ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܡܫܪܪܢܐ (CFA)

ܛܥܢܐ ܕܝܗܝ̈ܒܬܐ (loading the data)

ܟܡܕܒܩܚ ܥܡܘ̈ܕܐ ܬܪܝܨܐܝܬ ܡܢ ܓܠܝܘܢܐ (worksheet)، ܥܡ ܣܕܪܐ ܕܪ̈ܫܐ (header row) – ܟܪܫܡܚ ܓܘ ܐܩܣܠ، ܟܢܣܚܚ، ܘܟܡܕܒܩܚ ܠܐܟܐ:

ܬܘܩܢܐ ܕܡܘܕܝܠ (model)

ܐܝܡܢ ܡܦܠܚܝܚ (When to use)؟

ܐܝܡܢ ܕܫܘܐܠܐ ܥܠ ܒܢܝܢܐ ܝܠܗ: ܦܢܩܝܬܐ ܕܫܘܐ̈ܠܐ (questionnaire) ܕ-12 ܦܣܘ̈ܩܐ (items) ܓܪܓ ܡܫܚܐ ܬܠܬܐ ܡܦܗ̈ܡܢܘܬܐ – ܐܝܬܘܬܐ ܕܡܢ ܟܢܘܫܬܐ، ܬܘܟܠܢܐ ܥܠ ܡܘܬܒ̈ܐ ܘܫܘܬܦܘܬܐ – ܐܪܒܥܐ ܦܣܘ̈ܩܐ ܩܐ ܟܠ ܡܦܗܡܢܘܬܐ. ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܡܫܪܪܢܐ (confirmatory factor analysis) ܟܒܚܪ ܐܢ ܝܗܝ̈ܒܬܐ ܟܦܐܝܝ ܥܡ ܐܗܐ ܦܘܠܓܐ. Pallant (2020، ܨܚܚܐ 15) ܟܦܪܫܐ ܒܝܢܝ ܬܪܝܢ ܐܘܪ̈ܚܬܐ: ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܡܒܨܝܢܐ (EFA) "ܡܦܠܚܐ ܝܠܗ ܓܘ ܕܪ̈ܓܐ ܩܕܡܝ̈ܐ ܕܒܘܨܝܐ ܩܐ ܕܒܨܚ ܐܣܘܪ̈ܐ ܒܝܢܝ ܓܘܕܐ ܕܡܫܬܚܠܦ̈ܢܐ"، ܘܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܡܫܪܪܢܐ ܝܠܗ "ܓܘܕܐ ܕܐܘܪ̈ܚܬܐ ܡܣܘܒܟ̈ܬܐ ܝܬܝܪ، ܕܡܦܠܚܐ ܝܠܗ ܓܘ ܕܪܓܐ ܒܬܪܝܐ ܕܒܘܨܝܐ ܩܐ ܕܫܪܪܚ ܗܘܦܘܬܣ̈ܝܣ ܝܚܝܕ̈ܝܐ ܥܠ ܒܢܝܢܐ ܕܐܝܬ ܒܫܬܐܣܐ ܕܓܘܕܐ ܕܡܫܬܚܠܦ̈ܢܐ". Field (2024، ܦܣܩܐ 18.4.1) ܟܡܬܢܐ ܗܘ ܦܘܪܫܢܐ – "ܐܢ ܒܨܝܬܘܢ ܝܗܝ̈ܒܬܐ ܝܢ ܒܚܪܝܬܘܢ ܗܘܦܘܬܣܝܣ (hypothesis) ܝܚܝܕܝܬܐ" – ܘܟܡܘܣܦ ܕܒܘܚܪܢܐ ܕܗܘܦܘܬܣ̈ܝܣ ܥܠ ܒܢܝܢܐ ܕܡܫܬܚܠܦ̈ܢܐ ܟܣ̈ܝܐ (latent variables) ܘܐܣܘܪ̈ܐ ܒܝܢܬܗܘܢ "ܣܢܝܩܐ ܝܠܗ ܚܙܡܐ ܕܬܘܟܢܐ (software) ܐܚܪܢܐ (IBM SPSS AMOS، R ܝܢ Mplus)". ܓܘ EFA ܟܠ ܦܣܘܩܐ ܟܛܥܢ ܥܠ ܟܠ ܥܠ̈ܠܬܐ ܘܬܘܟܢܐ ܟܡܫܟܚ ܒܢܝܢܐ؛ ܓܘ CFA ܒܨܘܝܬܐ ܟܣܝܡܐ ܡܢ ܩܕܡ ܐܝܢܐ ܦܣܘܩܐ ܟܛܥܢ ܥܠ ܐܝܢܐ ܥܠܬܐ، ܘܟܠ ܛܥܢܐ ܐܚܪܢܐ ܩܝܡܐ ܝܠܗ ܠܣܦܝܩܘܬܐ – ܘܡܛܠ ܗܕܐ ܡܘܕܝܠ (model) ܡܨܐ ܕܡܬܒܚܪ.

ܡܦܠܚܢܘ̈ܝܬܐ ܕܡܬܚܙܝܢ ܣܓܝ: ܬܪܝܨܘܬܐ ܕܒܢܝܢܐ (construct validity) ܕܦܢܩܝܬܐ ܕܫܘܐ̈ܠܐ (ܐܢ ܦܣܘ̈ܩܐ (items) ܟܡܬܟܢܫܝ ܠܦܘܬ ܬܐܘܪܝܐ)، ܒܘܚܪܢܐ ܕܚܕܢܘܬܐ ܕܡܫܘܚܬܐ (unidimensionality) ܕܣܒܠܬܐ (scale) ܩܕܡ ܕܚܫܒܚ ܡܢܝܢܐ ܘܐܠܦܐ ܩܐ ܕܝܠܗ̇، ܦܘܚܡܐ ܒܝܢܝ ܒܢܝܢܐ ܕܚܕ ܥܠܬܐ (factor) ܘܕܟܡܐ ܥܠ̈ܠܬܐ (ܠܘܚܐ 7.21 ܕ-APA، 2020، ܝܠܗ ܚܬܝܬܐܝܬ ܦܘܚܡܐ ܗܕܟܐ)، ܘܫܪܝܪܘܬܐ ܡܪܟܒܬܐ (composite reliability؛ ω) – ܕܠܐ ܟܣܝܡܐ ܛܥ̈ܢܐ ܫܘ̈ܝܐ ܐܝܟ ܐܠܦܐ. CFA ܝܠܗ "ܡܘܕܝܠ ܕܡܫܘܚܬܐ" (measurement model) ܕ-SEM: ܦܘܫܩܐ ܕܫܒ̈ܝܠܐ ܟܡܚܝܕ ܓܐܪ̈ܐ ܒܝܢܝ ܡܫܬܚܠܦ̈ܢܐ ܚܙ̈ܝܐ (observed variables)، CFA ܟܡܚܝܕ ܥܠ̈ܠܬܐ ܟܣ̈ܝܬܐ (latent factors) ܥܡ ܦܣܘ̈ܩܐ، ܘ-ܡܘܕܝܠ ܕܫܘܝ̈ܘܬܐ ܒܢܝܢܝ̈ܬܐ (SEM ܓܡܝܪܐ) ܟܡܚܝܕ ܬܪܘܬܝܗܝ – ܓܐܪ̈ܐ ܒܝܢܝ ܥܠ̈ܠܬܐ ܟܣ̈ܝܬܐ. ܦܐܬ̈ܐ ܩܪܝ̈ܒܐ: ܐܠܦܐ ܕ-Cronbach ܘܡܢܝܢܐ ܕܣܒܠܬܐ، ܫܪܝܪܘܬܐ ܘܬܪܝܨܘܬܐ – ܡܦܗ̈ܡܢܘܬܐ، ܒܢܝܢܐ ܕܦܢܩܝܬܐ ܕܫܘܐ̈ܠܐ.

ܚܘܫܒܐ: ܡܢ ܡܘܕܝܠ ܠܡܐܛܪܝܟܣ ܕܫܘܚܠ̈ܦܐ ܡܫܘܬ̈ܦܐ

ܡܘܕܝܠ (model). ܟܠ ܦܣܘܩܐ (item) ܝܠܗ ܛܥܢܐ (loading؛ λ) ܐܥܦܐ ܥܠܬܐ (factor) ܕܝܠܗ، ܘܥܡ ܫܪܟܐ (residual) ܝܚܝܕܝܐ ܕܝܠܗ (θ): x = λF + e. ܡܢ ܗܪܟܐ ܟܐܬܐ ܡܐܛܪܝܟܣ ܕܫܘܚܠ̈ܦܐ ܡܫܘܬ̈ܦܐ (covariance matrix) ܕܡܘܕܝܠ "ܟܡܣܟܐ" ܕܚܙܐ: Σ = ΛΦΛ′ + Θ – ܛܥ̈ܢܐ، ܫܘܚܠ̈ܦܐ ܘܐܣܘܪ̈ܐ ܕܥܠ̈ܠܬܐ، ܘܫܘܚܠ̈ܦܐ ܕܫܪ̈ܟܐ. ܓܘ ܥܠܬܐ، ܐܣܘܪܐ ܒܝܢܝ ܬܪܝܢ ܦܣܘ̈ܩܐ ܟܠܗ ܟܥܒܪ ܒܓܘ ܥܠܬܐ (λ₁λ₂φ)؛ ܒܝܢܝ ܥܠ̈ܠܬܐ – ܒܓܘ ܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation) ܒܝܢܬܗܘܢ. Raykov (2024) ܟܡܬܢܐ ܡܘܕܝܠ ܕܦܣܘ̈ܩܐ "congeneric" – ܦܣܘ̈ܩܐ ܕܟܡܫܚܝ ܗܘ ܡܢܝܢܐ ܫܪܝܪܐ ܒܚܕ̈ܝܘܬܐ ܘܒܚܬܝܬܘܬܐ (precision) ܦܪ̈ܝܫܬܐ – ܐܝܟ ܚܕ ܒܫܪܪܐ ܥܡ ܡܘܕܝܠ ܕܚܕ ܥܠܬܐ (Jöreskog, 1971, as cited in Raykov)، ܘܡܨܐ ܕܡܬܒܚܪ ܥܡ ܐܪܒܥܐ ܦܣܘ̈ܩܐ ܘܠܥܠ.

Identification. ܠܥܠܬܐ ܟܣܝܬܐ (latent factor) ܠܝܬ ܚܕ̈ܝܘܬܐ ܕܡܫܘܚܬܐ – ܣܢܝܩܘܬܐ ܐܝܬ ܕܣܝܡܚ ܠܗܝܢ. Rosseel (2012، ܦܣܩܐ 4) ܟܡܬܢܐ ܬܪܝܢ ܐܘܪ̈ܚܬܐ: "(1) ܩܐ ܟܠ ܡܫܬܚܠܦܢܐ ܟܣܝܐ، ܕܩܝܡܚ ܛܥܢܐ (loading) ܕܚܕ ܡܢ ܡܚܘ̈ܝܢܐ (ܣܓܝ ܓܗ̈ܐ ܩܕܡܝܐ) ܠܡܢܝܢܐ ܩܝܡܐ (ܠܦܘܬ ܥܝܕܐ، 1.0)، ܝܢ (2) ܕܡܬܩܢܚ ܫܘܚܠ̈ܦܐ ܕܡܫܬܚܠܦ̈ܢܐ ܟܣ̈ܝܐ". ܩܕܡܝܬܐ ܝܠܗ̇ ܓܘܒܝܐ ܡܩܕܡܐ (default) ܕ-lavaan (ܘܕ-AMOS)، ܬܪܬܝܬܐ – std.lv = TRUE؛ ܬܪܘܬܝܗܝ ܟܝܗܒܝ ܗܝ ܦܐܝܘܬܐ، ܗܢܝ ܡܢܝ̈ܢܐ ܡܫܘܬ̈ܦܐ (coefficients) ܡܬܩ̈ܢܐ ܘܗܘ ω – ܒܣ ܠܐ ܡܬܩ̈ܢܐ ܟܡܫܬܚܠܦܝ. ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom): ܡܢܝܢܐ ܕܫܘܚܠ̈ܦܐ ܘܫܘܚܠ̈ܦܐ ܡܫܘܬ̈ܦܐ ܕ-p ܦܣܘ̈ܩܐ، p(p + 1)/2، ܒܨܝܪ ܡܢܝܢܐ ܕܦܪܡܝ̈ܛܪܐ (parameters) ܕܡܫܬܥܪܝ. ܓܘ ܡܬܠܐ ܕ-Rosseel (ܬܫܥܐ ܒܘܚܪ̈ܢܐ، ܬܠܬܐ ܥܠ̈ܠܬܐ) – 45 moments ܘ-21 ܦܪܡܝ̈ܛܪܐ: df = 24. Brown (2015، ܦܐܬܐ 61-62) ܟܟܢܫ ܢܡܘ̈ܣܐ ܕ-identification: ܟܠ ܥܠܬܐ ܣܢܝܩܐ ܝܠܗ ܚܕ̈ܝܘܬܐ (marker ܝܢ ܫܘܚܠܦܐ 1)؛ ܡܢܝܢܐ ܕ-moments ܓܪܓ ܕܗܘܐ ܠܟܡܐ ܐܝܟ ܡܢܝܢܐ ܕܦܪܡܝ̈ܛܪܐ؛ ܥܠܬܐ ܝܚܝܕܝܐ ܣܢܝܩܐ ܝܠܗ ܠܟܡܐ ܬܠܬܐ ܦܣܘ̈ܩܐ – ܘܥܡ ܬܠܬܐ ܚܬܝܬܐܝܬ ܗܘ "just-identified" ܝܠܗ (df = 0)، ܘ"ܒܚܪܢܐ ܕܦܐܝܘܬܐ ܠܐ ܝܠܗ ܚܫܝܚܐ"، ܐܦ ܐܢ ܡܨܚ ܬܘܒ ܕܒܚܪܚ ܛܥ̈ܢܐ؛ ܥܠܬܐ ܕܬܪܝܢ ܦܣܘ̈ܩܐ identified ܝܠܗ ܒܣ ܐܝܡܢ ܕܐܣܝܪܐ ܝܠܗ ܥܡ ܥܠܬܐ ܐܚܪܢܐ، ܘ"ܡܛܠ ܕܦܘܫ̈ܪܐ ܗܕܟܐ ܦܬܝ̈ܚܐ ܝܢܐ ܠ-empirical under-identification، ܡܩܪܒܐ ܝܠܗ ܠܟܡܐ ܬܠܬܐ ܦܣܘ̈ܩܐ ܩܐ ܟܠ ܡܫܬܚܠܦܢܐ ܟܣܝܐ".

ܫܘܥܪܐ (estimation). ܫܘܥܪܐ ܕܡܬܚܙܝܢܘܬܐ ܥܠܝܬܐ (maximum likelihood, ML) ܐܝܟ ܓܘ lavaan: ܟܒܨܚ ܦܪܡܝ̈ܛܪܐ (parameters) ܕܟܡܙܥܪܝ ܦܘܪܫܢܐ ܒܝܢܝ Σ ܘܡܐܛܪܝܟܣ ܚܙܝܐ S، F = log|Σ| + tr(SΣ⁻¹) − log|S| − p، ܥܡ S ܒܦܠܓܐ N ܘ-χ² = N·F؛ ܛܥܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ (standard errors) – ܡܐܛܪܝܟܣ ܕܡܘܕܥܢܘܬܐ ܡܣܟܝܬܐ (Information: Expected ܓܘ ܡܦܩܢܐ ܕ-lavaan). ܦܐܬܐ ܟܚܫܒ ܒܐܘܪܚܐ ܕ-Fisher scoring ܗܠ ܕܡܦܩܢܐ ܕܐܣܛܘܟܣܐ (derivative) ܙܥܘܪܐ ܗܘܐ ܡܢ 10⁻¹⁰؛ ܥܠ ܝܗܝ̈ܒܬܐ ܕ-Holzinger ܘ-Swineford (1939، ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Rosseel) ܟܡܦܢܐ ܡܦܩܢܐ ܕܡܐܡܪܐ (χ²(24) = 85.306، CFI .931، RMSEA .092 [.071, .114]، SRMR .065، ܡܚܘ̈ܝܢܐ ܕܫܘܢܝܐ (modification indices) 18.631، 36.411، 34.145، 14.946) ܘ-lavaan 0.6-17 ܓܘ ܫܬܐ ܡܘܕܝ̈ܠܐ ܘܓܘ ܫܒܥܐ ܡܘܕܝ̈ܠܐ ܥܠ ܦܐܝܠ ܕܡܬܠܐ (sample data file).

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܘܚܐ 1 – ܦܐܝܘܬܐ (fit). ܐܝܟ ܓܘ ܦܐܬܐ ܕܦܘܫܩܐ ܕܫܒ̈ܝܠܐ (path analysis): χ² ܥܡ p (ܡܘܕܝܠ ܝܠܗ ܗܘܦܘܬܣܝܣ ܕܣܦܝܩܘܬܐ (null hypothesis) – ܟܒܥܝܚ p ܪܒܐ ܡܢ .05)، ܘܒܬܪ CFI ܘ-TLI (ܠܥܠ ܡܢ .95 ܛܒܐ، ܠܥܠ ܡܢ .90 ܡܩܒܠܐ)، RMSEA ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) 90% (ܗܠ .06 ܛܒܐ، ܗܠ .08 ܡܩܒܠܐ) ܘ-SRMR (ܗܠ .08). ܡܒܘܥܐ ܕܬܚܘ̈ܡܐ: Hu ܘ-Bentler (1999، ܦܐܬܐ 27)، ܓܘ ܢܣܝܘ̈ܢܐ ܕܡܘܕܝ̈ܠܐ ܕ-CFA ܒܚܘܫܒܢܐ (simulations)، ܡܛܝܠܗܘܢ ܠܫܘܠܡܐ ܕ"ܛܝܡܐ ܕܦܣܩܐ ܩܪܝܒ ܠ-.95" ܩܐ TLI ܘ-CFI، "ܩܪܝܒ ܠ-.08" ܩܐ SRMR ܘ"ܩܪܝܒ ܠ-.06" ܩܐ RMSEA ܣܢܝܩ̈ܐ ܝܢܐ ܩܐ ܕܦܠܛܚ ܦܐܝܘܬܐ ܛܒܬܐ ܩܘܒܠ ܐܚܪ̈ܢܐ، ܘܡܩܪܒܠܗܘܢ ܕܩܪܚ ܬܪܝܢ ܡܚܘ̈ܝܢܐ ܒܚܕ ܓܗܐ – SRMR ܘܚܕ ܐܚܪܢܐ. Brown (2015، ܦܐܬܐ 74-75) ܟܡܚܝܠ ܕ"ܩܪܝܒ ܠ-" ܠܐ ܝܠܗ ܒܓܕܫܐ: ܬܚܘ̈ܡܐ ܫܚܠܦܠܗܘܢ ܠܦܘܬ ܫܪ̈ܛܐ ܕܡܘܕܝܠ؛ ܓܢܒܝܗܝ ܟܡܝܬܐ Browne ܘ-Cudeck (1993: RMSEA ܬܚܘܬ .08 – "ܛܥܝܘܬܐ ܕܩܘܪܒܐ ܡܩܒܠܬܐ"؛ ܡܢ .10 ܘܠܥܠ – ܕܡܣܠܚ)، MacCallum ܘܐܚܪ̈ܢܐ (1996: .08-.10 – "ܡܨܥܝܬܐ") ܘ-Bentler (1990: CFI ܘ-TLI ܒܝܢܝ .90 ܘ-.95 – ܡܨܝ ܕܡܚܘܝܝ ܦܐܝܘܬܐ ܡܩܒܠܬܐ؛ ܬܚܘܬ .90 – ܕܚܫܕܚ ܒܡܘܕܝܠ)، ܘܐܦ ܒܘܩܪܐ ܕܠܦܘܬܗ ܬܚܘ̈ܡܐ ܕ-Hu ܘ-Bentler ܢܛܘܪ̈ܐ ܝܢܐ ܝܬܝܪ ܡܢ ܕܣܢܝܩ ܩܐ ܡܘܕܝ̈ܠܐ ܕ-CFA ܥܡ ܦܣܘ̈ܩܐ ܘܥܠ̈ܠܬܐ ܣܓܝ̈ܐܐ (Marsh et al., 2004). ܘܬܘܒ ܡܢ Hu ܘ-Bentler (ܦܐܬܐ 1): TLI ܘ-RMSEA ܟܡܨܠܝ ܕܡܣܠܝ ܡܘܕܝ̈ܠܐ ܬܪ̈ܝܨܐ ܓܘ ܕܘܡܝܐ (sample) ܙܥܘܪܐ. χ² ܪܓܝܫܐ ܝܠܗ ܠܪܒܘܬܐ ܕܕܘܡܝܐ (sample size)، ܘܡܛܠ ܗܕܐ ܟܩܪܚ ܟܠ ܡܚܘ̈ܝܢܐ ܒܚܕ ܓܗܐ – ܘ-Brown (ܦܐܬܐ 74) ܟܡܘܣܦ ܕܦܐܝܘܬܐ ܟܠܢܝܬܐ ܒܣ ܡܢܬܐ ܝܠܗ̇ ܡܢ ܒܚܪܢܐ: ܐܦ ܕܘܟ̈ܝܬܐ ܕܥܨܝܪܘܬܐ ܡܢܬܢܝ̈ܬܐ (localized strain؛ ܡܚܘ̈ܝܢܐ ܕܫܘܢܝܐ)، ܐܦ ܦܘܫܩܐ ܕܫܘܥ̈ܪܐ ܘܕܠܝܬ Heywood. ܡܘܕܝܠ ܕܫܬܐܣܐ ܩܐ CFI/TLI – ܟܠ ܦܣܘ̈ܩܐ ܠܐ ܐܣܝܪ̈ܐ ܝܢܐ (Rosseel, 2012, Section 4.2).

ܠܘܚܐ 2 – ܛܥ̈ܢܐ (loadings). ܩܐ ܟܠ ܦܣܘܩܐ (item): ܛܥܢܐ ܠܐ ܡܬܩܢܐ (ܓܘ ܦܣܘܩܐ ܩܕܡܝܐ – 1، ܩܝܡܐ، ܕܠܐ ܛܥܝܘܬܐ ܬܩܝܢܬܐ)، ܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error)، z، p ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) 95%؛ ܛܥܢܐ ܡܬܩܢܐ (standardized؛ Std.all ܓܘ lavaan – "ܐܦ ܡܫܬܚܠܦ̈ܢܐ ܟܣ̈ܝܐ ܘܐܦ ܚܙ̈ܝܐ ܡܬܩ̈ܢܐ ܝܢܐ"، Rosseel، ܦܣܩܐ 4.2) ܝܠܗ ܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation) ܒܝܢܝ ܦܣܘܩܐ ܘܥܠܬܐ (factor)، ܘ-R² – ܡܪܒܥܐ ܕܝܠܗ: ܡܢܬܐ ܕܫܘܚܠܦܐ (variance) ܕܦܣܘܩܐ ܕܥܠܬܐ ܟܡܦܫܩܐ (ܒܠܫܢܐ ܕ-EFA – "ܫܘܬܦܘܬܐ" (communality)؛ Field, 2024، ܦܣܩܐ 18.4.2). Field (ܦܣܩܐ 18.4.7) ܟܡܩܪܒ ܕܠܐ ܚܙܚ ܪܫܝܡܘܬܐ (significance) ܕܛܥܢܐ ܓܘ ܕܘܡܝܐ (sample) ܪܒܐ، "ܒܝܬܝܪ ܡܛܠ ܕܛܥܢܐ ܓܢܒܗ ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size) ܝܠܗ"، ܘܕܦܫܩܚ ܛܥ̈ܢܐ ܕܛܝܡܐ ܫܪܝܪܐ (absolute value) ܕܝܠܗܘܢ ܠܥܠ ܡܢ .4 ܝܠܗ (Stevens، 2002، ܐܝܟ ܕܡܬܝܬܐ ܝܠܗ ܓܘ Field؛ ܐܝܬ ܐܢܫ̈ܐ ܕܟܣܦܩܝ ܒ-.3) – "ܠܝܬ ܚܪܫܘܬܐ ܓܘ ܐܢܝ ܡܢܝ̈ܢܐ". ܦܐܬܐ ܟܪܫܡ ܛܥܢܐ ܡܬܩܢܐ ܬܚܘܬ .40.

ܠܘܚܐ 3 – ܥܠ̈ܠܬܐ (factors). ܫܘܚܠܦܐ (variance) ܕܟܠ ܥܠܬܐ (ܒܐܘܪܚܐ ܕ-marker – ܒܚܕ̈ܝܘܬܐ ܕܦܣܘܩܐ ܩܕܡܝܐ) ܘܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ (correlations) ܒܝܢܝ ܥܠ̈ܠܬܐ ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval). Brown (2015، ܦܐܬܐ 28): ܐܣܘܪ̈ܐ ܒܝܢܝ ܥܠ̈ܠܬܐ "ܠܥܠ ܡܢ .80 ܝܢ .85 ܡܨܝ ܕܡܚܘܝܝ ܬܪܝܨܘܬܐ ܡܦܪܫܢܝܬܐ (discriminant validity) ܟܪܝܗܬܐ"، ܘܡܨܐ ܕܗܘܐ ܕܦܘܫܪܐ ܦܫܝܛܐ ܝܬܝܪ ܛܒܐ ܝܬܝܪ ܝܠܗ؛ ܓܘ ܦܐܬܐ 147 ܗܘ ܟܡܝܬܐ ܡܬܠܐ ܕܝܠܗ – ܬܪܝܢ ܥܠ̈ܠܬܐ ܥܡ r = .87 ܕܚܕܝܠܗܘܢ ܠܚܕ ܥܠܬܐ. ܦܐܬܐ ܟܡܙܗܪ ܡܢ .85؛ ܦܐܬܐ ܟܦܚܡ ܓܘ ܓܗܐ ܗܕܟܐ ܥܡ ܡܘܕܝܠ (model) ܥܡ ܥܠ̈ܠܬܐ ܒܨܝܪ̈ܐ (AIC/BIC ܘ-Δχ² – ܡܪܗܛܘܢ ܬܪܝܢ ܡܘܕܝ̈ܠܐ). ܐܣܘܪܐ ܠܥܠ ܡܢ 1 ܝܠܗ ܦܘܫܪܐ ܠܐ ܡܩܒܠܐ.

ܠܘܚܐ 4 – ܫܪܝܪܘܬܐ (reliability؛ ܦܣܩܐ ω)، ܠܘܚܐ 5 – ܡܚܘ̈ܝܢܐ ܕܫܘܢܝܐ (modification indices؛ ܦܣܩܐ ܕܠܬܚܬ)، ܨܘܪܬܐ ܕܡܘܕܝܠ – ܚܘ̈ܕܪܐ ܡܓܪ̈ܓܐ (ellipses) ܩܐ ܥܠ̈ܠܬܐ، ܡܪ̈ܒܥܐ ܡܓܪ̈ܓܐ (rectangles) ܩܐ ܦܣܘ̈ܩܐ، ܛܥ̈ܢܐ ܡܬܩ̈ܢܐ ܥܠ ܓܐܪ̈ܐ ܘܐܣܘܪ̈ܐ ܥܠ ܩܫ̈ܬܐ؛ APA (2020، ܨܘܪܬܐ 7.8) ܟܡܝܬܐ ܡܬܠܐ ܕܨܘܪܬܐ ܗܕܟܐ. ܦܣܩܐ ܕܡܫܟܚ̈ܢܘܬܐ (results paragraph) ܘܟܘܬܐ ܕ"ܩܪܝܢܐ ܕܦܐܪܐ" – ܐܝܟ ܓܘ ܡܚܫܒ̈ܢܐ ܐܚܪ̈ܢܐ.

ܫܪܝܪܘܬܐ ܡܪܟܒܬܐ (ω)

Raykov (2024، ܫܘܝܘܬܐ 13، ܠܦܘܬ Bollen، 1980، ܐܝܟ ܕܡܬܝܬܐ ܝܠܗ ܓܘܗ) ܟܝܗܒ ܫܪܝܪܘܬܐ (reliability) ܕܡܢܝܢܐ ܕܓܘܡܪܐ ܕܦܣܘ̈ܩܐ congeneric ܥܡ ܛܥܝ̈ܘܬܐ ܠܐ ܐܣܝܪ̈ܐ: ρ = (Σλ)² / ((Σλ)² + Σθ) (ܓܘ identification ܕܓܘܗ ܫܘܚܠܦܐ ܕܥܠܬܐ 1؛ ܒܐܘܪܚܐ ܕ-marker ܟܡܥܦܚ (Σλ)² ܒܫܘܚܠܦܐ ܕܥܠܬܐ – ܗܘ ܛܝܡܐ)، ܘܓܘ ܛܥܝ̈ܘܬܐ ܐܣܝܪ̈ܐ ܟܡܘܣܦܚ ܠܡܢܝܢܐ ܬܚܬܝܐ ܬܪܝܢ ܙܒ̈ܢܐ ܫܘܚܠ̈ܦܐ ܡܫܘܬ̈ܦܐ (covariances) ܒܝܢܬܗܘܢ (ܫܘܝܘܬܐ 15). ܐܗܐ ܝܠܗ ω ܕܦܐܬܐ ܟܛܒܥ ܩܐ ܟܠ ܥܠܬܐ (factor)، ܡܢ ܫܘܥ̈ܪܐ ܕ-ML ("ܕܝܠܝܘܬܐ ܕܠܐ ܡܫܬܚܠܦܢܘܬܐ (invariance property) ܕܫܘܥ̈ܪܐ ܕ-ML"، ܫܘܝܘܬܐ 14)، ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) 95% ܒܐܘܪܚܐ ܕ-delta (Raykov & Marcoulides, 2004، ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Raykov؛ Raykov ܟܡܥܗܕ ܐܦ bootstrap). Brown (2015، ܦܐܬܐ 309-316، ܫܘܝ̈ܘܬܐ 8.2-8.3) ܟܡܝܬܐ ܗܝ ܫܘܝܘܬܐ ܘܡܬܠܐ ܓܡܝܪܐ – ܦܢܩܝܬܐ ܕܫܘܐ̈ܠܐ (questionnaire) ܕܦܘܢ̈ܝܐ ܠܥܨܝܪܘܬܐ ܕܡܚܘܬܐ (traumatic stress)، 500 ܡܫܬܘܬܦ̈ܢܐ، ܬܪܝܢ ܥܠ̈ܠܬܐ ܘܫܪܟܐ ܐܣܝܪܐ: ρ = .919 ܘ-.823. ܡܟܝܢܐ ܕܦܐܬܐ ܟܡܦܢܐ ܡܬܠܐ ܡܢ ܡܐܛܪܝܟܣ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ (correlation matrix) ܕܓܘ ܟܬܒܐ – ܛܥ̈ܢܐ، ܫܪ̈ܟܐ، χ²(18) = 20.52 ܘܬܪܝܢ ܛܝ̈ܡܐ ܕ-ρ. ܓܢܒܗ – ܐܠܦܐ ܕ-Cronbach (Cronbach's alpha) ܡܢ ܗܢܝ ܡܫܬܘܬܦ̈ܢܐ.

ܩܡܘܕܝ ܬܪܘܬܝܗܝ؟ Field (2024، ܦܣܩܐ 18.9.3): ܐܠܦܐ ܟܣܝܡ "ܕܟܠ ܦܣܘ̈ܩܐ (items) ܟܛܥܢܝ ܒܐܘܪܚܐ ܫܘܝܬܐ ܥܠ ܚܕ ܥܠܬܐ (factor)" (tau-equivalence)، ܫܪܛܐ "ܟܪܝܐ ܘܠܐ ܫܪܝܪܐ ܒܓܠܝܘܬܐ"، ܘܕܠܐ ܐܗܐ ܗܘ ܟܡܙܥܪ ܫܪܝܪܘܬܐ (reliability). Raykov (2024) ܟܡܘܣܦ ܓܢܒܐ ܐܚܪܢܐ: ܥܡ ܛܥ̈ܢܐ ܠܐ ܫܘ̈ܝܐ ܐܠܐ ܪ̈ܡܐ ܒܐܘܪܚܐ ܫܘܝܬܐ، ܦܘܪܫܢܐ ܙܥܘܪܐ ܛܒܐ ܝܠܗ (negligible)، ܘܥܡ ܛܥܝ̈ܘܬܐ ܐܣܝܪ̈ܐ ܐܠܦܐ ܡܨܐ ܕܣܠܩ ܠܥܠ ܡܢ ܫܪܝܪܘܬܐ – ܘܡܛܠ ܗܕܐ ܗܘ ܟܡܙܗܪ ܡܢ "ܩܪ̈ܝܬܐ ܟܠܢܝ̈ܬܐ ܕܫܒܩܚ ܐܠܦܐ". ܡܐ ܕܟܦܚܡܚ ܓܘ ܠܘܚܐ 4: ω ܪܡܐ ܒܪܫܝܡܘܬܐ ܡܢ α – ܛܥ̈ܢܐ ܦܪ̈ܝܫܐ ܝܢܐ ܚܕ ܡܢ ܐܚܪܢܐ؛ ܬܪܘܬܝܗܝ ܩܪܝ̈ܒܐ – ܐܠܦܐ ܡܣܦܩ ܝܠܗ ܩܐ ܐܗܐ ܣܒܠܬܐ (scale). ω ܣܝܡܐ ܝܠܗ ܒܣ ܓܘ ܡܘܕܝܠ (model) ܕܓܘܗ ܟܠ ܦܣܘܩܐ ܟܛܥܢ ܥܠ ܚܕ ܥܠܬܐ (ܥܡ ܛܥܢܐ ܥܠ ܥܠ̈ܠܬܐ ܣܓܝ̈ܐܐ – ܠܐ ܟܡܬܛܒܥ).

ܡܚܘ̈ܝܢܐ ܕܫܘܢܝܐ (modification indices)

Rosseel (2012، ܦܣܩܐ 4.2): "ܐܢ ܦܐܝܘܬܐ ܠܐ ܝܠܗ̇ ܛܒܬܐ ܒܣܓܝ، ܡܨܐ ܕܗܘܐ ܡܘܬܪܐ ܕܒܚܪܚ ܡܚܘ̈ܝܢܐ ܕܫܘܢܝܐ (MIs) ܘܫܘ̈ܢܝܐ ܡܣܟ̈ܝܐ ܕܦܪܡܝ̈ܛܪܐ (EPCs)… ܡܚܘ̈ܝܢܐ ܕܫܘܢܝܐ ܟܝܗܒܝ ܫܘܥܪܐ ܓܫܡܢܝܐ ܕܟܡܐ χ² ܒܕ ܙܥܪ ܐܢ ܦܪܡܝܛܪ (parameter) ܝܚܝܕܝܐ ܒܕ ܗܘܐ ܡܫܘܚܪܪܐ. ܫܘܢܝܐ ܡܣܟܝܐ ܕܦܪܡܝܛܪ ܝܠܗ ܛܝܡܐ ܕܒܕ ܗܘܐ ܠܦܪܡܝܛܪ ܐܢ ܥܠܝܠܐ ܗܘܐ ܐܝܟ ܦܪܡܝܛܪ ܚܐܪܐ". ܠܘܚܐ 5 ܟܛܒܥ ܗܠ ܥܣܪܐ ܦܪܡܝ̈ܛܪܐ ܩܝ̈ܡܐ – ܛܥ̈ܢܐ ܥܠ ܥܠ̈ܠܬܐ ܣܓܝ̈ܐܐ (cross-loadings) ܘܐܣܘܪ̈ܐ ܕܫܪ̈ܟܐ (residual correlations) – ܕܡܚܘܝܢܐ ܕܝܠܗܘܢ ܝܬܝܪ ܝܠܗ ܡܢ 3.84 (χ²(1) ܒܪܡܐ .05)، ܥܡ EPC ܠܐ ܡܬܩܢܐ ܘܡܬܩܢܐ (sepc.all: ܩܐ ܛܥܢܐ – ܒܣܒܠܬܐ ܕܛܥܢܐ ܡܬܩܢܐ، ܩܐ ܫܪ̈ܟܐ – ܐܣܘܪܐ ܕܫܪ̈ܟܐ). ܬܚܘܡܐ 3.84 – Brown (2015، ܦܐܬܐ 102): ܡܚܘܝܢܐ ܕܫܘܢܝܐ ܝܠܗ ܣܛܐܛܝܣܛܝܩ χ² ܥܡ ܚܕ ܕܪܓܐ ܕܚܐܪܘܬܐ، ܘܡܢ 3.84 ܘܠܥܠ "ܦܐܝܘܬܐ ܟܠܢܝܬܐ ܕܡܘܕܝܠ ܡܨܝܐ ܕܡܬܛܝܒܐ ܒܪܫܝܡܘܬܐ" ܐܢ ܦܪܡܝܛܪ ܡܫܘܚܪܪܐ ܗܘܐ (ܒܫܪܪܐ ܣܓܝ ܓܗ̈ܐ ܟܡܓܪܓܚ ܠ-4). ܙܘܗܪܐ: ܡܚܘܝܢܐ ܕܫܘܢܝܐ ܪܡܙܐ ܝܠܗ، ܠܐ ܦܣܝܚܘܬܐ – Brown (ܦܐܬܐ 142) ܟܡܚܘܐ ܕܡܚܘ̈ܝܢܐ ܕܫܘܢܝܐ ܡܨܝ ܕܡܚܘܝܝ ܐܘܠܨܢ̈ܐ "ܕܠܐ ܝܢܐ ܡܒܘܥܐ ܫܪܝܪܐ ܕܚܣܝܪܘܬܐ ܕܦܐܝܘܬܐ"، ܘܡܢ ܗܪܟܐ "ܚܫܝܚܘܬܐ ܕܫܬܐܣܐ ܓܠܝܐ ܕܡܐ ܕܐܝܬ ܒܓܘܗ، ܕܡܦܗܡܢܘܬܐ ܘܕܢܣܝܘܢܐ" ܩܐ ܟܠ ܫܘܢܝܐ. ܟܠ ܫܘܢܝܐ ܓܘ ܡܘܕܝܠ ܒܬܪ ܚܙܝܐ ܕܝܗܝ̈ܒܬܐ ܟܥܒܕ ܦܘܫܩܐ ܡܒܨܝܢܐ (exploratory)، ܘܦܐܝܘܬܐ ܕܛܘܝܒܬܐ ܝܠܗ̇ ܗܕܟܐ ܠܐ ܒܕ ܡܬܦܢܝܐ ܓܘ ܕܘܡܝܐ (sample) ܐܚܪܢܐ؛ ܟܡܫܚܪܪܚ ܦܪܡܝܛܪ ܒܣ ܐܝܡܢ ܕܐܝܬ ܠܗ ܦܘܫܩܐ ܕܡܐ ܕܐܝܬ ܒܓܘܗ (ܬܪܝܢ ܦܣܘ̈ܩܐ ܒܢܘܣܚܐ ܩܪܝܒ ܚܕ – "ܟܝܢܐ ܠܝ ܥܠ ܡܐ ܕܗܘܝܐ ܓܘ ܟܢܘܫܬܐ" ܘ"ܚܫܝܚܐ ܝܠܗ ܩܐ ܕܝܝ ܡܐ ܕܗܘܝܐ ܓܘ ܟܢܘܫܬܐ ܕܝܝ" ܓܘ ܦܐܝܠ ܕܡܬܠܐ)، ܘܟܡܬܢܚ ܡܘܕܝܠ ܫܪܫܝܐ ܘܫܘܢܝܐ.

ܫܪ̈ܛܐ ܘܙܘܗܪ̈ܐ (Assumptions and warnings)

ܡܘܕܝܠ ܩܕܡ ܝܗܝ̈ܒܬܐ. CFA ܟܒܚܪ ܗܘܦܘܬܣܝܣ (hypothesis) ܥܠ ܒܢܝܢܐ؛ ܐܢ ܒܢܝܢܐ ܠܐ ܝܠܗ ܝܕܝܥܐ – ܟܫܪܚ ܒܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܡܒܨܝܢܐ (EFA)، ܘܟܒܚܪܚ ܓܘ ܕܘܡܝܐ (sample) ܐܚܪܢܐ. ܢܘܪܡܠܝܘܬܐ ܕܡܫܬܚܠܦ̈ܢܐ ܣܓܝ̈ܐܐ (multivariate normality): ܫܘܥܪܐ ML ܟܣܝܡ ܠܗ̇؛ ܬܒܝܪܘܬܐ ܟܡܨܠܝܐ χ² ܘܛܥܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ (standard errors). ܦܣܘ̈ܩܐ ܕ-Likert (Likert items): Rhemtulla ܘܐܚܪ̈ܢܐ (2012، ܦܐܬܐ 354) ܦܚܡܠܗܘܢ ܒܚܘܫܒܢܐ (simulation) ܫܘܥܪܐ ML ܥܡ ܫܘܥܪܐ ܩܐ ܝܗܝ̈ܒܬܐ ܕܛܟܣܐ (ordinal) ܓܘ ܦܣܘ̈ܩܐ ܕ-2-7 ܓܢ̈ܣܐ (categories)، ܘܡܩܪܒܠܗܘܢ ܫܘܥܪܐ ܕܛܟܣܐ "ܩܐ ܦܣܘ̈ܩܐ ܥܡ ܒܨܝܪ ܡܢ 5 ܓܢ̈ܣܐ"، ܘ-ML "ܐܝܡܢ ܕܐܝܬ 5 ܓܢ̈ܣܐ ܘܠܥܠ، ܕܘܡܝܐ ܙܥܘܪܐ ܝܠܗ ܘܬܚܘ̈ܡܐ ܕܓܢ̈ܣܐ ܩܪܝܒ ܡܫܘܚܬܢ̈ܝܐ (symmetric) ܝܢܐ"؛ ܥܡ 6-7 ܓܢ̈ܣܐ ܦܐܪ̈ܐ ܕܡܝ̈ܐ ܗܘܘ ܓܘ ܬܪܘܬܝܗܝ ܐܘܪ̈ܚܬܐ. ܬܪܝܢ ܚܣܝܪ̈ܘܬܐ: ML ܕܒܚܝܪܐ ܗܘܐ ܬܡܢ ܥܡ ܛܥܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ ܚܣܝ̈ܢܬܐ (robust) ܗܘܐ (ܓܘ ܦܐܬܐ – ܫܚܝ̈ܡܬܐ)، ܘ-ML ܡܨܠܝܐ ܗܘܐ ܐܝܡܢ ܕܬܚܘ̈ܡܐ ܠܐ ܡܫܘܚܬܢ̈ܝܐ ܗܘܘ ܒܣܓܝ ܘܒܝܬܝܪ ܓܘ ܛܥ̈ܢܐ ܪ̈ܡܐ (ܦܐܬܐ 370). Raykov (2024) ܟܡܛܐ ܠܗܘ ܫܘܠܡܐ. ܡܛܠ ܗܕܐ ܡܬܠܐ ܒܣܒܠܬܐ (scale) 1-7، ܘܦܐܬܐ ܟܡܙܗܪ ܥܠ ܦܣܘܩܐ ܥܡ ܒܨܝܪ ܡܢ ܚܡܫܐ ܛܝ̈ܡܐ؛ ܩܐ ܫܘܥܪܐ ܕܛܟܣܐ (WLSMV) – ܚܙܝܡܘܢ ܦܣܩܐ R.

ܪܒܘܬܐ ܕܕܘܡܝܐ (sample size). Brown (2015، ܦܐܬܐ 380) ܟܡܢܐ ܢܡܘ̈ܣܐ ܕܨܒܥܐ ܕܡܬܚܙܝܢ ܣܓܝ – "N ≥ 100-200"، "ܠܟܡܐ 5-10 ܡܫܬܘܬܦ̈ܢܐ ܩܐ ܟܠ ܦܪܡܝܛܪ (parameter) ܚܐܪܐ" – ܘܟܡܙܗܪ ܕ"ܦܫܛܐ ܕܝܠܗܘܢ ܠܝܗܝ̈ܒܬܐ ܕܒܨܘܝܐ ܝܚܝܕܝܐ ܟܪܝܗܐ ܝܠܗ"؛ ܐܘܪܚܐ ܚܬܝܬܬܐ ܝܠܗ̇ ܦܘܫܩܐ ܕܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ (statistical power) ܠܦܘܬ ܡܘܕܝܠ (model؛ ܨܚܚܐ 10 ܕܝܠܗ – ܠܐ ܓܘ ܦܐܬܐ). Field (2024، ܦܣܩܐ 18.5.3، ܥܠ EFA): "ܕܘܡܝܐ ܕ-300 ܘܠܥܠ ܒܠܟܝ ܒܕ ܝܗܒ ܦܘܫܪܐ ܩܝܡܐ"، ܘܡܐ ܕܟܦܣܩ ܝܠܗ ܐܦ ܛܥ̈ܢܐ (loadings) ܘܫܘܬܦܘܬܐ (communality). ܦܐܬܐ ܟܡܙܗܪ ܠܦܘܬ ܣܘܦܐ ܥܠܝܐ ܕܢܡܘ̈ܣܐ ܕ-Brown ܟܡܝܬܐ: ܒܨܝܪ ܡܢ 200 ܡܫܬܘܬܦ̈ܢܐ ܝܢ ܒܨܝܪ ܡܢ ܚܡܫܐ ܩܐ ܦܪܡܝܛܪ. ܦܘܫܪܐ ܠܐ ܡܩܒܠܐ (Heywood): "ܫܘܥ̈ܪܐ ܥܡ ܛܝ̈ܡܐ ܠܒܪ ܡܢ ܬܚܘܡܐ" (Brown, 2015, p. 61) – ܕܡܬܚܙܐ ܣܓܝ ܒܝܬܝܪ ܝܠܗ ܫܘܚܠܦܐ ܕܫܪܟܐ ܬܚܘܬ ܣܦܝܩܘܬܐ، ܘܓܘ ܡܘܕܝܠ ܕܓܘܗ ܟܠ ܦܣܘܩܐ ܟܛܥܢ ܥܠ ܚܕ ܥܠܬܐ ܐܦ ܛܥܢܐ ܡܬܩܢܐ ܠܥܠ ܡܢ 1؛ "ܡܘܕܝܠ ܕܡܫܘܚܬܐ ܠܐ ܒܕ ܡܬܚܫܒ ܡܩܒܠܐ" ܥܡ ܫܘܥܪܐ ܗܕܟܐ (ܦܐܬܐ 162). ܥܠ̈ܠܬܐ ܠܦܘܬ Brown (ܦܐܬܐ 163): ܒܝܬܝܪ ܡܘܕܝܠ ܛܥܝܐ، under-identification، ܘܕܘܡܝܐ ܙܥܘܪܐ؛ ܦܐܬܐ ܟܡܚܘܐ ܦܘܫܪܐ ܘܟܪܫܡ ܠܗ. ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (missing values) – ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (listwise deletion) ܥܠ ܟܠ ܦܣܘ̈ܩܐ ܕܡܘܕܝܠ (ܓܘܒܝܐ ܡܩܕܡܐ (default) ܕ-lavaan؛ FIML – ܠܐ ܓܘ ܦܐܬܐ، ܚܙܝܡܘܢ ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ).

ܡܘܕܝ ܠܐ ܟܚܫܒܐ ܐܗܐ ܦܐܬܐ. ܛܟܣܐ ܬܪܝܢܐ (second order؛ ܥܠܬܐ ܕܥܠ̈ܠܬܐ)، ܫܘܥܪܐ ܚܣܝܢܐ (MLR) ܘܩܐ ܝܗܝ̈ܒܬܐ ܕܛܟܣܐ (WLSMV)، FIML، ܦܘܚܡܐ ܕܓܘ̈ܕܐ ܘܠܐ ܡܫܬܚܠܦܢܘܬܐ ܕܡܫܘܚܬܐ، ܐܘܠܨ̈ܢܐ ܕܫܘܝܘܬܐ (equality constraints)، ܡܢܝ̈ܢܐ ܕܥܠ̈ܠܬܐ (factor scores)، ܡܨܥܝ̈ܬܐ (intercepts).

ܘܕܟܝ ܟܥܒܕܚ ܐܗܐ ܒ-SPSS ܘ-AMOS؟

ܓܘ SPSS Statistics ܠܝܬ CFA: ܦܘܩܕܢܐ FACTOR (Analyze › Dimension Reduction › Factor) ܝܠܗ ܦܘܫܩܐ ܡܒܨܝܢܐ (exploratory) ܒܠܚܘܕ، ܘ-Pallant (2020، ܨܚܚܐ 10) ܟܡܥܗܕܐ ܕܠܝܬ ܓܘܗ ܡܢܬܐ ܩܐ ܡܘܕܝ̈ܠܐ ܕܫܘܝ̈ܘܬܐ ܒܢܝܢܝ̈ܬܐ (structural equations)، "ܐܠܐ ܟܡܥܕܪ ܠܬܘܣܦܬܐ ܕܫܡܗ̇ AMOS". ܓܘ AMOS ܟܨܐܪܚ: ܚܘܕܪܐ ܡܓܪܓܐ (ellipse) ܩܐ ܟܠ ܥܠܬܐ (factor)، ܡܪܒܥܐ ܡܓܪܓܐ (rectangle) ܩܐ ܟܠ ܦܣܘܩܐ (item)، ܓܐܪܐ ܡܢ ܥܠܬܐ ܠܟܠ ܦܣܘܩܐ ܕܝܠܗ، ܚܘܕܪܐ ܕܫܪܟܐ (residual) ܩܐ ܟܠ ܦܣܘܩܐ (AMOS ܟܡܘܣܦ ܘܟܩܝܡ ܓܐܪܐ ܕܝܠܗ ܠ-1)، ܘܩܫܬܐ ܕܬܪܝܢ ܓܢܒ̈ܐ ܒܝܢܝ ܥܠ̈ܠܬܐ؛ AMOS ܟܩܝܡ ܛܥܢܐ (loading) ܕܦܣܘܩܐ ܩܕܡܝܐ ܠ-1 – ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ (default) ܕܗܪܟܐ. ܓܘ Analysis Properties › Output ܟܪܫܡܚ Standardized estimates، Squared multiple correlations ܘ-Modification indices. ܦܘܪ̈ܫܢܐ ܡܣܟ̈ܝܐ: AMOS ܟܚܫܒ χ² ܐܝܟ (N − 1)F_min (Byrne, 2016, p. 93)، ܘ-lavaan، Mplus ܘ-LISREL ܡܢ ܢܘܣܚܐ 9.1 – ܐܝܟ N·F (Brown, 2015, p. 67)، ܐܝܟ ܦܐܬܐ؛ ܘܡܛܠ ܗܕܐ χ² ܦܪܝܫܐ ܝܠܗ ܒܦܘܚܡܐ (N − 1)/N ܘܛܥܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ (standard errors) ܒܦܘܚܡܐ ܕܥܩܪܐ ܕܝܠܗ؛ ܛܥ̈ܢܐ ܚܕ ܝܢܐ. ܦܐܬܐ ܠܐ ܟܡܦܩ ܣܝܢܬܐܟܣ (syntax) SPSS (ܠܝܬ ܡܐ ܕܡܪܗܛܚ)، ܐܠܐ ܣܩܪܝܦܬ (script) R (lavaan) ܕܡܘܕܝܠ ܕܣܝܡܐ ܝܠܗ.

ܘܕܟܝ ܟܥܒܕܚ ܐܗܐ ܒ-R؟ (And how do you do it in R?)

lavaan: ܟܠ ܥܠܬܐ (factor) ܓܘ ܣܕܪܐ ܥܡ ܦܘܩܕܢܐ =~ ("ܟܡܬܚܘܐ ܒ-"؛ Rosseel، 2012، ܠܘܚܐ 1)، ܐܣܘܪܐ ܕܫܪ̈ܟܐ (residual correlation) ܒ-~~، ܘ-cfa() ܟܡܘܣܦ ܒܠܚܘܕܗ̇ ܫܘܚܠ̈ܦܐ ܕܫܪ̈ܟܐ، ܫܘܚܠ̈ܦܐ ܕܥܠ̈ܠܬܐ ܘܐܣܘܪ̈ܐ ܒܝܢܬܗܘܢ (ܬܡܢ، ܠܘܚܐ 3). summary(fit, fit.measures = TRUE, standardized = TRUE) ܟܝܗܒ ܠܘ̈ܚܐ 1-3، modindices() – ܠܘܚܐ 5. ܩܘܦܬܐ "ܡܚܬܬܐ ܕܣܩܪܝܦܬ R" ܓܘ ܡܦܩܢܐ (output) ܟܟܬܒ ܣܩܪܝܦܬ (script) ܕܡܘܕܝܠ ܕܣܝܡܠܘܟܘܢ؛ ܣܩܪܝܦܬ ܕܠܬܚܬ ܪܗܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ (sample data file). ܢܡܘܣܐ ܕܣܐܝܛ (site rule) ܩܐ ܣܘܪܝܬ ܒ-R: ܦܐܝܠ UTF-8، ܡܥܝܪ̈ܢܘܬܐ ܕܟܫܪܝ ܒܡܠܬܐ ܕܣܘܪܝܬ، ܫܡ̈ܗܐ ܩܨܝܪ̈ܐ ܒܐܢܓܠܝܙܝܐ ܩܐ ܫܘܝܘܬܐ (formula)، ܘܐܬܪܐ (locale) UTF-8 ܩܐ ܫܡܐ ܕܓܠܝܘܢܐ ܘܩܐ ܫܡ̈ܗܐ ܥܒܪ̈ܝܐ (ܓܘ Windows: R 4.2 ܘܠܥܠ، ܝܢ Sys.setlocale('LC_ALL', 'Hebrew')).

# ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܡܫܪܪܢܐ – ܦܪܘܦܣܘܪ ܣܛܐܛ. ܐܗܐ ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8؛ ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ
library(readxl)   # ܩܪܝܢܐ ܕܐܩܣܠ
library(lavaan)   # ܦܘܩܕ̈ܢܐ cfa, fitMeasures, standardizedSolution, modindices

# ܛܥܢܐ: ܛܘܦܣܐ ܬܩܝܢܐ – ܣܕܪܐ = ܡܫܬܘܬܦܢܐ، ܥܡܘܕܐ = ܦܣܘܩܐ؛ ܓܠܝܘܢܐ "נתונים"
d <- read_excel("C:/Rdata/DATA_cfa_example_heb.xlsx", sheet = "נתונים")
items <- c(paste0("שייכות_", 1:4), paste0("אמון_", 1:4), paste0("השתתפות_", 1:4))
d <- as.data.frame(d[, items])
names(d) <- c(paste0("b", 1:4), paste0("t", 1:4), paste0("p", 1:4))   # ܫܡ̈ܗܐ ܩܨܝܪ̈ܐ ܒܐܢܓܠܝܙܝܐ ܩܐ ܡܘܕܝܠ

# ܡܘܕܝܠ: ܬܠܬܐ ܥܠ̈ܠܬܐ ܐܣܝܪ̈ܐ، ܐܪܒܥܐ ܦܣܘ̈ܩܐ ܩܐ ܟܠ ܚܕ
model <- "
  belong =~ b1 + b2 + b3 + b4
  trust  =~ t1 + t2 + t3 + t4
  partic =~ p1 + p2 + p3 + p4
"
fit <- cfa(model, data = d)                     # ML، ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ: 314 ܡܢ 320
summary(fit, fit.measures = TRUE, standardized = TRUE, rsquare = TRUE)
# ܠܘܚܐ 1: χ²(51) = 51.083, p = .470; CFI 1.000, TLI 1.000 (.9999), RMSEA .002 [.000, .036], SRMR .031
# ܠܘܚܐ 2: b2 0.966 (SE 0.082), Std.all b1 .747 … t4 .333 (ܦܣܘܩܐ ܗܦܝܟܐ – ܛܥܢܐ ܟܪܝܗܐ)
# ܠܘܚܐ 3: ܐܣܘܪ̈ܐ ܕܥܠ̈ܠܬܐ .509, .515, .253

# ܠܘܚܐ 5 – ܡܚܘ̈ܝܢܐ ܕܫܘܢܝܐ ܠܥܠ ܡܢ 3.84، ܡܢ ܪܒܐ ܠܙܥܘܪܐ
mi <- modindices(fit, sort. = TRUE)
mi[mi$mi > 3.84, c("lhs", "op", "rhs", "mi", "epc", "sepc.all")]   # b2 ~~ b3: 8.024, EPC 0.250, sepc.all .299

# ܡܚܘܝܢܐ ω ܩܐ ܟܠ ܥܠܬܐ (Raykov, 2024، ܫܘܝܘܬܐ 13) ܡܢ ܫܘܥ̈ܪܐ
est <- lavInspect(fit, "est")
sapply(colnames(est$lambda), function(f){ l <- est$lambda[, f]; i <- l != 0
  num <- sum(l[i])^2 * est$psi[f, f]; num / (num + sum(est$theta[i, i])) })   # .799, .726, .756

# ܦܣܘ̈ܩܐ ܥܡ 2-4 ܓܒܝ̈ܬܐ ܕܦܘܢܝܐ: ܫܘܥܪܐ ܩܐ ܝܗܝ̈ܒܬܐ ܕܛܟܣܐ (ܠܐ ܓܘ ܦܐܬܐ)
# fit_ord <- cfa(model, data = d, ordered = names(d), estimator = "WLSMV")

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

ܟܡܬܢܚ ܡܘܕܝܠ (model؛ ܐܝܢܝ ܦܣܘ̈ܩܐ ܥܠ ܐܝܢܝ ܥܠ̈ܠܬܐ، ܥܠ̈ܠܬܐ ܐܣܝܪ̈ܐ ܝܢܐ، ܣܝܡܬܐ ܕܣܒܠܬܐ)، ܬܘܟܢܐ (software) ܘܐܘܪܚܐ ܕܫܘܥܪܐ، N ܘܛܝܒܘܬܐ ܕܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (missing values)؛ ܦܐܝܘܬܐ (fit؛ χ² ܥܡ df ܘ-p، CFI، TLI، RMSEA ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval)، SRMR)؛ ܛܥ̈ܢܐ ܡܬܩ̈ܢܐ (standardized loadings؛ ܦܬܝܘܬܐ، ܘܓܘ ܠܘܚܐ – ܟܠܗܘܢ)، ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ (correlations) ܒܝܢܝ ܥܠ̈ܠܬܐ ܘܫܪܝܪܘܬܐ (reliability)؛ ܘܟܠ ܫܘܢܝܐ ܓܘ ܡܘܕܝܠ ܒܬܪ ܪܗܛܐ ܩܕܡܝܐ – ܥܡ ܥܠܬܐ. APA (2020، ܦܣܩܐ 6.44) ܟܒܥܐ ܕܡܦܫܩܚ ܩܘܨ̈ܪܐ CFA، CFI، RMSEA ܓܘ ܡܬܚܙܝܢܘܬܐ ܩܕܡܝܬܐ ܕܝܠܗܘܢ؛ ܦܣܩܐ 6.36 – ܕܠܐ ܣܦܝܩܘܬܐ ܩܕܡ ܢܘܩܙܐ ܩܐ ܡܐ ܕܠܐ ܡܨܐ ܕܣܠܩ ܠܥܠ ܡܢ 1 (ܛܥ̈ܢܐ ܡܬܩ̈ܢܐ، ܐܣܘܪ̈ܐ، R²، ω، CFI، RMSEA، p)، ܘܥܡ ܣܦܝܩܘܬܐ ܩܐ ܛܥ̈ܢܐ ܠܐ ܡܬܩ̈ܢܐ. ܩܐ ܦܘܚܡܐ ܕܡܘܕܝ̈ܠܐ (ܚܕ ܥܠܬܐ ܩܘܒܠ ܬܠܬܐ) – ܠܘܚܐ (table) ܐܝܟ ܠܘܚܐ 7.21 ܕ-APA: ܣܕܪܐ ܩܐ ܟܠ ܡܘܕܝܠ ܥܡ χ²، df، ܡܚܘ̈ܝܢܐ ܕܦܐܝܘܬܐ (fit indices) ܘ-RMSEA، ܘܡܥܝܪܢܘܬܐ ܕܟܡܬܢܝܐ ܟܠ ܡܘܕܝܠ. ܘܒܕܘܟܬܐ ܕܪܫܝܡܬܐ ܐܪܝܟܬܐ ܕܛܥ̈ܢܐ – ܨܘܪܬܐ ܥܡ ܡܢܝ̈ܢܐ ܡܫܘܬ̈ܦܐ (coefficients؛ APA, 2020, Figure 7.8).

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

"ܕܫܪܪܚ" ܒܢܝܢܐ ܕܐܫܬܟܚ ܓܘ ܗܢܝ ܝܗܝ̈ܒܬܐ. EFA ܘܒܬܪܗ CFA ܥܠ ܗܘ ܕܘܡܝܐ (sample) ܠܐ ܝܠܗ ܫܘܪܪܐ – ܐܗܐ ܗܘ ܒܢܝܢܐ ܝܠܗ ܬܪܝܢ ܙܒ̈ܢܐ.

ܕܫܚܪܪܚ ܦܪܡܝ̈ܛܪܐ (parameters) ܠܦܘܬ ܡܚܘ̈ܝܢܐ ܕܫܘܢܝܐ (modification indices) ܗܠ ܕܦܐܝܘܬܐ ܛܒܬܐ ܗܘܝܐ. ܡܘܕܝܠ (model) ܕܒܢܝܐ ܝܠܗ ܡܢ ܝܗܝ̈ܒܬܐ ܡܒܨܝܢܐ (exploratory) ܝܠܗ؛ ܟܡܬܢܚ ܡܘܕܝܠ ܫܪܫܝܐ ܘܟܠ ܫܘܢܝܐ ܥܡ ܥܠܬܐ (Rosseel, 2012: ܡܚܘܝܢܐ ܕܫܘܢܝܐ ܝܠܗ "ܫܘܥܪܐ ܓܫܡܢܝܐ").

ܕܩܪܚ p < .05 ܕ-χ² ܐܝܟ "ܛܒܐ". ܗܦܝܟܐ ܝܠܗ – ܐܗܐ ܝܠܗ ܡܣܠܝܢܘܬܐ ܕܡܘܕܝܠ (model)؛ ܘܓܘ ܕܘܡܝܐ (sample) ܪܒܐ ܟܩܪܚ ܠܗ ܥܡ ܡܚܘ̈ܝܢܐ ܐܚܪ̈ܢܐ.

ܕܛܥܝܚ ܕܗܦܟܚ ܦܣܘ̈ܩܐ ܕܒܠܐ. ܦܣܘܩܐ (item) ܕܠܐ ܗܘܐ ܗܦܝܟܐ ܟܛܥܢ ܒܠܐ ܘܟܡܢܚܬ ω ܘ-α؛ ܐܢ ܦܣܘܩܐ ܡܢ ܩܕܡ ܗܦܝܟܐ ܝܠܗ ܘܛܥܢܐ (loading) ܬܘܒ ܟܪܝܗܐ ܝܠܗ (אמון_4 ܓܘ ܡܬܠܐ، .33) – ܐܘܠܨܢܐ ܕܢܘܣܚܐ ܝܠܗ، ܠܐ ܐܘܠܨܢܐ ܕܪܡܙܢܘܬܐ (coding).

ܕܡܬܢܚ ܒܣ ܐܠܦܐ. ܐܝܡܢ ܕܛܥ̈ܢܐ (loadings) ܦܪ̈ܝܫܐ ܝܢܐ ܚܕ ܡܢ ܐܚܪܢܐ، ω ܚܬܝܬܐ ܝܬܝܪ ܝܠܗ (Field, 2024, Section 18.9.3)؛ ܟܡܬܢܚ ܬܪܘܬܝܗܝ، ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval).

ܕܠܐ ܚܙܚ ܦܘܫܪܐ ܠܐ ܡܩܒܠܐ. ܫܘܚܠܦܐ ܕܫܪܟܐ (residual variance) ܬܚܘܬ ܣܦܝܩܘܬܐ ܝܢ ܐܣܘܪܐ ܕܥܠ̈ܠܬܐ ܠܥܠ ܡܢ 1 ܟܐܡܪܝ ܕܡܘܕܝܠ (model) ܠܐ ܦܐܐ ܝܠܗ ܠܝܗܝ̈ܒܬܐ، ܐܦ ܐܝܡܢ ܕܡܚܘ̈ܝܢܐ ܛܒ̈ܐ ܟܡܬܚܙܝ.

ܥܠܬܐ (factor) ܥܡ ܬܪܝܢ ܦܣܘ̈ܩܐ. identified ܝܠܗ ܒܣ ܒܓܘ ܐܣܘܪܐ ܥܡ ܥܠܬܐ ܐܚܪܢܐ، ܘܫܘܥ̈ܪܐ ܕܝܠܗ ܠܐ ܩܝ̈ܡܐ ܝܢܐ؛ ܠܟܡܐ ܬܠܬܐ ܦܣܘ̈ܩܐ (items) ܩܐ ܟܠ ܥܠܬܐ.

ܡܒܘ̈ܥܐ

American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://doi.org/10.1037/0000165-000

Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). Guilford Press.

Byrne, B. M. (2016). Structural equation modeling with AMOS: Basic concepts, applications, and programming (3rd ed.). Routledge.

Field, A. (2024). Discovering statistics using IBM SPSS statistics (6th ed.). SAGE.

Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1-55. https://doi.org/10.1080/10705519909540118

Pallant, J. (2020). SPSS survival manual: A step by step guide to data analysis using IBM SPSS (7th ed.). Routledge.

Raykov, T. (2024). Reliability. In A. L. Nichols & J. E. Edlund (Eds.), The Cambridge handbook of research methods and statistics for the social and behavioral sciences: Vol. 2. Performing research (pp. 189-210). Cambridge University Press.

Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354-373. https://doi.org/10.1037/a0029315

Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02

Holzinger ܘ-Swineford (1939) – ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Rosseel (2012)؛ Jöreskog (1971)، Bollen (1980) ܘ-Raykov ܘ-Marcoulides (2004) – ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Raykov (2024)؛ Stevens (2002) ܘ-Guadagnoli ܘ-Velicer (1988) – ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Field (2024)؛ Bentler (1990)، Browne ܘ-Cudeck (1993)، MacCallum ܘܐܚܪ̈ܢܐ (1996) ܘ-Marsh ܘܐܚܪ̈ܢܐ (2004) – ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Brown (2015). ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ (site rule)، ܓܘ ܪܫܝܡܬܐ ܕܡܒܘ̈ܥܐ (reference list) ܟܡܬܚܙܝ ܒܣ ܡܒܘ̈ܥܐ ܕܩܪܝ̈ܐ ܝܢܐ ܓܘ ܫܪܫܐ ܕܝܗܝ. ܥܝܕܐ ܕܣܐܝܛ (site convention): ܓܘܒܝܐ ܕܡܙܗܪܚ ܡܢ .85 (Brown: ".80 ܝܢ .85") ܘܕܡܙܗܪܚ ܬܚܘܬ 200 ܡܫܬܘܬܦ̈ܢܐ ܘܬܚܘܬ ܚܡܫܐ ܩܐ ܦܪܡܝܛܪ (ܣܘܦܐ ܥܠܝܐ ܕܢܡܘ̈ܣܐ ܕ-Brown ܟܡܝܬܐ ܘܟܒܩܪ). ܚܘܫܒܢܐ ܓܘ ܦܐܬܐ ܡܫܪܪܐ ܝܠܗ ܩܘܒܠ ܚܙܡܐ lavaan 0.6-17 ܓܘ R.