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Nested LMM (Hiyerarşik Karma Model)

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

Nested LMM (Hiyerarşik Karma Model)

⚡ Advanced · Mixed Models · Nested

v1.0.1

Sport Sciences context — fixed effect (treatment) + nested random effects. sicrama_yuksekligi_cm ~ tedavi + (1|kulup/antrenor/sporcu). Difference from VARCOMP: a fixed effect (e.g. treatment/group comparison) is added.

kulup/antrenor/sporcu 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 Sport Sciences, if different treatments are applied to the same athletes, 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

  1. Continuous DV, categorical fixed effect.
  2. Nested structure: antrenor within kulup, sporcu within antrenor.
  3. Random effects ~ Normal(0, σ²).
  4. ≥1 observation in each treatment-sporcu 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 — Sport Sciences

📂 samples/Ileri_Duzey_v102/spor-bilimleri/108_nested_lmm.xlsx · n = 216 · Treatment: Control/Treatment-A/Treatment-B · Hierarchy: club/coach/athlete

⬇ Download the example data set (.xlsx)

kulup antrenor sporcu tedavi sicrama_yuksekligi_cm
KULUP_01 ANTRENOR_01_01 SPORCU_01_01_01 Kontrol 52.504
KULUP_01 ANTRENOR_01_01 SPORCU_01_01_01 Tedavi-A 58.621
KULUP_01 ANTRENOR_01_01 SPORCU_01_01_01 Tedavi-B 63.005
KULUP_01 ANTRENOR_01_01 SPORCU_01_01_02 Kontrol 51.329
KULUP_01 ANTRENOR_01_01 SPORCU_01_01_02 Tedavi-A 59.977
… … … … …

📊 MerQur Output (summary)

Nested LMM (sicrama_yuksekligi_cm ~ tedavi + (1|kulup/antrenor/sporcu)) 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 kulup 16.00 antrenor 6.25 sporcu 4.00 Residual 6.25

📄 APA 7 Yorumu

A Nested LMM was fitted on 216 nested observations (club=6) in the field of Sport Sciences. Relative to the control group, Treatment-A increased sicrama_yuksekligi_cm 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

  • Defining “crossed” instead of “nested” — the coach IDs should not recur across each club.
  • Optimizer crashing (lbfgs llf=inf) — MerQur resolves this with a bfgs/cg cascade.
  • Treatment × club 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.