Mixed Models (GLMM)

Clustered data — patients within hospitals, cells within animals, students within schools — violate the independence assumption of standard regression. Licklider detects hierarchical structure, selects an appropriate mixed model, and discloses both fixed and random effect estimates with the full model specification required by journals.

STEP 1 — The Scenario

Researcher Profile

A clinical researcher conducting a multi-site observational study across 6 hospitals. The outcome is post-operative pain score (NRS, 0–10) at 24 hours. Predictors include treatment type (pharmacological vs. non-pharmacological), age, and sex. Patients are nested within hospitals, creating a two-level hierarchical structure.

Research Question

"Is pharmacological treatment associated with lower post-operative pain at 24 hours, after accounting for patient characteristics and between-hospital variability?"

Dataset

• 6 hospitals (sites); 180 total patients (n=20–35 per hospital)
• Outcome: Post-operative pain NRS (0–10), continuous
• Fixed effects: Treatment (binary), Age (continuous), Sex (binary)
• Random effect: Hospital (site-level random intercept)

STEP 2 — Licklider Analysis Path

1. Data Upload & Clustering Detection

Licklider detects the Hospital column with 6 unique values. It asks: "Patients appear to be grouped by Hospital. Should Hospital be treated as a random effect?" Variable & ID Mapping (2.1.2) confirms the nesting structure: patients within hospitals.

2. Data Contract Declaration

Observation unit: one patient. Level-2 clustering unit: hospital. Fixed effects: Treatment, Age, Sex (pre-specified). Random effect: Hospital random intercept (to account for unmeasured between-hospital differences in baseline pain).

3. Intraclass Correlation (ICC)

The null model (random intercept only, no predictors) is fitted first. The ICC is calculated: the proportion of total variance attributable to between-hospital differences. ICC >0.05 confirms that mixed modeling is necessary (and that standard regression would be invalid).

4. LMM Fitting

Linear mixed model: PainScore ~ Treatment + Age + Sex + (1|Hospital). Fixed effect estimates (β, SE, t, p, 95% CI) are reported for each predictor. Random effect variance (between-hospital σ²) and residual variance are reported. REML estimation is used for variance components.

5. Model Comparison

If the researcher wants to test whether adding a random slope (e.g., treatment effect varies by hospital) improves the model, Licklider fits the extended model and compares with a likelihood ratio test (LRT) or AIC/BIC.

6. Figure Generation

Coefficient plot (forest-style) showing fixed effect estimates with 95% CI. A panel of site-level predicted means with overall model prediction overlaid is available as a supplementary figure.

STEP 3 — Guards & Disclosures Activated

Pseudoreplication Detection (4.5.1)

If the researcher submits data without a Hospital column and treats all 180 patients as independent, Licklider's pseudoreplication guard flags: "Multiple observations share a common hospital of care — standard regression may underestimate standard errors. A mixed model with hospital as a random effect is recommended."

Confounding Disclosure (4.6.2)

Hospital is a potential confounder: hospitals differ in patient case-mix, protocols, and resources. The random effect approach adjusts for between-hospital differences but does not eliminate unmeasured within-hospital confounding. Licklider discloses this limitation in the Methods text.

Independence Formal Check (4.6.1)

Licklider confirms via the ICC calculation that observations within hospitals are not independent (ICC confirms clustering). The assumption check result (ICC value and p) is reported.

Effect Size Reporting (4.1.2)

Marginal R² (variance explained by fixed effects alone) and conditional R² (variance explained by fixed + random effects) are reported. These are the appropriate effect size measures for mixed models (Nakagawa & Schielzeth approach).

Causal Language Detection (3.1.5)

Observational data — the causal language guard enforces "was associated with" rather than "caused" or "reduced" in a causal sense, and discloses confounding limitations.

STEP 4 — Export Package

• Figure: Coefficient forest plot — fixed effects with 95% CI — 300 dpi TIFF/PDF
• Statistical Report: Full LMM output (fixed effects: β, SE, t, p, 95% CI; random effects: variance components, ICC); null model ICC; marginal and conditional R²; model comparison table (if applicable)
• Methods Text: "Post-operative pain scores were modeled using a linear mixed model with hospital as a random intercept. Fixed effects included treatment type, age, and sex. The intraclass correlation coefficient from the null model was [ICC value], confirming the appropriateness of mixed modeling. Fixed effect estimates are presented as β (95% CI). Marginal R²=[value], Conditional R²=[value]. Analyses were conducted using Licklider (version X.X)."
• Figure Legend: Predictor labels, β estimates, CI method, ICC disclosure, n (patients), n (sites)
• Preprocessing Audit Log: Cluster detection; ICC calculation; any excluded sites or patients