⚙️ Variable Selection
- Dependent variable: HbA1c
- Factor (categorical): visit
- Factor (categorical): clinical
- Factor (categorical): doctor_no
Data Preview (First 5 Rows)
| patient_id | visit | clinical | doctor_no | HbA1c |
|---|---|---|---|---|
| H0001 | V1 | K_Ankara | D01 | 6.49 |
| H0002 | V1 | K_Ankara | D01 | 5.74 |
| H0003 | V1 | K_Ankara | D01 | 6.67 |
| H0004 | V2 | K_Ankara | D01 | 6.62 |
| H0005 | V2 | K_Ankara | D01 | 7.59 |
n = 288 · Columns: patient_id, visit, clinical, doctor_no, HbA1c
📈 MerQur Output
─────────────────────────────────────────────
clinical (P) effect: F = 10.37, p < .001 *** doctor_no (within clinic, F): F = 7.57, p < .001 ***
visit (R) effect: F = 14.20, p < .001 *** outcome: HbA1c
💬 Interpretation
We modeled HbA1c in a nested design (clinic > doctor > visit): the clinic level (F = 10.37, p < .001), the doctor
level (F = 7.57, p < .001) and the visit/replication level (F = 14.20, p < .001) all make significant contributions.
Nested LMM correctly handles hierarchies where sub-units are nested within super-units (each doctor belongs to only
one clinic); by partitioning variance into levels it shows each layer’s share. In medicine it is used to correctly
separate effects in clinic>doctor>patient hierarchies.
⚠ 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.
📚 MerQur’a Atıf
Örücü, Ö. K. (2026). MerQur: Integrated Academic Data Analysis & Reporting Platform [Computer software] (Version 1.0.0). https://doi.org/10.53463/merqur.2026001
📝 Üretim Notu — Bu sayfadaki örnek veri sentetik olarak üretilmiştir (sabit SEED=42, generator: samples/Ileri_Duzey_v102/_generate_v102_datasets.py). Sayfa içeriği Anthropic Claude desteği ile hazırlanmış, akademik doğruluk yazar tarafından kontrol edilmiştir.