Hierarchical Bayesian Regression
v1.0.2
Health Sciences context — multilevel regression with a random intercept varying across hastane units. It estimates the agri_skoru_VAS ~ opioid_dozu_mg relationship separately for each hospital and reports the posterior distribution + 95% CrI. PyMC NOT REQUIRED — statsmodels MixedLM + Empirical Bayes BLUP.
🎯 What is it for?
If your data are hierarchical (student-school, patient-hospital, measurement-device, etc.), OLS regression ignores within-group correlation → type-I error increases. Hierarchical Bayesian learns each group’s own intercept and reports it together with the 95% CrI. With BF₁₀ (LMM vs OLS), whether group-level variance is needed is tested.
📌 When is it used?
- Hospital-level clustered data in the Health Sciences (≥10-20 individuals per hospital)
- ICC > 0.05 — group-level variance must be taken into account
- Shrinkage-corrected ranking for the question “Which hospital performs high/low?”
⚙ Assumptions
- Random effect ~ Normal(0, σ²hospital).
- Within-group residual ~ Normal(0, σ²).
- At least 10 observations per group is recommended; if fewer, an informative prior is critical.
📊 How to Run It in MerQur
Panel assignments (form fields in the program):
- Columns:
{'dv': 'HbA1c', 'fixed': ['yas', 'BMI'], 'group': 'klinik'} - Parameters:
{}
📊 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/104_hierarchical_bayesian_clinical_random.xlsx
🎬 Scenario
We analyze clinic-nested data with a Bayesian hierarchical model. For stable
estimates in multi-center data, this is appropriate.
⚙️ Variable Selection
- Dependent variable: HbA1c
- Cluster: clinical
- Predictor(s): age
Data Preview (First 5 Rows)
| clinical | age | BMI | HbA1c |
|---|---|---|---|
| K_Ankara | 52 | 23.65 | 9.01 |
| K_Ankara | 25 | 34.06 | 9.0 |
| K_Ankara | 69 | 27.91 | 9.04 |
| K_Ankara | 72 | 26.29 | 9.46 |
| K_Ankara | 44 | 19.92 | 8.73 |
n = 200 · Columns: clinical, age, BMI, HbA1c
📈 MerQur Output
─────────────────────────────────────────────
sigma^2_u (group) = 0.491 (46.5%) sigma^2_eps (residual) = 0.566 (53.5%) outcome: HbA1c, group: clinical
💬 Interpretation
We analyzed clinic-nested data with a Bayesian hierarchical (multilevel) model: 46.5% of variability is
between-clinic, 53.5% within-clinic (ICC ~ 0.47 — high). This shows clinics make a large difference in HbA1c
outcomes. The Bayesian hierarchical model is the Bayesian version of LMM — it estimates group effects with posterior
distributions and balances small groups via “partial pooling”. In medicine it is powerful for producing stable
estimates even in small groups within multi-center (clinic/doctor/patient) data.
⚠ Common Mistakes
- If any group has <5 observations, the group-level estimate is unreliable — a more informative prior is required.
- A random slope (random slope of opioid_dozu_mg) is not the default; if a cross-level interaction is present it must be added explicitly.
- If ICC < 0.05, OLS may be sufficient — check BF₁₀.
📚 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.