ܡܘܕܝܠ ܕܫܘܝ̈ܘܬܐ ܒܢܝܢܝ̈ܬܐ (SEM)

ܡܚܫܒܢܐ (calculator)

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)

ܡܕܒܪܢܐ (guide)

ܐܝܡܢ ܡܦܠܚܝܚ (When to use)؟

ܐܡܢ ܕܗܘܦܘܬܣܝܣ (hypothesis) ܥܠ ܐܣܘܪ̈ܐ ܒܝܢܝ ܪ̈ܥܝܢܐ ܝܠܗ ܕܟܠ ܚܕ ܡܢܝܗܝ ܡܫܘܚܐ ܝܠܗ ܒܟܡܐ ܦܣܘ̈ܩܐ (items). Byrne (2016، ܦܐܬܐ 54) ܟܬܚܡܐ: ܡܘܕܝܠ ܕܫܘܝ̈ܘܬܐ ܒܢܝܢܝ̈ܬܐ (structural equation modeling) ܓܡܝܪܐ "ܟܡܚܒܫ ܐܦ ܡܘܕܝܠ ܕܡܫܘܚܬܐ ܘܐܦ ܡܘܕܝܠ ܒܢܝܢܝܐ"، ܗܕܟܐ ܕ"ܡܫܬܚܠܦ̈ܢܐ ܟܣ̈ܝܐ ܡܢܝܗܝ ܐܣܝܪ̈ܐ ܝܢܐ ܒܓܐܪ̈ܐ ܕܚܕ ܐܘܪܚܐ، ܕܐܘܪܚܐ ܕܝܗܝ ܟܡܚܘܝܐ ܗܘܦܘܬܣ̈ܝܣ ܥܠ ܒܢܝܢܐ ܥܠܬܢܝܐ ܕܡܫܬܚܠܦ̈ܢܐ ܓܘ ܡܘܕܝܠ". ܓܘ ܦܐܝܠ ܕܡܬܠܐ: ܬܘܟܠܢܐ ܥܠ ܡܘܬܒ̈ܐ ← ܕܝܠܢܝܘܬܐ ܠܟܢܫܐ ← ܫܘܬܦܘܬܐ، ܘܬܘܒ ܓܐܪܐ ܬܪܝܨܐ ܡܢ ܬܘܟܠܢܐ ܠܫܘܬܦܘܬܐ – ܡܘܕܝܠ ܕܡܨܥܝܘܬܐ (mediation)، ܐܪܒܥܐ ܦܣܘ̈ܩܐ ܩܐ ܟܠ ܪܥܝܢܐ.

ܬܠܬܐ ܦܐܬ̈ܐ ܓܘ ܐܗܐ ܡܢܬܐ ܟܡܦܢܝ ܥܠ ܫܘܐ̈ܠܐ ܩܪ̈ܝܒܐ. ܦܘܫܩܐ ܕܫܒ̈ܝܠܐ ܟܨܐܪ ܓܐܪ̈ܐ ܒܝܢܝ ܡܫܬܚܠܦ̈ܢܐ ܚܙ̈ܝܐ (ܡܬܠܐ ܡܢܝ̈ܢܐ ܕܣܒ̈ܠܬܐ)، ܘܡܛܠ ܗܕܐ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܕܝܠܗ ܠܐ ܝܢܐ ܡܬܘܪ̈ܨܐ ܩܐ ܛܥܝܘܬܐ ܕܡܫܘܚܬܐ؛ ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܡܫܪܪܢܐ ܟܒܚܪ ܒܠܚܘܕ ܡܘܕܝܠ ܕܡܫܘܚܬܐ – ܥܠ̈ܠܬܐ ܐܣܝܪ̈ܐ ܝܢܐ، ܕܠܐ ܐܘܪܚܐ؛ SEM ܓܡܝܪܐ ܟܡܚܝܕ ܬܪܘܝܗܝ. Kline (2023، ܦܐܬܐ 264) ܟܡܦܫܩ ܦܘܪܫܢܐ: ܓܘ ܦܘܫܩܐ ܕܫܒ̈ܝܠܐ (path analysis)، disturbance ܕܡܫܬܚܠܦܢܐ ܬܠܝܐ ܟܡܚܒܫ ܐܦ ܥܠ̈ܠܬܐ ܕܫܒܝ̈ܩܐ ܝܢܐ ܘܐܦ ܛܥܝܘܬܐ ܕܡܫܘܚܬܐ، ܐܠܐ ܓܘ SEM disturbances ܕܥܠ̈ܠܬܐ endogenous "ܟܡܚܘ̈ܝܢ ܒܠܚܘܕ ܥܠ̈ܠܬܐ ܕܫܒܝ̈ܩܐ ܝܢܐ" – ܛܥܝܘܬܐ ܕܡܫܘܚܬܐ ܐܝܬܝܐ ܓܘ ܡܢܬܐ ܕܡܫܘܚܬܐ، ܘܡܛܠ ܗܕܐ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܕܫܒ̈ܝܠܐ ܒܝܢܝ ܥܠ̈ܠܬܐ "ܡܬܘܪ̈ܨܐ ܝܢܐ ܩܐ ܛܥܝܘܬܐ ܕܡܫܘܚܬܐ". ܦܐܬ̈ܐ ܩܪ̈ܝܒܐ: ܐܠܦܐ ܕ-Cronbach ܘܡܢܝܢܐ ܕܣܒܠܬܐ، ܒܢܝܢܐ ܕܦܢܩܝܬܐ ܕܫܘܐ̈ܠܐ.

ܡܠܝܘܬܐ: ܡܢ ܫܒ̈ܝܠܐ ܠܡܐܛܪܝܟܣ ܕܫܘܚܠ̈ܦܐ ܡܫܘܬܦ̈ܐ

ܡܘܕܝܠ. ܬܪܝܢ ܛܟܣ̈ܐ ܕܫܘܝ̈ܘܬܐ: ܓܘ ܡܘܕܝܠ ܕܡܫܘܚܬܐ (measurement model) ܟܠ ܦܣܘܩܐ ܛܥܢܐ (loading) ܝܠܗ ܙܒܢ ܥܠܬܐ ܕܝܠܗ ܘܬܘܒ ܫܪܟܐ (x = Λη + ε، ܐܝܟ ܓܘ CFA)؛ ܓܘ ܡܘܕܝܠ ܒܢܝܢܝܐ (structural model) ܟܠ ܥܠܬܐ endogenous ܚܘܠܛܐ ܝܠܗ ܕܥܠ̈ܠܬܐ ܕܟܡܢܒܝ ܠܗ ܘܬܘܒ disturbance (η = Bη + ζ). ܡܢ ܐܟܐ ܡܐܛܪܝܟܣ ܕܫܘܚܠ̈ܦܐ ܡܫܘܬܦ̈ܐ (covariance matrix) ܕܟܢܦܩ ܡܢ ܡܘܕܝܠ: Σ = Λ(I − B)⁻¹Ψ(I − B)⁻ᵀΛ′ + Θ، ܐܡܢ ܕ-Ψ ܟܡܚܒܫܐ ܫܘܚܠ̈ܦܐ ܘܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܕܥܠ̈ܠܬܐ exogenous ܘܫܘܚܠ̈ܦܐ ܕ-disturbances. Rosseel (2012، ܠܘܚܐ 1) ܟܡܚܘܝܐ ܬܠܬܐ ܐܘܦܪܛܘܪ̈ܐ ܕܟܬܚܡܝ ܡܘܕܝܠ ܐܝܟ ܐܗܐ ܓܘ lavaan: =~ ("ܡܫܘܚܐ ܝܠܗ ܒܝܕ")، ~ ("ܡܢܒܝܐ ܝܠܗ ܒܝܕ") ܘ-~~ (ܫܘܚܠܦܐ ܡܫܘܬܦܐ).

identification. Kline (2023، ܦܐܬܐ 265، ܢܡܘܣܐ 15.1 – "ܢܡܘܣܐ ܕ-identification ܕܬܪܝܢ ܕܪ̈ܓܐ"، ܠܦܘܬ Anderson ܘ-Gerbing, 1988، ܘ-Bollen, 1989، ܐܝܟ ܕܡܬܚܙܝܢ ܓܒܗ): ܡܘܕܝܠ ܓܡܝܪܐ identified ܝܠܗ ܐܢ (1) ܡܢܬܐ ܕܡܫܘܚܬܐ، ܐܡܢ ܕܟܬܝܒܐ ܝܠܗ ܐܝܟ CFA، identified ܝܠܗ، ܘ-(2) ܡܢܬܐ ܒܢܝܢܝܬܐ identified ܝܠܗ – ܘܟܠ ܡܘܕܝܠ ܒܢܝܢܝܐ ܪܩܘܪܣܝܒܝܐ (ܕܠܐ ܚܘܕ̈ܪܐ) identified ܝܠܗ (ܗܘ ܕܘܟܬܐ، ܦܐܬܐ 110، ܢܡܘܣܐ 7.4). ܡܛܠ ܗܕܐ ܦܐܬܐ ܟܩܒܠ ܒܠܚܘܕ ܡܘܕܝ̈ܠܐ ܪܩܘܪܣܝܒ̈ܝܐ، ܘܟܒܥܐ ܩܐ ܟܠ ܥܠܬܐ ܠܩܠܝܠܐ ܬܪܝܢ ܦܣܘ̈ܩܐ. ܦܣܩܬܐ ܕܣܒܠܬܐ – ܐܝܟ ܓܘ CFA: marker (ܓܘܒܝܐ ܡܩܕܡܐ ܕ-lavaan ܘܕ-AMOS) ܝܢ std.lv؛ ܓܘ std.lv، ܐܝܟ ܓܘ lavaan، ܐܦ ܫܘܚܠ̈ܦܐ ܕ-disturbances ܕܥܠ̈ܠܬܐ endogenous ܩܝ̈ܡܐ ܝܢܐ ܥܠ 1، ܘܡܛܠ ܗܕܐ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܠܐ ܡܬܩ̈ܢܐ ܦܪ̈ܝܫܐ ܝܢܐ – ܒܣ ܦܐܝܘܬܐ ܘܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܡܬܩ̈ܢܐ ܐܝܟ ܚܕ̈ܕܐ ܝܢܐ.

ܫܘܥܪܐ. ܡܬܚܙܝܢܘܬܐ ܥܠܝܬܐ (maximum likelihood, ML) ܐܝܟ ܓܘ lavaan، ܒܗܘ ܡܫܩܠܢܐ ܓܘܦܗ ܕܦܐܬܐ ܕ-CFA (Fisher scoring ܥܡ ܝܕܥܬܐ ܡܣܟܝܬܐ، ܥܕܡܐ ܕܡܢܝܢܐ ܕܫܘܢܝܐ (derivative) ܒܨܝܪ ܡܢ 10⁻¹⁰؛ χ² = N·F). ܫܘܪܪܐ: ܦܐܬܐ ܟܥܒܕ ܬܘܒ ܡܬܠܐ ܓܡܝܪܐ ܕ-Rosseel (2012، ܦܣܩܐ 5.1، ܦܐܬܐ 18-20) – ܝܗܝ̈ܒܬܐ ܕ-industrialization ܘܕܝܡܘܩܪܐܛܝܐ ܦܘܠܝܛܝܩܝܬܐ ܕ-Bollen (1989, as cited in Rosseel)، 75 ܡܬ̈ܘܬܐ، ܬܠܬܐ ܥܠ̈ܠܬܐ، ܬܠܬܐ ܫܒ̈ܝܠܐ ܘܐܫܬܐ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܕܫܪ̈ܟܐ: χ²(35) = 38.125، p = .329، ܫܒ̈ܝܠܐ 1.483، 0.572 ܘ-0.837، ܘܟܠ 34 ܣܕܪ̈ܐ ܕܡܦܩܢܐ ܛܒܝܥܐ (ܫܘܥܪܐ، ܛܥܝܘܬܐ ܬܩܝܢܬܐ، z ܘ-Std.all) ܥܕܡܐ ܠܡܢܝܢܐ ܬܠܝܬܝܐ؛ ܘ-lavaan 0.6-17 ܒܫܒܥܐ ܡܘܕܝ̈ܠܐ – ܥܡ ܡܥܒܕ̈ܢܘܝܬܐ ܠܐ ܬܪ̈ܝܨܬܐ (:=)، ܫܪ̈ܟܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ، ܒܘܚܪܢܐ ܕܦܘܪܫܢܐ ܒܝܢܝ ܕܪ̈ܓܐ ܘܡܚܘ̈ܝܢܐ ܕܫܘܢܝܐ.

ܒܢܝܢܐ ܕܬܪܝܢ ܕܪ̈ܓܐ

ܐܢ ܡܘܕܝܠ (model) ܓܡܝܪܐ ܠܐ ܝܠܗ ܦܐܝܐ – ܐܝܟܐ ܝܠܗ ܥܘܩܬܐ: ܓܘ ܡܫܘܚܬܐ، ܓܘ ܒܢܝܢܐ، ܝܢ ܓܘ ܬܪܘܝܗܝ؟ Kline (2023، ܦܐܬܐ 265) ܟܡܚܘܝܐ ܒܢܝܢܐ ܕܬܪܝܢ ܕܪ̈ܓܐ ܕ-Anderson ܘ-Gerbing (1988، ܐܝܟ ܕܡܬܚܙܝܢ ܓܒܗ): ܓܘ ܕܪܓܐ 1 ܟܟܬܒܚ ܡܘܕܝܠ ܐܝܟ CFA – ܗܢܝ ܥܠ̈ܠܬܐ (factors) ܘܦܣܘ̈ܩܐ (items) ܓܘܦܝܗܝ، ܟܠ ܥܠ̈ܠܬܐ ܐܣܝܪ̈ܐ ܥܡ ܚܕ̈ܕܐ – ܘܟܒܚܪܚ ܦܐܝܘܬܐ ܕܝܠܗ؛ "ܐܢ ܦܐܝܘܬܐ ܕܡܘܕܝܠ ܕ-CFA ܟܪܝܗܬܐ ܝܠܗ، ܦܐܝܘܬܐ ܕܡܘܕܝܠ ܒܢܝܢܝܐ ܡܨܝܐ ܕܗܘܝܐ ܒܝܫܬܐ ܒܝܫ". ܓܘ ܕܪܓܐ 2، ܥܡ ܡܘܕܝܠ ܕܡܫܘܚܬܐ ܦܐܝܐ، ܟܦܚܡܚ ܡܘܕܝܠ ܒܢܝܢܝܐ ܥܡܗ ܒܒܘܚܪܢܐ ܕܦܘܪܫܢܐ ܕ-χ²: ܡܘܕܝܠ ܒܢܝܢܝܐ ܡܩܢܢܐ (nested) ܝܠܗ ܓܘ ܡܘܕܝܠ ܕܡܫܘܚܬܐ (ܫܒܝܠܐ ܕܠܐ ܬܚܘܡܐ ܝܠܗ = ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕܩܝܡܐ ܝܠܗ ܥܠ ܨܦܪܐ). ܐܡܢ ܕܡܢܬܐ ܒܢܝܢܝܬܐ ܒܚܬܝܬܘܬܐ just-identified ܝܠܗ – ܐܝܬ ܫܒܝܠܐ ܝܢ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܟܠ ܬܪܝܢ ܥܠ̈ܠܬܐ، ܐܝܟ ܓܘ ܡܘܕܝܠ ܕܡܬܠܐ – "ܦܐܝܘܬܐ ܕܡܘܕܝܠ ܒܢܝܢܝܐ ܘܕ-CFA ܐܝܟ ܚܕ̈ܕܐ ܝܢܐ، ܡܛܠ ܕܡܘܕܝ̈ܠܐ ܫܘ̈ܝܐ ܝܢܐ". ܦܐܬܐ ܟܡܪܗܛ ܬܪܘܝܗܝ ܕܪ̈ܓܐ ܘܟܡܚܘܝܐ ܠܗܘܢ ܐܟܚܕܐ ܓܘ ܠܘܚܐ 1.

ܬܪܝܢ ܙܘܗܪ̈ܐ ܕ-Kline (ܦܐܬܐ 266-268). ܩܕܡܝܐ، ܡܘܕܝ̈ܠܐ ܫܘ̈ܝܐ: ܐܡܢ ܕܡܘܕܝܠ ܒܢܝܢܝܐ ܘܕܡܫܘܚܬܐ ܫܘ̈ܝܐ ܝܢܐ، "ܫܬܐܣܐ ܝܚܝܕܝܐ" ܩܐ ܓܘܒܝܐ ܕܡܘܕܝܠ ܥܡ ܓܐܪ̈ܐ "ܡܠܝܐ ܝܠܗ (ܝܥܢܝ ܚܘܬܡܐ، ܠܐ ܦܘܫܩܐ) ܝܢ ܣܡܝܟܐ ܝܠܗ ܒܬܘܩܢܐ ܕܒܘܨܝܐ (research design) (ܡܬܠܐ ܩܕܡܝܘܬܐ ܒܙܒܢܐ ܓܘ ܡܫܘܚܬܐ)"؛ ܘܓܘ ܬܘܢܝܐ ܣܢܝܩܘܬܐ ܐܝܬ "ܕܡܘܕܝܚ ܕܐܝܬ ܡܘܕܝ̈ܠܐ ܫܘ̈ܝܐ ܓܘ ܟܠ ܕܪܓܐ" ܘܕܡܦܫܩܚ ܩܡܘܕܝ ܓܒܝܐ ܝܠܗ ܡܘܕܝܠ. ܬܪܝܢܐ، ܩܝܡܘܬܐ ܕܛܥ̈ܢܐ (loadings): ܐܡܢ ܕܡܫܢܚ ܡܢܬܐ ܒܢܝܢܝܬܐ، ܛܥ̈ܢܐ ܓܪܓ ܕܫܚܠܦܝ ܩܠܝܠ ܒܠܚܘܕ؛ ܫܘܢܝܐ ܪܒܐ ܝܠܗ "interpretational confounding" – ܣܘܟܠܐ ܕܥܠܬܐ ܟܫܚܠܦ ܠܦܘܬ ܡܐ ܕܟܡܢܒܐ ܠܗ. ܘܬܘܒ: ܡܚܘ̈ܝܢܐ ܕܦܐܝܘܬܐ (fit indices) ܟܠܢ̈ܝܐ ܡܥܒܕ̈ܐ ܝܢܐ ܒܝܫ ܡܢ ܡܢܬܐ ܕܡܫܘܚܬܐ، ܕܣܓܝ ܙܒ̈ܢܐ ܐܝܬ ܠܗ ܣܓܝ ܒܝܫ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom)، ܘܡܛܠ ܗܕܐ ܦܐܝܘܬܐ ܛܒܬܐ ܕܡܘܕܝܠ ܟܠܗ ܡܨܝܐ ܕܡܛܫܝܐ ܥܘܩܬܐ ܓܘ ܡܢܬܐ ܒܢܝܢܝܬܐ (McDonald ܘ-Ho, 2002، ܐܝܟ ܕܡܬܚܙܝܢ ܓܒ Kline، ܦܐܬܐ 268).

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܘܚܐ 1 – ܦܐܝܘܬܐ ܓܘ ܬܪܘܝܗܝ ܕܪ̈ܓܐ. ܣܕܪܐ ܩܐ ܡܘܕܝܠ ܕܡܫܘܚܬܐ ܘܣܕܪܐ ܩܐ ܡܘܕܝܠ ܒܢܝܢܝܐ، ܥܡ ܗܢܝ ܡܚܘ̈ܝܢܐ ܘܗܢܝ ܬܚܘ̈ܡܐ ܓܘܦܝܗܝ ܐܝܟ ܓܘ ܦܐܬܐ ܕ-CFA: χ² (ܒܥܝܚ p ܪܒܐ ܡܢ .05)، CFI ܘ-TLI (ܠܥܠ ܡܢ .95 ܛܒ، ܠܥܠ ܡܢ .90 ܡܩܒܠܐ)، RMSEA ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) 90% (ܥܕܡܐ .06 ܛܒ، ܥܕܡܐ .08 ܡܩܒܠܐ) ܘ-SRMR (ܥܕܡܐ .08) – ܬܚܘ̈ܡܐ ܕ-Hu ܘ-Bentler (1999، ܦܐܬܐ 27)، "ܩܪܝܒܐ ܠ-" ܘܠܐ ܢܡܘ̈ܣܐ، ܘܦܬܝܘ̈ܬܐ ܕ-Brown (2015، ܦܐܬܐ 74-75) ܟܡܝܬܐ؛ Kline (2023، ܦܐܬܐ 268، 421) ܠܐ ܟܡܠܟ ܕܣܡܟܚ ܥܠ ܬܚܘ̈ܡܐ ܩܝ̈ܡܐ ܡܢ ܟܠ ܓܒܐ، ܕܠܐ ܒܘܚܪܢܐ ܕܦܐܝܘܬܐ ܕܘܟܬܢܝܬܐ. ܓܘ ܡܥܝܪܢܘܬܐ – ܒܘܚܪܢܐ ܕܦܘܪܫܢܐ Δχ² ܒܝܢܝ ܕܪ̈ܓܐ، ܝܢ ܡܘܕܥܢܘܬܐ ܕܡܘܕܝ̈ܠܐ ܫܘ̈ܝܐ ܝܢܐ.

ܠܘܚܐ 2 – ܫܒ̈ܝܠܐ. ܩܐ ܟܠ ܫܒܝܠܐ: b (ܠܐ ܡܬܩܢܐ)، ܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error)، z، p، ܬܚܘܡܐ ܕܬܘܟܠܢܐ 95% ܘ-β (Std.all) – ܒܟܡܐ ܣܛܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܟܫܚܠܦܐ ܥܠܬܐ ܡܢܒܝܬܐ ܐܡܢ ܕܡܢܒܝܢܐ ܟܣܠܩ ܒܚܕܐ ܣܛܝܘܬܐ ܬܩܝܢܬܐ (standard deviation) ܘܡܢܒ̈ܝܢܐ ܐܚܪ̈ܢܐ ܕܝܠܗ ܩܝ̈ܡܐ ܝܢܐ. ܓܘ ܡܥܝܪܢܘܬܐ – R² ܕܟܠ ܥܠܬܐ endogenous: ܡܢܬܐ ܕܫܘܚܠܦܐ (variance) ܕܝܠܗ ܕܡܢܒ̈ܝܢܐ ܟܡܦܫܩܝ (Byrne, 2016، ܦܐܬܐ 212، ܥܠ SMC ܕܟܠ ܥܠܬܐ ܬܠܝܬܐ: ܣܛܐܛܝܣܛܝܩܝܐ "ܕܠܐ ܬܠܝܐ ܝܠܗ ܒܚܕ̈ܝܘܬܐ ܕܡܫܘܚܬܐ").

ܠܘܚܐ 3 – ܡܥܒܕ̈ܢܘܝܬܐ ܬܪ̈ܝܨܬܐ، ܠܐ ܬܪ̈ܝܨܬܐ ܘܟܠܢ̈ܝܬܐ (ܦܣܩܐ ܠܬܚܬ). ܠܘܚܐ 4 – ܛܥ̈ܢܐ ܕܡܘܕܝܠ ܕܡܫܘܚܬܐ، ܐܝܟ ܠܘܚܐ 2 ܓܘ ܦܐܬܐ ܕ-CFA. ܠܘܚܐ 5 – ܫܘܚܠ̈ܦܐ: ܩܐ ܥܠܬܐ exogenous – ܫܘܚܠܦܐ ܘܐܣܘܪܐ ܕܚܕ̈ܕܐ ܥܡ exogenous ܐܚܪ̈ܢܐ؛ ܩܐ ܥܠܬܐ endogenous – ܫܘܚܠܦܐ ܕ-disturbance، ܘܛܝܡܐ ܡܬܩܢܐ ܕܝܠܗ ܝܠܗ 1 − R².

ܠܘܚܐ 6 – ܫܪ̈ܟܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ. ܩܐ ܟܠ ܙܘܓܐ ܕܦܣܘ̈ܩܐ: ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܚܙܝܐ ܒܨܝܪ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕܟܢܦܩ ܡܢ ܡܘܕܝܠ (ܟܠ ܡܐܛܪܝܟܣ ܡܬܩܢܐ ܝܠܗ ܒܣܪܛܐ ܡܨܠܝܢܐ ܕܝܠܗ – cor.bollen ܓܘ lavaan، ܓܘܒܝܐ ܡܩܕܡܐ ܓܘ ܟܬܒܐ ܕ-Kline, 2023، ܦܐܬܐ 147). ܫܪ̈ܟܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ، ܠܐ ܐܝܟ ܫܪ̈ܟܐ ܕܫܘܚܠܦܐ ܡܫܘܬܦܐ (covariance)، "ܡܨܝ ܕܡܬܦܚܡܝ ܬܪܝܨܐܝܬ ܒܝܢܝ ܙܘܓ̈ܐ ܦܪ̈ܝܫܐ" (ܗܘ ܕܘܟܬܐ، ܦܐܬܐ 145). Kline ܓܘ ܡܬܠ̈ܐ ܕܝܠܗ ܟܪܫܡ ܛܝܡܐ ܫܪܝܪܐ ܠܥܠ ܡܢ .10 ܐܝܟ ܐܬܐ ܕܡܘܕܝܠ ܠܐ ܟܡܦܫܩ ܛܒ ܐܣܘܪܐ ܒܝܢܝ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ (ܦܐܬܐ 146، ܠܘܚܐ 9.4) – ܦܐܬܐ ܟܡܛܠܠ ܠܗܘܢ. Kline (ܦܐܬܐ 422) ܟܡܚܝܠ ܕܬܘܢܝܐ ܕܡܚܘ̈ܝܢܐ ܕܦܐܝܘܬܐ ܟܠܢ̈ܝܐ ܒܠܚܘܕ "ܠܐ ܣܦܩ": "ܡܕܡ̈ܝܐ ܫܪ̈ܝܪܐ ܕܦܐܝܘܬܐ" ܐܝܬܝ̈ܐ ܓܘ ܫܪ̈ܟܐ (ܦܐܬܐ 268). ܠܘܚܐ 7 – ܡܚܘ̈ܝܢܐ ܕܫܘܢܝܐ (modification indices): ܐܝܟ ܓܘ CFA، ܘܬܘܒ ܫܒ̈ܝܠܐ ܕܠܐ ܬܚܘ̈ܡܐ ܝܢܐ ܘܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܥܠ̈ܠܬܐ ܝܢ disturbances (ܐܦ ܫܒܝܠܐ ܕܗܘܐ ܣܐܓܪ ܚܘܕܪܐ ܟܡܬܚܙܐ، ܐܝܟ ܓܘ lavaan، ܘܪܫܝܡܐ ܝܠܗ). ܨܘܪܬܐ – ܡܢܬܐ ܒܢܝܢܝܬܐ: β ܥܠ ܓܐܪ̈ܐ، R² ܠܬܚܬ ܡܢ ܟܠ ܥܠܬܐ endogenous.

ܡܥܒܕ̈ܢܘܝܬܐ ܠܐ ܬܪ̈ܝܨܬܐ (ܡܨܥܝܘܬܐ)

ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ (indirect effect) ܕܬܘܟܠܢܐ ܥܠ ܫܘܬܦܘܬܐ ܒܝܕ ܕܝܠܢܝܘܬܐ ܝܠܗ product ܕܬܪܝܢ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܥܠ ܐܘܪܚܐ – a·b – ܘܡܥܒܕܢܘܬܐ ܟܠܢܝܬܐ (total effect) ܝܠܗ ܬܪܝܨܬܐ ܘܬܘܒ ܠܐ ܬܪܝܨܬܐ (Kline, 2023، ܦܐܬܐ 125؛ ܐܡܢ ܕܐܝܬ ܟܡܐ ܐܘܪ̈ܚܬܐ، ܦܐܬܐ ܟܡܟܢܫ products ܕܟܠܗܘܢ، ܐܝܟ ܡܐܛܪܝܟܣ ܕܡܥܒܕ̈ܢܘܝܬܐ ܟܠܢ̈ܝܬܐ (I − B)⁻¹ − I). ܓܘ lavaan ܟܬܚܡܚ ܠܗܘܢ ܒܐܘܦܪܛܘܪ :=، ܘܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܕܝܗܝ ܚܫܝ̈ܒܐ ܝܢܐ "ܒܐܘܪܚܐ ܕ-delta (Sobel, 1982)" (Rosseel, 2012, Section 7.4) – ܗܘ ܚܘܫܒܢܐ ܓܘܦܗ ܓܘ ܦܐܬܐ. ܓܘ ܐܘܪܚܐ ܕܬܪܝܢ ܫܒ̈ܝܠܐ ܐܗܐ ܝܠܗ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕ-Sobel (Kline, p. 125, Equation 8.2)، ܐܡܢ ܕܓܘ ܚܕ ܡܘܕܝܠ ܐܦ ܫܘܚܠܦܐ ܡܫܘܬܦܐ (covariance) ܒܝܢܝ ܬܪܝܢ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܟܥܐܠ ܠܚܘܫܒܢܐ.

ܬܚܘܡܐ. Kline (2023، ܦܐܬܐ 128): ܒܘܚܪܢܐ ܕ-Sobel "ܟܡܣܒܐ ܢܘܪܡܠܝܘܬܐ، ܒܣ ܦܘܠ̈ܓܐ ܕܫܘܥܪ̈ܐ ܕ-product ܣܓܝ ܙܒ̈ܢܐ ܠܐ ܝܢܐ ܢܘܪܡܠ̈ܝܐ؛ ܣܓܝ ܙܒ̈ܢܐ ܠܐ ܫܘ̈ܝܐ ܝܢܐ"، ܘܡܛܠ ܗܕܐ ܠܐ ܘܠܐ ܠܡܦܫܩܐ ܛܝ̈ܡܐ ܕ-p ܕܝܠܗ ܒܝܬܝܪܘܬܐ؛ ܚܠܦܐ ܝܠܗ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܕ-bootstrap (ܗܘ ܕܘܟܬܐ، ܦܐܬܐ 128-129، ܥܡ ܙܘܗܪܐ ܕܕܠܐ ܙܪܥܐ (random seed) ܩܝܡܐ ܬܚܘ̈ܡܐ ܡܨܝ ܕܫܚܠܦܝ ܒܝܢܝ ܪ̈ܗܛܐ). ܦܐܬܐ ܟܛܒܥ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܢܘܪܡܠܝܐ (b ± 1.96·SE، ܐܝܟ parameterEstimates())، ܘܣܩܪܝܦܬ ܕ-R ܕܓܘ ܡܦܩܢܐ ܟܡܚܒܫ ܦܘܩܕܢܐ ܩܐ bootstrap؛ bootstrap ܓܘܦܗ، ܓܘ ܒܪܐܘܙܪ – ܠܦܘܬ ܐܘܪܚܐ، ܥܡ ܬܚܘ̈ܡܐ ܕܕܪ̈ܓܐ ܡܢ ܡܐܐ ܘܡܬܘܪ̈ܨܐ ܡܢ ܡܣܒ ܒܐܦ̈ܐ (bias-corrected) ܘܗܢܝ ܕܘ̈ܡܝܐ ܓܘܦܝܗܝ ܐܝܟ ܓܘ lavaan ܥܡ ܗܘ ܙܪܥܐ ܓܘܦܗ – ܟܚܫܒ ܦܐܬܐ ܡܨܥܝܘܬܐ ܒܝܢܝ ܥܠ̈ܠܬܐ ܟܣ̈ܝܬܐ. ܓܘ ܦܐܝܠ ܕܡܬܠܐ ܦܘܪܫܢܐ ܙܥܘܪܐ ܝܠܗ: ܬܚܘܡܐ ܕ-delta ܩܐ ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ [0.164, 0.398]، ܘܬܚܘܡܐ ܕܕܪ̈ܓܐ ܡܢ ܡܐܐ ܡܢ 5,000 ܓܘ̈ܒܝܐ ܕ-bootstrap (ܙܪܥܐ 2026) [0.171, 0.414] – ܠܐ ܫܘܝܐ، ܐܝܟ ܕܡܣܟܝܐ ܗܘܐ. ܘܦܘܫܩܐ: "ܡܨܥܝܘܬܐ" ܛܥܢܬܐ ܥܠܬܢܝܬܐ ܝܠܗ، ܘܓܘ ܡܘܕܝܠ ܕܒܘܨܝܐ ܕܚܕ ܙܒܢܐ (cross-sectional study) ܕܡܬܠܐ، ܡܘܕܝܠ ܥܡ ܓܐܪ̈ܐ ܒܐܘܪܚܐ ܗܦܝܟܬܐ ܦܐܝܐ ܝܠܗ ܠܝܗܝ̈ܒܬܐ ܒܗܘ ܟܡܐ ܓܘܦܗ (ܦܣܩܐ "ܒܢܝܢܐ ܕܬܪܝܢ ܕܪ̈ܓܐ").

ܫܪ̈ܛܐ ܘܙܘܗܪ̈ܐ (Assumptions and warnings)

ܪܒܘܬܐ ܕܕܘܡܝܐ (sample size). Kline (2023، ܦܐܬܐ 16): "ܠܝܬ ܢܡܘܣܐ ܕܨܒܥܐ ܦܫܝܛܐ ܩܐ ܪܒܘܬܐ ܕܕܘܡܝܐ ܕܦܠܚ ܓܘ ܟܠ ܒܘܨ̈ܝܐ". ܐܝܟ ܢܘܩܙܐ ܕܫܘܪܝܐ ܗܘ ܟܡܝܬܐ ܢܡܘܣܐ ܕ-N:q ܕ-Jackson (2003، ܐܝܟ ܕܡܬܚܙܐ ܓܒܗ) – ܦܘܚܡܐ ܕ-20 ܡܫܬܘܬܦ̈ܢܐ ܩܐ ܟܠ ܦܪܡܝܛܪ (parameter) ܡܫܘܥܪܐ ܡܠܝܟܐ ܝܠܗ، 10 "ܒܨܝܪ ܐܝܕܝܐܠ"، ܘܠܬܚܬ ܡܢ ܗܕܐ "ܐܦ ܬܘܟܠܢܐ ܕܦܐܪ̈ܐ" ܟܢܚܬ – ܘܪܒܘܬܐ ܕܕܘܡܝܐ ܡܨܥܝܬܐ ܓܘ ܣܩܘܪ̈ܐ ܕܒܘܨ̈ܝܐ ܕ-SEM، ܒܩܘܪܒܐ 200؛ "ܥܡ N < 100، ܩܪܝܒܐܝܬ ܟܠ ܙܢܐ ܕ-SEM ܡܨܐ ܕܗܘܐ ܠܐ ܡܨܝܢܐ" ܐܠܐ ܐܢ ܡܘܕܝܠ ܣܓܝ ܦܫܝܛܐ ܝܠܗ. ܦܐܬܐ ܟܡܙܗܪ ܠܬܚܬ ܡܢ 200 ܡܫܬܘܬܦ̈ܢܐ (ܘܒܢܘܣܚܐ ܚܪܝܦܐ ܒܝܫ ܠܬܚܬ ܡܢ 100) ܘܠܬܚܬ ܡܢ ܦܘܚܡܐ 10:1. ܓܘ ܦܐܝܠ ܕܡܬܠܐ: 314 ܡܫܬܘܬܦ̈ܢܐ ܘ-27 ܦܪ̈ܡܝܛܪܐ – 11.6:1.

ܢܘܪܡܠܝܘܬܐ (normality) ܘܦܣܘ̈ܩܐ ܕ-Likert – ܐܝܟ ܓܘ CFA: ܫܘܥܪܐ ML ܟܡܣܒܐ ܢܘܪܡܠܝܘܬܐ ܕܣܓܝ ܡܫܬܚܠܦ̈ܢܐ؛ ܠܦܘܬ Rhemtulla ܘܐܚܪ̈ܢܐ (2012، ܦܐܬܐ 354) ML ܦܐܝܐ ܝܠܗ ܩܐ ܦܣܘ̈ܩܐ ܥܡ 5 ܓܢ̈ܣܐ ܘܠܥܠ، ܘܫܘܥܪܐ ܩܐ ܝܗܝ̈ܒܬܐ ܛܟܝ̈ܣܬܐ – ܠܩܠܝܠܐ ܒܨܝܪ ܡܢ ܗܕܐ. ܦܘܫܪܐ ܠܐ ܡܩܒܠܐ: ܫܘܚܠܦܐ ܕܫܪܟܐ ܝܢ disturbance ܬܚܝܬ ܨܦܪܐ (ܓܘ ܥܠܬܐ endogenous – R² ܠܥܠ ܡܢ 1)، ܝܢ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕܥܠ̈ܠܬܐ ܠܥܠ ܡܢ 1؛ "ܠܐ ܡܦܫܩܝܬܘܢ ܦܐܪ̈ܐ ܡܢ ܦܘܫܪܐ ܕܠܐ ܡܩܒܠܐ ܝܠܗ" (Kline, 2023, p. 421; Brown, 2015, pp. 162-163). ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (missing values) – ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (listwise deletion) ܥܠ ܟܠ ܦܣܘ̈ܩܐ ܕܡܘܕܝܠ (ܓܘܒܝܐ ܡܩܕܡܐ ܕ-lavaan). ܫܘܢܝܐ ܕܡܘܕܝܠ ܒܬܪ ܪܗܛܐ: Kline (ܦܐܬܐ 266) ܟܡܙܗܪ ܕ"ܐܘܪܚܐ ܟܡܦܠܚ ܫܘܚܠܦܐ ܕܓܕܫܐ" ܐܡܢ ܕܡܫܢܚ ܘܒܚܪܚ ܥܠ ܗܢܝ ܝܗܝ̈ܒܬܐ ܓܘܦܝܗܝ، ܘܕܕܠܐ ܦܐܝܘܬܐ ܥܡ ܝܗܝ̈ܒܬܐ ܚܕ̈ܬܬܐ "ܠܐ ܝܕܝܥܐ ܝܠܗ ܐܢ ܡܘܕܝܠ ܒܕ ܗܘܐ ܥܒܝܕܐ ܬܘܒ"؛ Byrne (2016، ܦܐܬܐ 206-208) ܟܡܚܘܝܐ ܐܘܪܚܐ – ܡܘܣܦܬܐ ܕܫܒ̈ܝܠܐ "ܕܐܝܬ ܠܗܘܢ ܣܘܟܠܐ ܬܐܘܪܝܐ" ܠܦܘܬ ܡܚܘ̈ܝܢܐ ܕܫܘܢܝܐ، ܘܒܬܪ ܗܕܐ ܫܩܠܬܐ ܕܫܒ̈ܝܠܐ ܠܐ ܪܫܝܡ̈ܐ "ܩܐ ܚܣܝܟܘܬܐ (parsimony)" – ܘܟܡܟܢܫܐ (ܦܐܬܐ 217) ܕܠܝܬ "ܢܡܘ̈ܣܐ ܩܫܝ̈ܐ" ܐܝܡܢ ܕܟܠܚ، ܠܒܪ ܡܢ ܝܕܥܬܐ ܬܐܘܪܝܬܐ، ܡܬܩܠܢܘܬܐ ܕܡܚܘ̈ܝܢܐ ܘ"ܥܝܢܐ ܦܬܝܚܬܐ ܥܠ ܚܣܝܟܘܬܐ". ܬܪܘܝܗܝ ܐܘܪ̈ܚܬܐ ܟܡܛܝ ܠܗܘ ܢܘܩܙܐ ܓܘܦܗ: ܟܠ ܫܘܢܝܐ ܟܡܬܢܚ ܠܗ، ܘܡܘܕܝܠ ܕܫܚܠܦܠܗ ܗܕܟܐ ܟܒܥܐ ܥܒܕܐ ܡܢ ܪܝܫ ܓܘ ܝܗܝ̈ܒܬܐ ܚܕ̈ܬܬܐ.

ܡܘܕܝ ܠܐ ܟܚܫܒܐ ܐܗܐ ܦܐܬܐ. ܡܘܕܝ̈ܠܐ ܠܐ ܪܩܘܪܣܝܒ̈ܝܐ (ܚܘܕ̈ܪܐ، ܡܥܒܕ̈ܢܘܝܬܐ ܕܚܕ ܥܠ ܐܚܪܢܐ)، ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܢܝ disturbances، ܥܠܬܐ ܥܡ ܦܣܘܩܐ ܝܚܝܕܝܐ، ܡܫܬܚܠܦ̈ܢܐ ܚܙ̈ܝܐ (observed variables) ܓܘ ܡܢܬܐ ܒܢܝܢܝܬܐ (ܡܬܠܐ ܥܘܡܪܐ ܐܝܟ ܡܢܒܝܢܐ)، ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܕ-bootstrap (ܓܘ ܦܐܬܐ ܡܨܥܝܘܬܐ ܒܝܢܝ ܥܠ̈ܠܬܐ ܟܣ̈ܝܬܐ)، RMSEA ܕܡܢܬܐ ܒܢܝܢܝܬܐ ܒܠܚܘܕ (RMSEA-P, Kline, p. 268)، ܦܘܚܡܐ ܕܓܘ̈ܕܐ ܘܠܐ ܡܫܬܚܠܦܢܘܬܐ ܕܡܫܘܚܬܐ، ܫܘܥܪܐ ܚܣܝܢܐ (MLR) ܘܩܐ ܝܗܝ̈ܒܬܐ ܛܟܝ̈ܣܬܐ (WLSMV)، FIML، ܐܣܘܪ̈ܐ ܕܫܘܝܘܬܐ.

ܘܕܟܝ ܟܥܒܕܚ ܐܗܐ ܒ-SPSS ܘ-AMOS؟

ܓܘ SPSS Statistics ܠܝܬ ܡܘܕܝ̈ܠܐ ܕܫܘܝ̈ܘܬܐ ܒܢܝܢܝ̈ܬܐ؛ Pallant (2020، ܨܚܚܐ 10) ܟܐܡܪܐ ܕܗܘ "ܟܣܡܟ ܡܘܣܦܬܐ ܕܫܡܗ AMOS". ܓܘ AMOS ܟܨܐܪܚ ܡܘܕܝܠ ܕܡܫܘܚܬܐ (measurement model) ܐܝܟ ܓܘ CFA (ܚܘܕܪܐ ܡܓܪܓܐ ܩܐ ܟܠ ܥܠܬܐ، ܡܪܒܥܐ ܡܓܪܓܐ ܩܐ ܟܠ ܦܣܘܩܐ، ܚܘܕܪܐ ܕܫܪܟܐ ܩܐ ܟܠ ܦܣܘܩܐ)، ܘܒܕܘܟܬܐ ܕܩܫܬܐ ܕܬܪܝܢ ܐܘܪ̈ܚܬܐ ܒܝܢܝ ܥܠ̈ܠܬܐ ܕܐܝܬ ܒܝܢܝ ܕܝܗܝ ܗܘܦܘܬܣܝܣ ܥܠܬܢܝܬܐ – ܓܐܪܐ ܕܚܕ ܐܘܪܚܐ؛ ܩܐ ܟܠ ܥܠܬܐ endogenous ܟܡܘܣܦܚ ܚܘܕܪܐ ܕ-disturbance (AMOS ܟܩܝܡ ܓܐܪܐ ܕܝܠܗ ܥܠ 1). Byrne (2016، ܨܚܚܐ 6) ܟܡܚܘܝܐ ܡܘܕܝܠ ܓܡܝܪܐ ܐܝܟ ܐܗܐ ܦܣܥܬܐ ܒܬܪ ܦܣܥܬܐ. ܓܘ Analysis Properties › Output ܟܪܫܡܚ Standardized estimates، Squared multiple correlations ܘ-Modification indices (Byrne, 2016، ܦܐܬܐ 210: ܕܒܥܚ ܐܦ SMC). ܦܘܪܫܢܐ ܡܣܟܝܐ ܐܝܟ ܓܘ CFA: AMOS ܟܚܫܒ χ² = (N − 1)F_min (Byrne, 2016, p. 93)، ܐܠܐ lavaan ܘܦܐܬܐ – N·F (Brown, 2015, p. 67)؛ ܫܘܥܪ̈ܐ ܐܝܟ ܚܕ̈ܕܐ ܝܢܐ، ܘ-χ² ܘܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܩܠܝܠ ܦܪ̈ܝܫܐ ܝܢܐ.

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

lavaan: ܡܘܕܝܠ ܕܡܫܘܚܬܐ ܓܘ ܣܕܪ̈ܐ ܕ-=~، ܫܒ̈ܝܠܐ ܓܘ ܣܕܪ̈ܐ ܕ-~، ܪܘ̈ܫܡܐ ܩܕܡ ܡܢܒ̈ܝܢܐ (a*trust)، ܘܡܥܒܕ̈ܢܘܝܬܐ ܬܚܘܡ̈ܐ ܓܘ := (Rosseel, 2012, Section 7.4)؛ sem() ܡܢ ܓܢܗ ܟܡܘܣܦܐ ܫܘܚܠ̈ܦܐ ܕܫܪ̈ܟܐ ܘܕ-disturbances ܘܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܥܠ̈ܠܬܐ exogenous. button ܕ"ܡܚܬܬܐ ܕܣܩܪܝܦܬ ܕ-R" ܓܘ ܡܦܩܢܐ ܟܟܬܒ ܣܩܪܝܦܬ (script) ܕܡܘܕܝܠ ܕܬܚܘܡܠܘܟܘܢ – ܬܪܘܝܗܝ ܕܪ̈ܓܐ، ܒܘܚܪܢܐ ܒܝܢܝ ܕܝܗܝ، ܫܪ̈ܟܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܘܡܚܘ̈ܝܢܐ ܕܫܘܢܝܐ. ܣܩܪܝܦܬ ܕܠܬܚܬ ܪܗܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ (lavaan 0.6-17).

# ܡܘܕܝܠ ܕܫܘܝ̈ܘܬܐ ܒܢܝܢܝ̈ܬܐ – ܦܪܘܦܣܘܪ ܣܛܐܛ. ܐܗܐ ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8؛ ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܡܫܪܐ ܒܚܕܐ ܡܠܬܐ ܕܣܘܪܝܬ
library(readxl)   # ܩܪܝܢܐ ܕܐܩܣܠ
library(lavaan)   # ܦܘܢܩܣܝ̈ܘܢܐ: cfa, sem, lavTestLRT, 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))   # ܫܡܗ̈ܐ ܩܨܝܪ̈ܐ ܒܐܢܓܠܝܙܝܐ ܩܐ ܡܘܕܝܠ

# ܕܪܓܐ 1: ܡܘܕܝܠ ܕܡܫܘܚܬܐ – ܬܠܬܐ ܥܠ̈ܠܬܐ ܐܣܝܪ̈ܐ
meas <- "
  belong =~ b1 + b2 + b3 + b4
  trust  =~ t1 + t2 + t3 + t4
  partic =~ p1 + p2 + p3 + p4
"
fit1 <- cfa(meas, data = d)                 # ܦܐܪܐ: χ²(51) = 51.083, p = .470, CFI 1.000, RMSEA .002, SRMR .031

# ܕܪܓܐ 2: ܬܘܟܠܢܐ ← ܕܝܠܢܝܘܬܐ ← ܫܘܬܦܘܬܐ، ܘܬܘܒ ܬܘܟܠܢܐ ← ܫܘܬܦܘܬܐ
model <- paste0(meas, "
  belong ~ a*trust
  partic ~ b*belong + c*trust
  ind := a*b
  tot := c + a*b
")
fit <- sem(model, data = d)                 # ML، ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ: 314 ܡܢ 320
summary(fit, fit.measures = TRUE, standardized = TRUE, rsquare = TRUE)
# ܗܘ χ²(51) = 51.083 ܓܘܦܗ – ܡܢܬܐ ܒܢܝܢܝܬܐ just-identified ܝܠܗ، ܘܡܛܠ ܗܕܐ ܫܘܝܐ ܝܠܗ ܠܕܪܓܐ 1
# ܫܒ̈ܝܠܐ: a 0.531 (SE 0.078, β .509), b 0.529 (SE 0.089, β .521), c -0.014 (p = .874, β -.013)
# ܦܐܪ̈ܐ: ind 0.281 (SE 0.060), β .266; tot 0.267 (SE 0.076); R²: belong .259, partic .265

# ܫܪ̈ܟܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ – ܪܒܐ ܒܛܝܡܐ ܫܪܝܪܐ .078 (b1, p1)؛ ܡܚܘ̈ܝܢܐ ܕܫܘܢܝܐ ܠܥܠ ܡܢ 3.84 – b2 ~~ b3: 8.024
round(residuals(fit, type = "cor.bollen")$cov, 3)
mi <- modindices(fit, sort. = TRUE)
mi[mi$mi > 3.84, c("lhs", "op", "rhs", "mi", "epc", "sepc.all")]

# ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕ-bootstrap ܩܐ ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ (ܠܐ ܓܘ ܦܐܬܐ) – ܕܪ̈ܓܐ ܡܢ ܡܐܐ، 5000 ܓܘ̈ܒܝܐ، ܙܪܥܐ ܩܝܡܐ
set.seed(2026)
fitb <- sem(model, data = d, se = "bootstrap", bootstrap = 5000)
pe <- parameterEstimates(fitb, boot.ci.type = "perc")
pe[pe$op == ":=", ]                          # ܦܐܪܐ: ind: [0.171, 0.414]; tot: [0.124, 0.427]

# ܕܠܐ ܫܒܝܠܐ ܬܪܝܨܐ (ܡܨܥܝܘܬܐ ܓܡܝܪܬܐ) – ܡܘܕܝܠ ܡܩܢܢܐ ܝܠܗ، ܘܡܨܝܚ ܕܒܚܪܚ ܠܗ
model2 <- paste0(meas, "
  belong ~ trust
  partic ~ belong
")
fit2 <- sem(model2, data = d)
lavTestLRT(fit2, fit1)                       # ܦܐܪܐ: Δχ²(1) = 0.025, p = .875

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

Kline (2023، ܦܐܬܐ 420-422) ܟܡܢܝܐ ܡܘܕܝ ܟܡܬܢܚ: ܬܘܟܢܝܬܐ (software) ܘܢܘܣܚܐ ܕܝܠܗ ܘܣܝܢܬܐܟܣ (syntax) ܕܡܘܕܝܠ ܐܚܪܝܐ (ܓܘ ܡܘܣܦܬܐ ܝܢ ܓܘ ܡܐܢܐ ܡܘܣܦܢܐ)؛ ܐܘܪܚܐ ܕܫܘܥܪܐ، ܘܐܢ ܫܘܥܪܐ ܡܬܟܢܫܠܗ ܘܦܘܫܪܐ ܡܩܒܠܐ ܝܠܗ؛ ܦܣܩ̈ܬܐ ܕܓܘܒܝܐ ܒܝܢܝ ܡܘܕܝ̈ܠܐ، ܥܡ ܒܘܚܪ̈ܢܐ ܕܦܘܪܫܢܐ ܒܝܢܝ ܡܘܕܝ̈ܠܐ ܡܩܢ̈ܢܐ؛ ܡܢܝܢܐ ܕܫܘܢܝ̈ܐ ܓܘ ܡܘܕܝܠ ܘܥܠܬܐ ܬܐܘܪܝܬܐ ܩܐ ܟܠ ܚܕ، ܘܥܡ ܦܘܪܫܢܐ ܓܠܝܐ ܒܝܢܝ ܡܐ ܕܬܚܘܡܐ ܝܠܗ ܡܢ ܩܕܡ ܘܡܐ ܕܦܝܫܐ ܝܠܗ ܒܬܪ ܚܙܝܬܐ ܕܝܗܝ̈ܒܬܐ؛ ܫܘܥܪ̈ܐ ܠܐ ܡܬܩ̈ܢܐ ܥܡ ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܘܓܒܝܗܝ ܡܬܩ̈ܢܐ – "ܛܥܝܘܬܐ ܝܠܗ ܕܡܬܢܚ ܒܠܚܘܕ ܦܘܫܪܐ ܡܬܩܢܐ"؛ ܘܫܪ̈ܟܐ – "ܬܘܢܝܐ ܕܡܚܘ̈ܝܢܐ ܕܦܐܝܘܬܐ ܟܠܢ̈ܝܐ ܒܠܚܘܕ ܠܐ ܣܦܩ". ܡܢ ܦܐܬܐ: ܠܘܚܐ 1 (ܬܪܘܝܗܝ ܕܪ̈ܓܐ)، ܠܘܚܐ 2 ܘܠܘܚܐ 3، ܫܪ̈ܟܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܩܨܝܪܘܬܐ ("ܐܦ ܚܕ ܫܪܟܐ ܠܐ ܥܒܪ ܥܠ .10 ܒܛܝܡܐ ܫܪܝܪܐ ܕܝܠܗ")، ܘܨܘܪܬܐ ܥܡ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ (APA, 2020, Figure 7.8). APA (2020، ܦܣܩܐ 6.44) – ܕܬܚܡܚ SEM، CFI، RMSEA ܓܘ ܚܙܝܬܐ ܩܕܡܝܬܐ؛ ܦܣܩܐ 6.36 – ܕܠܐ ܨܦܪܐ ܩܕܡ ܢܘܩܙܐ ܩܐ β، R²، p، CFI ܘ-RMSEA، ܘܥܡ ܨܦܪܐ ܩܐ b.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܕܫܘܪܚ ܥܠ ܕܪܓܐ 1. ܡܘܕܝܠ ܒܢܝܢܝܐ ܥܡ ܡܘܕܝܠ ܕܡܫܘܚܬܐ ܕܠܐ ܝܠܗ ܦܐܝܐ – ܠܐ ܡܨܝܚ ܕܝܕܥܚ ܐܝܟܐ ܝܠܗ ܥܘܩܬܐ. ܟܒܚܪܚ ܡܢ ܩܕܡ CFA.

"ܡܘܕܝܠ ܦܐܝܐ ܝܠܗ، ܘܡܛܠ ܗܕܐ ܐܘܪܚܐ ܬܪܝܨܐ ܝܠܗ". ܐܡܢ ܕܡܢܬܐ ܒܢܝܢܝܬܐ just-identified ܝܠܗ، ܦܐܝܘܬܐ ܐܝܟ ܗܝ ܕ-CFA ܝܠܗ – ܠܐ ܟܐܡܪܐ ܡܕܡ ܥܠ ܐܘܪܚܐ ܕܓܐܪ̈ܐ؛ ܘܐܦ ܓܘ ܡܘܕܝܠ ܡܩܢܢܐ، ܡܘܕܝ̈ܠܐ ܫܘ̈ܝܐ ܥܡ ܓܐܪ̈ܐ ܗܦܝ̈ܟܐ ܦܐܝ̈ܐ ܝܢܐ ܒܗܘ ܟܡܐ ܓܘܦܗ.

ܕܩܪܝܚ p ܕܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܐܝܟ ܡܕܡ ܦܣܩܢܐ. ܦܘܠܓܐ ܕ-product ܠܐ ܝܠܗ ܢܘܪܡܠܝܐ؛ ܟܡܬܢܚ ܬܚܘܡܐ ܕܬܘܟܠܢܐ، ܘܛܒ ܒܝܫ bootstrap.

ܕܡܬܢܚ β ܒܠܚܘܕ. ܟܡܬܢܚ ܐܦ b ܥܡ ܛܥܝܘܬܐ ܬܩܝܢܬܐ (Kline, 2023, p. 422).

ܕܣܦܩܚ ܥܡ ܡܚܘ̈ܝܢܐ ܟܠܢ̈ܝܐ. CFI ܘ-RMSEA ܛܒ̈ܐ ܡܨܝ ܕܡܛܫܝ ܙܘܓܐ ܕܦܣܘ̈ܩܐ ܕܡܘܕܝܠ ܠܐ ܟܡܦܫܩ – ܠܘܚܐ 6.

ܕܡܘܣܦܚ ܘܫܩܠܚ ܫܒ̈ܝܠܐ ܥܕܡܐ ܕܦܐܐ. ܟܠ ܫܘܢܝܐ – ܥܡ ܥܠܬܐ ܬܐܘܪܝܬܐ، ܡܬܢܝܐ، ܘܓܘ ܕܘܡܝܐ ܚܕܬܐ ܩܕܡ ܕܦܣܩܚ.

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.

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

Kline, R. B. (2023). Principles and practice of structural equation modeling (5th ed.). Guilford Press.

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

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

Anderson ܘ-Gerbing (1988)، Bollen (1989)، Jackson (2003) ܘ-McDonald ܘ-Ho (2002) – ܐܝܟ ܕܡܬܚܙܝܢ ܓܒ Kline (2023)؛ Bollen (1989) ܘ-Sobel (1982) – ܐܝܟ ܕܡܬܚܙܝܢ ܓܒ Rosseel (2012). ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ (site rule)، ܓܘ ܪܫܝܡܬܐ ܕܡܒܘ̈ܥܐ (reference list) ܟܡܬܚܙܝܢ ܒܠܚܘܕ ܡܒܘ̈ܥܐ ܕܡܬܩܪܝܢ ܓܘ ܢܘܣܚܐ ܫܪܫܝܐ. ܥܝ̈ܕܐ ܕܣܐܝܛ (site conventions): ܛܠܠܐ ܕܫܪ̈ܟܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܠܥܠ ܡܢ .10 (ܠܦܘܬ ܡܬܠ̈ܐ ܕ-Kline)، ܙܘܗܪܐ ܠܬܚܬ ܡܢ 200 ܡܫܬܘܬܦ̈ܢܐ ܘܡܢ ܦܘܚܡܐ 10:1، ܘܫܒ̈ܝܠܐ ܕܓܘܒܝܐ ܡܩܕܡܐ ܓܘ ܦܐܝܠ ܕܡܬܠܐ. ܚܘܫܒܢܐ ܓܘ ܦܐܬܐ ܡܫܪܪܐ ܝܠܗ ܩܘܒܠ ܚܙܡܐ lavaan 0.6-17 ܓܘ R ܘܩܘܒܠ ܡܦܩܢܐ ܛܒܝܥܐ ܕ-Rosseel (2012).