Crossed LMM (Crossed Random Mixed Model)
v1.0.1
Health Sciences context — the two random factors are NOT nested but crossed. laboratuvar_olcum ~ 1 + (1|lab_teknisyeni) + (1|hasta). Each lab_teknisyeni is paired with all hastas.
🎯 What is it for?
Different from the classical nested structure: each lab_teknisyeni pairs independently with different hasta’s (not every hasta under every lab_teknisyeni; crossed). In Health Sciences, 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).
- At least 1 observation in each (lab_teknisyeni, hasta) cell (empty cells affect the estimate).
- Random effects ~ Normal(0, σ²).
📊 How is it run in MerQur?
Panel assignments (form fields in the program):
- Dependent variable (DV):
HbA1c - Factor A:
ilac - Factor B:
klinik - A Type:
random - B Type:
random - SS method:
1
📊 Sample Dataset — Health Sciences
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 Health Sciences:
Tip/109_crossed_lmm_drug_clinical.xlsx
🎬 Scenario
We model a design where two random factors (drug x clinic) are crossed. For two
independent classification axes, crossed LMM is appropriate.
⚙️ Variable Selection
- Dependent variable: HbA1c
- Factor (categorical): drug
- 2nd Factor: clinical
Data Preview (First 5 Rows)
| drug | clinical | HbA1c |
|---|---|---|
| drug_1 | K_A | 7.79 |
| drug_1 | K_A | 7.37 |
| drug_1 | K_A | 7.77 |
| drug_1 | K_A | 7.85 |
| drug_1 | K_A | 7.87 |
n = 160 · Columns: drug, clinical, HbA1c
📈 MerQur Output
─────────────────────────────────────────────
drug (A): F = 2.24, p = 0.125 ns clinical (B): F = 4.31, p = 0.028 * A x B: F = 13.00, p < .001 *** outcome: HbA1c
💬 Interpretation
We modeled a design where two random factors are crossed rather than nested (each drug is given in each clinic): the
drug main effect is non-significant (p = 0.13), the clinic main effect is significant (p = 0.028), and the A x B
interaction is very strong (F = 13.00, p < .001) — so a drug’s effect DEPENDS on which clinic it is given in.
Crossed LMM, unlike nested, handles two independent grouping axes (drug x clinic, each drug in each clinic) at once.
In medicine it is the right choice for jointly analyzing the effects and interaction of two independent
classification axes.
⚠ Common Mistakes
- Specifying a crossed structure when the design is actually nested — make sure each (lab_teknisyeni, hasta) pair is genuinely independent.
- A very sparse matrix (many empty cells in lab_teknisyeni×hasta) — the model cannot be fit or is unstable.
- If the lab_teknisyeni-ICC is low and the hasta-ICC is high, shrinkage is tighter in estimating the hasta.
📚 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.