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Nested LMM (Hierarchical Mixed Model)

Research Disciplines → Agriculture, Forestry & Aquatic → ⚡ Nested LMM (Hierarchical Mixed Model)

Nested LMM (Hierarchical Mixed Model)

⚡ Advanced · Mixed Models · Nested

v1.0.1

Agriculture, Forestry & Aquatic context — fixed effect (treatment) + nested random effects. boy_artisi_m ~ tedavi + (1|saha/populasyon/aile). Difference from VARCOMP: a fixed effect (e.g. treatment/group comparison) is added.

saha/populasyon/aile nestedTedavi sabit etkenREMLFixed effect estimate + p

🎯 What is it for?

It accounts for the variance of the random factors while interpreting fixed effects in hierarchical data. In Agriculture, Forestry & Aquatic, if different treatments are applied within the same families, 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: population within site, family within population.
  3. Random effects ~ Normal(0, σ²).
  4. ≥1 observation in each treatment-family combination.

📊 How to Run It in MerQur?

1
Load data.
2
Analysis → ⚡ Advanced → Nested LMM.
3

Panel assignments (form fields in the program):

  • Dependent Variable: deger
  • Repeat Variable: blok
  • Upper Group: ust_grup
  • Nested Group: alt_grup_no
  • SS Type: 1
4
Estimator: REML.
5
▶ Run. Fixed effect β̂ + p + σ² for each random level.

📊 Sample Dataset — Agriculture, Forestry & Aquatic

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 Agriculture, Forestry & Aquatic:

Ziraat_Orman_Su/108_nested_lmm_R_P_F.xlsx

🎬 Scenario

In a replicated hierarchical breeding trial — block (block), upper group (upper_group), lower group (lower_group_no) — we
estimate the variance components and effects of a trait (value) in a single model. The nested LMM, in this structure where the
lower group is nested within the upper group, gives each level’s contribution with correct F tests: is the difference among
populations/families significant, is there a genotype-environment interaction?

⚙️ Variable Selection

  • Dependent (continuous): value
  • Replication (block): block
  • Upper group: upper_group
  • Lower group (nested): lower_group_no

Data Preview (First 5 Rows)

unit_id block upper_group lower_group_no value
B001 R1 P1 F01 43.23
B002 R1 P1 F01 48.59
B003 R1 P1 F01 43.18
B004 R2 P1 F01 41.92
B005 R2 P1 F01 43.46

n = 288 · Columns: unit_id, block, upper_group, lower_group_no, value

📈 MerQur Output

NESTED LMM (HIERARCHICAL MIXED MODEL) RESULT
─────────────────────────────────────────────

upper_group (P): F(3) = 4.92, p = 0.010 * | model: value ~ R + P + R*P + F(P) + R*F(P)
block (R), upper_group (P), lower_group_no (F nested in P)

💬 Interpretation

In a replicated hierarchical breeding trial — block, upper group (population), lower group (family, nested within
population) — we estimated the variance components and effects of a trait in a single model. The nested LMM, in
this nested structure, gives each level’s contribution with correct F tests (each effect uses the appropriate error
term — something ordinary ANOVA cannot do). The result: the upper group (population) is significant, F(3) = 4.92, p
= 0.010. So there is a genetic/structural difference among populations. This is the fundamental question of forest
breeding: at which level should selection be done? If the population difference is significant, choosing the right
population is the priority; if the family difference dominates, choosing families within a population is. The nested
LMM provides the statistical basis for this decision.

⚠ Common Mistakes

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

Tüm atıf formatları →

📝 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.