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CFA / SEM — Yapısal Eşitlik Modeli

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)

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

🎯 What is it for?

CFA: tests the fit of a predefined factor structure to the data. Whereas EFA explores the structure in the data, CFA confirms that structure.

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

  • CFA only: scale validity, testing a questionnaire model
  • CFA + SEM: testing chain 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?

  • Confirming factor structure in multiple Likert scales (CFA)
  • Testing the fit of a theoretical model to the data (SEM)
  • Alternative to mediation analysis (with latent variables)
  • Scale development — psychometric studies
  • Structural path analysis in social sciences (sequential causality)

⚙ Assumptions

  1. Continuous observed variables (at least ordinal, Likert with ≥4 categories).
  2. Multivariate normality (flexible for large n).
  3. The factor structure is predetermined (from EFA or from theory).
  4. N ≥ 200 is recommended; at least 3 observed variables per factor.
  5. 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

1

Select it from the Analysis tab

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

2

Number of factors + observed variables

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

3

Yapısal yollar (opsiyonel SEM)

For classical CFA, leave blank. For SEM, specify the directed relationships among latent factors:

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

Separate multiple paths with a semicolon (;).

4

Run

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

🧪 Example Application — Structural Equation Model

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

══ SEM — STRUCTURAL EQUATION MODELLING (CFA + Path) ══
n = 250

── MEASUREMENT MODEL (observed ←→ latent) ──
F1 =~ X11 + X12 + X13 # motivation
F2 =~ X21 + X22 + X23 # study
F3 =~ X31 + X32 + X33 # achievement

── STRUCTURAL MODEL (latent → latent) ──
F2 ~ F1 # motivation → study
F3 ~ F1 + F2 # motivation + study → achievement

── 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

OVERALL FIT: EXCELLENT

── STRUCTURAL PATH COEFFICIENTS (Structural Paths) ──
Target ← Source 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 Yorumu

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 are 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 influences achievement both directly and indirectly through studying.

⚠ Common Mistakes

  • Fewer than 3 observed variables per factor. A minimum of 3 and ideally 4-6 observed variables are needed for CFA. Too few observed variables create an identifiability problem.
  • CFA without EFA. First explore the structure with EFA, then confirm it with CFA on an independent sample.
  • Loops 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; with a small n, parameter estimates are unstable.
  • Overemphasizing the χ² p-value. With large n, χ² is overly strict; evaluate CFI/TLI/RMSEA together.

📚 Related Analyses

  • Exploratory Factor Analysis (EFA) — structure discovery
  • Path Analysis — observed-only path model
  • Mediation Analysis — simple mediating effect
  • Cronbach’s Alpha — scale reliability
  • ICC — inter-observer consistency

📚 If You Used This Analysis, Cite MerQur

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

References:

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