VARCOMP (Variance-Components Analysis)

⚡ Advanced · Mixed Models · Variance Decomposition

v1.0.1

Natural Sciences & Mathematics 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, in MerQur with a REML/ML cascade.

3-level nestedlaboratuvar/tezgah/tekrar
REML + ML fallbackICC + heritabilityσ²_laboratuvar ≈ 3.5

🎯 What is it for?

VARCOMP answers the question of which level contributes how much variance. Is the variability in the distribution of a single reaksiyon_verimi_pct measurement entirely random, or does it stem from systematic differences between laboratory and bench? With VARCOMP, σ²_laboratory, σ²_bench, σ²_replicate, 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 field of Natural Sciences & Mathematics
For sample-size calculation when designing a data-collection plan in which you will take the same measurement on different benches under different laboratories
To compute heritability / generalizability (σ² ratios)
Before even building a fixed-effect model — where does the variance lie primarily?

⚙ Assumptions

Continuous DV (reaksiyon_verimi_pct).
Nested structure: bench within laboratory, replicate within bench (no cross-level confounding).
Random effects ~ Normal (homoscedastic, mean 0).
Sufficient units at each level: ≥4-6 laboratories, each with ≥2 benches, 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 — Natural Sciences & Mathematics

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 Natural Sciences & Mathematics:

Fen_Matematik/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 lab it is used in
hierarchical structures (batch>sample>replicate) to see where uncertainty concentrates and in sampling/measurement
design; it underlies ratio estimates such as heritability (h2).

⚠ Common Mistakes

Forgetting the nested checkbox — the bench column is clustered under laboratory (e.g., TEZGAH_05_03 exists only within LABORATUVAR_05). If the checkbox is left unchecked, a crossed structure is assumed → the variance is partitioned incorrectly.
A single level at the second tier — if a laboratory has only a single bench beneath it, VARCOMP cannot estimate that level (σ²=bench≈0 ‘singular fit’ warning).
Continuous DV assumption — for Bernoulli/count data, a GLMM or a categorical-VARCOMP alternative is required 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.