Crossed LMM (Crossed Random Mixed Model)
v1.0.1
Agriculture, Forestry & Aquatic context — two random factors are NOT nested but crossed. puanlama ~ 1 + (1|hakemci_islah) + (1|genotip). Each hakemci_islah is paired with every genotip.
🎯 What is it for?
Different from the classic nested structure: each hakemci_islah mates independently with different genotypes (not every genotype under every hakemci_islah; crossed). In Agriculture, Forestry & Aquatic it estimates the random variance of the two effects separately.
📌 When is it used?
- Rater × ratee (each rater evaluates every sample)
- Operator × device (each operator uses every device)
- Measurement design with two random effects
⚙ Assumptions
- The two random factors are independent of each other (not nested).
- ≥1 observation in each (hakemci_islah, genotip) cell (empty cells make effects estimable only approximately).
- Random effects ~ Normal(0, σ²).
📊 How to Run It in MerQur?
Panel assignments (form fields in the program):
- Dependent Variable:
deger - Factor A:
faktor_a - Factor B:
faktor_b - A Type:
random - B Type:
random - SS Type:
1
📊 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/109_crossed_lmm_A_B.xlsx
🎬 Scenario
In a design where two random factors (factor_a, factor_b) are crossed — each A level pairs with each B level — we model the
outcome (value) (e.g. every genotype tested at every location). The crossed LMM takes A and B as crossed random effects; it thus
models the variability from both genotype and location at once and gives purified estimates.
⚙️ Variable Selection
- Dependent (continuous): value
- Crossed random effects: factor_a, factor_b
Data Preview (First 5 Rows)
| factor_a | factor_b | value |
|---|---|---|
| A1 | B1 | 53.8 |
| A1 | B1 | 55.31 |
| A1 | B1 | 50.68 |
| A1 | B1 | 55.81 |
| A1 | B1 | 56.05 |
n = 128 · Columns: factor_a, factor_b, value
📈 MerQur Output
─────────────────────────────────────────────
factor_a (random): F(3) = 0.38, p = 0.767 ns | value ~ factor_a + factor_b (crossed random)
💬 Interpretation
In a design where two random factors are crossed — each A level pairs with each B level — we modeled the outcome
(e.g. every genotype tested at every location). The crossed LMM takes A and B as crossed random effects, modeling
the variability from both genotype and location at once. The result: factor A is not significant (F(3) = 0.38, p =
0.77) — so there is no notable difference among its levels. Non-significance is also a finding: factor A’s
contribution to the outcome is negligible. Crossed designs differ from nested ones: here A and B are independently
crossed (every combination present), whereas in nested the sub-factor is embedded in the upper. The correct model
depends on the true structure of the design.
⚠ Common Mistakes
- Defining a crossed structure when the structure is nested — make sure that each (hakemci_islah, genotip) pair is truly independent.
- A very sparse matrix (many empty cells in hakemci_islah×genotip) — the fit cannot be performed or is unstable.
- If hakemci_islah-ICC is low + genotip-ICC is high, the shrinkage in the estimation of genotip is tighter.
📚 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.