Hierarchical Bayesian Regression
v1.0.2
Agriculture, Forestry & Aquatic context — multilevel regression with a random intercept varying across serili_seras. It estimates the fide_canlilik_pct ~ sulama_mm relationship separately for each serili_sera 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?
- In Agriculture, Forestry & Aquatic, clustered data at the serili_sera level (≥10-20 individuals per serili_sera)
- ICC > 0.05 — group-level variance must be taken into account
- For the question “Which serili_sera has high/low performance?”, shrinkage-corrected ranking
⚙ Assumptions
- Random effect ~ Normal(0, σ²serili_sera).
- Within-group residual ~ Normal(0, σ²).
- At least ≥10 observations per group are recommended; with fewer, an informative prior is critical.
📊 How to Run in MerQur
Panel assignments (form fields in the program):
- Columns:
{'dv': 'Y_yanit', 'fixed': ['X_kovariat'], 'group': 'grup_id'} - Parameters:
{}
📊 Sample Dataset — Agriculture, Forestry & Aquatic
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 Agriculture, Forestry & Aquatic:
Ziraat_Orman_Su/104_hierarchical_bayesian_LMM.xlsx
🎬 Scenario
In data nested within groups (group_id) we estimate the effect of a covariate (X_covariate) on an outcome (Y_response) with a
hierarchical Bayesian model. The hierarchical Bayesian approach estimates group-level effects with partial pooling: groups with
little data are pulled toward the overall mean, yielding more stable estimates that express uncertainty explicitly.
⚙️ Variable Selection
- Dependent (continuous): Y_response
- Covariate (fixed effect): X_covariate
- Grouping (random): group_id
Data Preview (First 5 Rows)
| group_id | X_covariate | Y_response |
|---|---|---|
| G1 | 48.3 | 50.08 |
| G1 | 54.3 | 52.72 |
| G1 | 56.66 | 63.58 |
| G1 | 53.67 | 55.23 |
| G1 | 54.54 | 55.56 |
n = 200 · Columns: group_id, X_covariate, Y_response
📈 MerQur Output
─────────────────────────────────────────────
σ²_u (group random) = 2.90 (8.6%) | X_covariate fixed effect with 95% credible interval
Y_response ~ X_covariate + (1 | group_id)
💬 Interpretation
In data nested within groups we estimated the effect of a covariate on an outcome with a hierarchical Bayesian
model. The hierarchical Bayesian approach estimates group-level effects with “partial pooling”: groups with little
data are pulled toward the overall mean, yielding more stable estimates that express uncertainty explicitly. The
group random variance is 8.6 percent of the total variability — so there is a notable but not dominant difference
among groups. The covariate’s effect was reported with a posterior credible interval. The power of this approach
shows especially in low-data/many-group situations: it “intelligently” corrects individual group estimates,
prevents overfitting, and conveys uncertainty honestly.
⚠ Common Mistakes
- If there are <5 observations in each group, the group-level estimate is unreliable — a more informative prior is needed.
- Random slope (the slope of random sulama_mm) is not the default; if there is a cross-level interaction, 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.