VARCOMP (Variance-Components Analysis)

⚡ Advanced · Mixed Models · Variance Decomposition

v1.0.1

Engineering context — in a hierarchical design, it decomposes how much of the total variance originates from which level (site, group, subgroup, error). Equivalent to SAS PROC VARCOMP, with a REML/ML cascade in MerQur.

3-level nestedfabrika/uretim_hatti/parti
REML + ML fallbackICC + heritabilityσ²_fabrika ≈ 18.0

🎯 What is it for?

VARCOMP answers the question of which level contributes how much variance. Is the variability in the distribution of a single urun_dayanim_MPa measurement entirely random, or does it stem from systematic differences between fabrika and uretim_hatti? With VARCOMP, σ²_fabrika, σ²_{uretim_hatti}, σ²_parti and σ²_residual are estimated separately; the percentage share of each is reported.

📌 When is it used?

When there is a multilevel sampling design (nested) in the Engineering field
For sample-size calculation when designing a data-collection plan in which you will take the same measurement on different uretim_hatti’s under different fabrika’s
To compute heritability / generalizability (σ² ratios)
Before even building a fixed-effect model — where does the variance primarily lie?

⚙ Assumptions

Continuous DV (urun_dayanim_MPa).
Nested structure: uretim_hatti within fabrika, parti within uretim_hatti (no cross-level confounding).
Random effects ~ Normal (homoskedastic, mean 0).
Sufficient units at each level: ≥4-6 fabrika, each with ≥2 uretim_hatti, is recommended.

📊 How to Run It in MerQur?

Data tab → Open File → load the dataset.

Analysis → ⚡ Advanced → VARCOMP.

Panel assignments (form fields in the program):

Columns: {'dv': 'deger', 'factors': [('ust_birim', False), ('alt_birim', True)]}
Parameters: {'estimator': 'REML'}

Estimation method: REML (default). You can switch to ML for the LRT.

▶ Run. A modal progress window opens. When estimation completes, σ², %, ICC and diagnostic notes are listed for each component.

📊 Sample Dataset — Engineering

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 Engineering:

Muhendislik/100_varcomp_3seviye_h2.xlsx

🎬 Scenario

We decompose measurement variability into nested levels (upper/lower unit). For
hierarchical variability, variance components is appropriate.

⚙️ Variable Selection

Dependent variable: value
Factor (categorical): upper_unit
Factor (categorical): lower_unit (nested)

Data Preview (First 5 Rows)

upper_unit	lower_unit	measurement_id	value
L_A	L_A_S01	L_A_S01_M01	51.41
L_A	L_A_S01	L_A_S01_M02	52.17
L_A	L_A_S01	L_A_S01_M03	40.6
L_A	L_A_S01	L_A_S01_M04	43.19
L_A	L_A_S01	L_A_S01_M05	48.91

n = 100 · Columns: upper_unit, lower_unit, measurement_id, value

📈 MerQur Output

VARCOMP (VARIANCE-COMPONENTS ANALYSIS) RESULT
─────────────────────────────────────────────

Random factors: upper_unit + lower_unit (nested within upper) % contribution of each component + residual

💬 Interpretation

We decomposed a measurement’s variability into nested levels — upper unit and lower unit within upper: the percent
contribution of each level and the residual were reported. Variance components analysis answers “how much of the
variability is between upper units, how much between lower units, how much within unit?”. In the field it is used
in hierarchical structures (region>plot>replicate) to see where uncertainty concentrates and in sampling design; it
underlies ratio estimates such as heritability (h2).

⚠ Common Mistakes

Forgetting the nested checkbox — the uretim_hatti column is clustered under fabrika (e.g. URETIM_HATTI_05_03 exists only in FABRIKA_05). If the checkbox is not checked, crossed is assumed → the variance is shared incorrectly.
A single level at the second level — if there is a single uretim_hatti under a fabrika, VARCOMP cannot estimate that level (σ²=uretim_hatti≈0 ‘singular fit’ warning).
Continuous DV assumption — for Bernoulli/count data, a GLMM or a categorical-VARCOMP alternative is needed instead of VARCOMP (outside MerQur’s scope).

📚 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

Tüm atıf formatları →

📝 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.