Crossed LMM (Crossed Random Mixed Model)
v1.0.1
Architecture, Planning & Design context — two random factors that are NOT nested but crossed. degerlendirme_puan ~ 1 + (1|hakem_mimari) + (1|proje). Each hakem_mimari is matched with all proje.
🎯 What is it for?
Different from a classical nested structure: each hakem_mimari is crossed independently with different projects (not every project under every hakem_mimari; crossed). In Architecture, Planning & Design, 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).
- ≥1 observation in each (hakem_mimari, proje) cell (empty cells bias the estimates).
- Random effects ~ Normal(0, σ²).
📊 How to Run It in MerQur?
Panel assignments (form fields in the program):
- Dependent variable (DV):
memnuniyet - Factor A:
tasarim_stili - Factor B:
bolge - A Type:
random - B Type:
random - SS method:
1
📊 Sample Dataset — Architecture, Planning & Design
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 Architecture, Planning & Design:
Peyzaj_Mimarligi/109_crossed_lmm_design_region.xlsx
🎬 Scenario
In a crossed design (each design in each region) we examine main effects and the
design x region interaction; crossed LMM is appropriate.
⚙️ Variable Selection
- Dependent: satisfaction | Factor A: design_style | Factor B: region
Data Preview (First 5 Rows)
| design_style | region | satisfaction |
|---|---|---|
| classic | center | 3.67 |
| classic | center | 3.35 |
| classic | center | 3.65 |
| classic | center | 3.71 |
| classic | center | 3.73 |
n = 160 · Columns: design_style, region, satisfaction
📈 MerQur Output
─────────────────────────────────────────────
design style: F = 1.23, p = 0.356 (non-significant) | region: F = 0.69, p = 0.584 (non-significant)
design x region interaction: F = 11.62, p < .001 *** (SIGNIFICANT)
💬 Interpretation
Unlike nesting, here two factors are crossed: each design style was applied in each region (fully factorial). A
striking result: both main effects are non-significant (design: p = 0.356, region: p = 0.584), but the interaction
is highly significant (F = 11.62, p < .001). This is a classic case of a “pure interaction”: design and region
alone say nothing, but TOGETHER — specific design-region combinations — they create a strong effect. So a design
style can be very successful in one region and fail in another; “there is no single design that suits everywhere”.
Looking only at the main effects and saying “nothing is significant” would be a major error. The crossed mixed
model is the right way to capture the design×region interaction in context-sensitive landscape design.
⚠ Common Mistakes
- Specifying crossed when the structure is nested — make sure that each (hakem_mimari, proje) pair is truly independent.
- Very sparse matrix (many empty cells in hakem_mimari×proje) — the fit fails or is unstable.
- If hakem_mimari-ICC is low and proje-ICC is high, the shrinkage on the proje 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.