CFA / SEM — Doğrulayıcı Faktör & Yapısal Eşitlik Modeli

Advanced · Latent Variable Modeling

Confirmatory Factor Analysis (CFA) + Structural Equation Model (SEM) combined in a single module. Measurement model only (CFA): validates the factor structure against the data. When structural paths are defined, it runs as SEM: directional causal relationships between latent factors are estimated. semopy 2.3.11 backend.

CFA — measurement model
SEM — structural paths
CFI / TLI / RMSEA / SRMR
Hu & Bentler kriterleri
semopy backend

🆕 v1.0.2 new feature: Structural paths (SEM)

Starting with v1.0.2, an optional “Structural paths” field has been added to the form. If left empty, a classic CFA runs (only covariance among latents). If filled, directional relationships among latent factors are estimated → a full Structural Equation Model. Syntax: F2 ~ F1; F3 ~ F1 + F2

🎯 What is it for?

CFA: tests how well a predefined factor structure fits the data. Whereas EFA discovers the structure in the data, CFA confirms that structure.

SEM: adds a structural model on top of CFA — causal directional relationships among latent factors (β path coefficients) are estimated.

CFA only: scale validity, survey model testing
CFA + SEM: testing chained causality such as motivation → studying → achievement
Fit indices: CFI, TLI, RMSEA, GFI, AGFI, NFI, AIC, BIC, log-likelihood
Standardized loading: the relationship of an observed variable with its factor
Path coefficients (SEM mode): latent → latent β + z + p

📌 When is it used?

Çoklu Likert ölçeklerinde faktör yapısı doğrulama (CFA)
Teorik modelin verilere uygunluk testi (SEM)
Mediation analizi alternatifi (latent değişkenli)
Ölçek geliştirme — psikometri çalışmaları
Sosyal bilimlerde yapısal yol analizi (sıralı nedensellik)

⚙ Assumptions

Continuous (at least ordinal, ≥4-category Likert) observed variables.
Multivariate normality (flexible at large n).
The factor structure is predefined (from EFA or theory).
N ≥ 200 is recommended; at least 3 observed variables per factor.
Structural paths (SEM mode): the causal ordering must be theoretically justified; cyclic relationships are prohibited (a DAG is required).

📊 How to Run It in MerQur?

Select it from the Analysis tab

Analysis → ⚡ Advanced → CFA / SEM (Confirmatory Factor & Structural Equation).

Number of factors + observed variables

Number of factors: 1-6. A separate VariableSelector opens for each factor; select ≥3 observed variables per factor.

Structural paths (optional SEM)

For classic CFA, leave it empty. For SEM, enter the directional relationships among latent factors:

F2 ~ F1 — F1 predicts F2
F3 ~ F1 + F2 — F1 and F2 together predict F3
F2 ~ F1; F3 ~ F2 — chained causality (mediator)

Separate multiple paths with a semicolon (;).

Run

Modal progress. In the Results tab you get the measurement model + (if any) the structural path coefficients. Table: all parameters (loading + path) with z/p.

🧪 Örnek Uygulama — Yapısal Eşitlik Modeli

250 students, 3 latent factors (motivation F1, study F2, achievement F3), each with 3 observed indicators.

══ SEM — YAPISAL EŞİTLİK MODELLEMESİ (CFA + Path) ══
n = 250

── MEASUREMENT MODEL (gözlenen ←→ latent) ──
F1 =~ X11 + X12 + X13 # motivasyon
F2 =~ X21 + X22 + X23 # çalışma
F3 =~ X31 + X32 + X33 # başarı

── STRUCTURAL MODEL (latent → latent) ──
F2 ~ F1 # motivasyon → çalışma
F3 ~ F1 + F2 # motivasyon + çalışma → başarı

── FIT INDICES ──
χ² = 28.42 df = 24 χ² p = 0.243
CFI = 0.999 TLI = 0.999
RMSEA = 0.013 GFI = 0.972
AIC = 5832.4 BIC = 5908.7

GENEL UYUM: MÜKEMMEL

── YAPISAL YOL KATSAYILARI (Structural Paths) ──
Hedef ← Kaynak β SE z p
F2 ← F1 0.457 0.0749 6.105 0.0000 ★
F3 ← F1 0.460 0.0736 6.247 0.0000 ★
F3 ← F2 0.537 0.0684 7.851 0.0000 ★

APA 7 Interpretation

The structural relationships among motivation, studying, and achievement were tested with a Structural Equation Model (SEM) (N = 250, ML estimation, semopy). The model fit indices met the acceptance criteria of Hu & Bentler (1999): χ²(24) = 28.42, p = .24; CFI = 1.00, TLI = 1.00, RMSEA = 0.01. All structural paths were significant: F1 (motivation) → F2 (studying): β = 0.46, p < .001; F1 → F3 (achievement): β = 0.46, p < .001; F2 → F3: β = 0.54, p < .001. The findings support a mediator model in which motivation affects achievement both directly and indirectly through studying.

⚠ Common Mistakes

<3 observed variables per factor. A minimum of 3, ideally 4-6, observed variables are needed for CFA. Too few observed variables create an identifiability problem.
CFA without doing EFA. First discover the structure with EFA, then confirm it with CFA on an independent sample.
A cycle in the structural paths. F1 ~ F2; F2 ~ F1 is prohibited (cyclic). A DAG (directed acyclic graph) is required.
Ignoring low loadings. Observed variables with a standardized loading < 0.4 are problematic — consider revising the scale.
Over-interpreting with N < 200. SEM requires a large sample; at small n, parameter estimates are unstable.
Over-emphasizing the χ² p-value. At large n, χ² is overly strict; evaluate CFI/TLI/RMSEA together.

📚 İlgili Analizler

Açıklayıcı Faktör Analizi (EFA) — yapı keşfi
Path Analysis — observed-only path model
Mediation Analysis — basit aracı etki
Cronbach’s Alpha — ölçek güvenilirliği
ICC — gözlemciler arası tutarlılık

📚 If You Used This Analysis, Cite MerQur

Örücü, Ö. K. (2026). MerQur: Integrated Academic Data Analysis & Reporting Platform [Computer software] (Version 1.0.0). https://doi.org/10.53463/merqur.2026001

Sources:

Brown, T. A. (2015). Confirmatory Factor Analysis for Applied Research (2nd ed.). Guilford Press.
Kline, R. B. (2015). Principles and Practice of Structural Equation Modeling (4th ed.). Guilford Press.
Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis. Structural Equation Modeling, 6(1), 1-55.
Igolkina, A. A., & Meshcheryakov, G. (2020). semopy: A Python package for structural equation modeling. Structural Equation Modeling, 27(6), 952-963.

CFA / SEM — Structural Equation Modeling