Crossed LMM (Crossed Random Mixed Model)
v1.0.1
Engineering context — two random factors that are NOT nested but crossed. hata_orani_ppm ~ 1 + (1|operator) + (1|parca_tipi). Each operator is matched with all parca_tipi.
🎯 What is it for?
Different from the classic nested structure: each operator is paired independently with different parca_tipi’s (not every parca_tipi under every operator; crossed). In Engineering it estimates the random variance of the two factors 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).
- Each (operator, parca_tipi) cell has ≥1 observation (empty cells affect the estimates).
- Random effects ~ Normal(0, σ²).
📊 How Is It Run 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 — Engineering
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 Engineering:
Muhendislik/109_crossed_lmm_A_B.xlsx
🎬 Scenario
We model a design where two random factors are crossed. For two independent
classification axes, crossed LMM is appropriate.
⚙️ Variable Selection
- Dependent variable: value
- Factor (categorical): factor_a
- 2nd Factor: 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
─────────────────────────────────────────────
A x B interaction: F = 14.67, p < .001 *** main effects ns (A: p=0.767, B: p=0.480) outcome: value
💬 Interpretation
We modeled a design where two random factors are crossed rather than nested (each level of A pairs with each level
of B): while the main effects are non-significant (A: p=0.77, B: p=0.48), the A x B interaction is very strong
(F = 14.67, p < .001) — so the effect depends on the COMBINATION of factors. Crossed LMM, unlike nested, handles
two independent grouping axes (e.g. method x block, each method in each block) at once. In the field it is the
right choice for jointly analyzing the effects and interaction of two independent classification axes.
⚠ Common Mistakes
- Specifying crossed when the structure is actually nested — make sure each (operator, parca_tipi) pair is genuinely independent.
- A very sparse matrix (many empty cells in operator×parca_tipi) — the fit cannot be obtained or is unstable.
- If the operator-ICC is low and the parca_tipi-ICC is high, the shrinkage in the parca_tipi estimate 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.