ܦܘܚܡܐ ܕܓܘ̈ܕܐ ܘܠܐ ܡܫܬܚܠܦܢܘܬܐ ܕܡܫܘܚܬܐ

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)؟

ܟܠ ܙܒܢܐ ܕܦܚܡܚ ܓܘ̈ܕܐ ܥܠ ܪܥܝܢܐ ܕܡܫܘܚܐ ܝܠܗ ܓܘ ܦܢܩܝܬܐ ܕܫܘܐ̈ܠܐ (questionnaire) – ܓܒܪ̈ܐ ܘܢܫ̈ܐ، ܬܪ̈ܒܝܬܐ، ܠܫܢ̈ܐ ܕܦܢܩܝܬܐ، ܐܘܪ̈ܚܬܐ ܕܡܫܕܪܬܐ، ܢܣܝܘܢܐ ܘܦܘܚܡܐ. Kline (2023، ܦܐܬܐ 393) ܟܬܚܡ: ܠܐ ܡܫܬܚܠܦܢܘܬܐ ܕܡܫܘܚܬܐ (measurement invariance) ܝܠܗ ܥܠ ܫܘܐܠܐ "ܐܢ ܠܡܢܝ̈ܢܐ ܕܡܚܘ̈ܝܢܐ ܕܡܫܬܚܠܦ̈ܢܐ ܬܐܘܪ̈ܝܐ ܐܝܬ ܗܘ ܣܘܟܠܐ ܝܢ ܦܘܫܩܐ ܓܘܦܗ" ܓܘ ܫܪ̈ܛܐ ܦܪ̈ܝܫܐ؛ ܕܠܐ ܗܝ "ܦܘܪ̈ܫܢܐ ܫܪ̈ܝܪܐ ܒܝܢܝ ܐ̱ܢܫ̈ܐ ܠܐ ܡܨܝ ܕܡܬܦܪܫܝ ܒܓܠܝܘܬܐ ܡܢ ܦܘܪ̈ܫܢܐ ܕܢܒܥܝ ܡܢ ܫܪ̈ܛܐ ܕܓܘܝܗܝ ܦܝܫܝܠܗܘܢ ܡܢܝ̈ܢܐ". Putnick ܘ-Bornstein (2016، ܦܐܬܐ 2) ܟܡܚܘܝ ܒܟܪܝܘܬ ܠܒܐ: ܐܢ ܒܟܝܐ ܘܣܠܩܐ ܒܡܬܩܠܐ ܟܣܗܕܝ ܥܠ ܪܡܐ ܕܟܪܝܘܬ ܠܒܐ ܓܒ ܢܫ̈ܐ ܒܣ ܠܐ ܓܒ ܓܒܪ̈ܐ، ܡܢܝܢܐ ܕܣܒܠܬܐ (scale score) ܕܟܡܚܒܫ ܠܗܘܢ ܒܕ ܡܚܘܝܐ ܕܓܒܪ̈ܐ "ܒܨܝܪ ܟܪܝܐ ܠܒܗܘܢ" ܝܢܐ – ܡܛܠ ܕܒܨܝܪ ܟܒܟܝ – ܐܦܢ ܐܢܝ̈ ܦܣܘ̈ܩܐ ܡܢ ܪܝܫܐ ܠܐ ܝܢܐ ܐܣܝܪ̈ܐ ܓܒܝܗܝ ܥܡ ܟܪܝܘܬ ܠܒܐ. ܘܒܐܘܪܚܐ ܗܦܝܟܬܐ، Kline (ܗܘ ܕܘܟܬܐ) ܟܡܥܗܕ ܕܠܐ ܡܫܬܚܠܦܢܘܬܐ ܠܐ ܟܐܡܪܐ ܕܓܘ̈ܕܐ ܫܘ̈ܝܐ ܝܢܐ ܒܪܡܐ ܕܪܥܝܢܐ: ܓܘ̈ܕܐ ܡܨܝ ܕܗܘܝ ܫܪܝܪܐܝܬ ܦܪ̈ܝܫܐ – ܘܠܐ ܡܫܬܚܠܦܢܘܬܐ ܝܠܗ ܡܐ ܕܟܡܨܝܐ ܠܫܘܥܪܐ ܕܐܗܐ ܦܘܪܫܢܐ ܕܠܐ ܚܘܠܛܐ ܕܡܫܘܚܬܐ.

Brown (2015، ܦܐܬܐ 241) ܟܦܠܓ ܫܘܐ̈ܠܐ ܠܬܪܝܢ: ܠܐ ܡܫܬܚܠܦܢܘܬܐ ܕܡܫܘܚܬܐ – ܛܥ̈ܢܐ، ܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܘܫܘܚܠ̈ܦܐ ܕܫܪ̈ܟܐ، ܝܥܢܝ ܕܟܝ ܦܣܘ̈ܩܐ ܟܡܫܚܝ؛ ܘܦܘܪܫܢܐ ܕܟܢܫܐ ܟܠܢܝܐ (population heterogeneity) – ܫܘܚܠ̈ܦܐ، ܫܘܚܠ̈ܦܐ ܡܫܘܬܦ̈ܐ ܘܡܨܥܝ̈ܬܐ ܕܥܠ̈ܠܬܐ ܓܘܦܝܗܝ، ܝܥܢܝ ܒܡܘܕܝ ܓܘ̈ܕܐ ܦܪ̈ܝܫܐ ܝܢܐ. ܦܐܬܐ ܟܡܦܢܐ ܥܠ ܬܪܘܝܗܝ، ܒܐܗܐ ܛܟܣܐ. ܓܘ ܦܐܝܠ ܕܡܬܠܐ: ܐܢ ܬܠܬܐ ܣܒ̈ܠܬܐ (ܕܝܠܢܝܘܬܐ، ܬܘܟܠܢܐ، ܫܘܬܦܘܬܐ) ܟܡܫܚܝ ܗܘ ܡܕܡ ܓܘܦܗ ܓܘ ܫܒܒܘܬܐ ܥܬܝܩܬܐ ܘܓܘ ܫܒܒܘܬܐ ܚܕܬܐ – ܘܐܢ ܐܝܢ، ܒܡܘܕܝ ܫܒܒܘ̈ܬܐ ܦܪ̈ܝܫܐ ܝܢܐ. ܦܐܬ̈ܐ ܩܪ̈ܝܒܐ: ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܡܫܪܪܢܐ (ܡܘܕܝܠ ܓܘ ܚܕܐ ܓܘܕܐ)، ܡܘܕܝܠ ܕܫܘܝ̈ܘܬܐ ܒܢܝܢܝ̈ܬܐ، ܒܘܚܪܢܐ t ܠܕܘ̈ܡܝܐ ܠܐ ܬܠܝ̈ܐ (ܦܘܚܡܐ ܕܡܢܝ̈ܢܐ ܕܣܒ̈ܠܬܐ ܚܙ̈ܝܐ – ܕܟܡܣܒܐ، ܕܠܐ ܒܘܚܪܢܐ، ܡܐ ܕܐܗܐ ܦܐܬܐ ܟܒܚܪܐ).

ܡܠܝܘܬܐ: ܗܘ ܡܘܕܝܠ ܓܘܦܗ، ܘܡܢܘ̈ܬܐ ܡܢܗ ܫܘ̈ܝܐ

ܡܘܕܝܠ. ܓܘ ܟܠ ܓܘܕܐ g، ܟܠ ܦܣܘܩܐ ܡܢܝܢܐ ܩܝܡܐ ܝܠܗ ܘܬܘܒ ܛܥܢܐ ܙܒܢ ܥܠܬܐ ܘܬܘܒ ܫܪܟܐ: x = ν_g + Λ_gξ + δ. ܡܢ ܐܟܐ ܬܪܝܢ ܡܐܛܪ̈ܝܟܣܐ ܕܟܢܦܩܝ ܡܢ ܡܘܕܝܠ – ܫܘܚܠ̈ܦܐ ܡܫܘܬܦ̈ܐ Σ_g = Λ_gΦ_gΛ_g′ + Θ_g ܘܡܨܥܝ̈ܬܐ μ_g = ν_g + Λ_gκ_g (Vandenberg ܘ-Lance, 2000، ܦܐܬܐ 42؛ Kline, 2023، ܦܐܬܐ 394، ܟܩܪܐ ܠܗ ܡܘܕܝܠ MACS – mean and covariance structure). ܡܘܕܝ̈ܠܐ ܕܠܐ ܡܫܬܚܠܦܢܘܬܐ ܦܪ̈ܝܫܐ ܝܢܐ ܒܠܚܘܕ ܒܐܝܢܝ ܦܪ̈ܡܝܛܪܐ ܐܣܝܪ̈ܐ ܝܢܐ ܕܗܘܝ ܫܘ̈ܝܐ ܒܝܢܝ ܓܘ̈ܕܐ:

ܫܡܗ̈ܐ "ܟܪܝܗܬܐ" ܘ"ܚܝܠܢܬܐ" ܠܐ ܝܢܐ ܐܝܟ ܚܕ̈ܕܐ: Kline (2023، ܦܐܬܐ 396-397)، Brown (2015، ܦܐܬܐ 243) ܘ-Putnick ܘ-Bornstein (2016، ܦܐܬܐ 3-4، ܠܦܘܬ Widaman ܘ-Reise, 1997، ܐܝܟ ܕܡܬܚܙܝܢ ܓܒܝܗܝ) ܟܩܪܝ ܠܛܥ̈ܢܐ ܫܘ̈ܝܐ "weak" ܘܠܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܫܘ̈ܝܐ "strong"؛ Vandenberg ܘ-Lance (2000، ܦܐܬܐ 12، ܠܦܘܬ Horn ܘ-McArdle, 1992، ܐܝܟ ܕܡܬܚܙܝܢ ܓܒܝܗܝ) ܟܩܪܝ ܠܐܣܟܝܡܐ "weak factorial invariance" ܘܠܛܥ̈ܢܐ ܫܘ̈ܝܐ "strong". ܡܛܠ ܗܕܐ Brown (ܗܘ ܕܘܟܬܐ) ܟܓܒܐ ܫܡܗ̈ܐ ܡܚܘܝܢ̈ܐ ("equal form, equal factor loadings, equal intercepts")، ܘܗܕܟܐ ܐܦ ܦܐܬܐ.

ܡܘܕܝ ܟܐܡܪ ܟܠ ܕܪܓܐ. ܛܥܢܐ ܫܘܝܐ – ܣܠܩܐ ܕܚܕܐ ܚܕܝܘܬܐ ܓܘ ܥܠܬܐ ܟܡܪܡܐ ܦܣܘܩܐ ܒܗܘ ܟܡܐ ܓܘܦܗ ܓܘ ܟܠ ܓܘ̈ܕܐ؛ Kline (2023، ܦܐܬܐ 396) ܟܡܥܗܕ ܕܡܫܕܝܢܘܬܐ ܡܨܝܐ ܕܢܒܥܐ ܡܢ ܕܪܥܝܢܐ ܓܘܦܗ ܫܢܝܐ ܝܠܗ ܒܝܢܝ ܬܪ̈ܒܝܬܐ، ܝܢ ܡܢ ܐܣܟܝ̈ܡܐ ܕܦܘܢܝܐ (ܓܘܒܝܐ ܕܣܦܪ̈ܐ ܝܢ ܕܡܨܥܬܐ ܕܣܒܠܬܐ). ܡܢܝܢܐ ܩܝܡܐ ܫܘܝܐ – ܡܫܬܘܬܦ̈ܢܐ ܡܢ ܓܘ̈ܕܐ ܦܪ̈ܝܫܐ ܥܡ ܗܘ ܪܡܐ ܓܘܦܗ ܓܘ ܥܠܬܐ ܡܣܟ̈ܝܐ ܝܢܐ ܕܫܩܠܝ ܗܘ ܡܢܝܢܐ ܓܘܦܗ ܓܘ ܦܣܘܩܐ؛ ܡܢܝܢܐ ܩܝܡܐ ܫܢܝܐ ܝܠܗ ܡܣܒ ܒܐܦ̈ܐ (bias) ܩܝܡܐ ܓܘ ܦܣܘܩܐ، "differential item functioning" (Brown, 2015, p. 261, Figure 7.4)، ܡܬܠܐ ܨܒܝܢܐ ܕܡܩܒܠܚ ܥܡ ܟܠ ܦܣܘܩܐ (Kline, p. 397). Vandenberg ܘ-Lance (2000، ܦܐܬܐ 38) ܟܡܘܣܦܝ ܕܦܘܪܫܢܐ ܓܘ ܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܠܐ ܝܠܗ ܟܠ ܙܒܢܐ ܡܣܒ ܒܐܦ̈ܐ – ܒܙܒ̈ܢܐ ܦܘܪܫܢܐ ܡܣܟܝܐ ܝܠܗ ܒܝܢܝ ܓܘ̈ܕܐ؛ ܐܗܐ ܫܘܐܠܐ ܬܐܘܪܝܐ ܝܠܗ.

ܫܘܥܪܐ ܘܫܘܪܪܐ. ܡܬܚܙܝܢܘܬܐ ܥܠܝܬܐ (ML) ܥܡ ܒܢܝܢܐ ܕܡܨܥܝ̈ܬܐ، ܐܝܟ cfa(…, group =, group.equal =) ܓܘ lavaan: χ² = Σ N_gF_g، Fisher scoring ܥܡ ܝܕܥܬܐ ܡܣܟܝܬܐ ܥܕܡܐ ܕܡܢܝܢܐ ܕܫܘܢܝܐ (derivative) ܩܪܝܒܐܝܬ ܨܦܪܐ ܝܠܗ، ܘܐܣܘܪ̈ܐ ܕܫܘܝܘܬܐ ܐܝܟ ܦܪܡܝܛܪ ܡܫܘܬܦܐ. ܦܐܬܐ ܟܥܒܕ ܬܘܒ ܥܕܡܐ ܠܡܢܝܢܐ ܛܒܝܥܐ ܡܬܠܐ ܕ-Kline (2023، ܨܚܚܐ 22) – ܝܗܝ̈ܒܬܐ ܕ-divergent thinking ܕ-Guo ܘܐܚܪ̈ܢܐ (2021، ܐܝܟ ܕܡܬܚܙܝܢ ܓܒ Kline) ܓܘ ܨܝܢ ܘܓܘ ܐܡܪܝܟܐ: ܠܘܚܐ 22.3 (ܟܠ ܡܘܕܝ̈ܠܐ، ܦܘܪ̈ܫܢܐ ܘܡܚܘ̈ܝܢܐ ܕܦܐܝܘܬܐ)، ܠܘܚܐ 22.4 (ܛܥ̈ܢܐ، ܫܘܚܠ̈ܦܐ ܕܫܪ̈ܟܐ ܘܥܠ̈ܠܬܐ ܒܪܡܙܢܘܬܐ ܕܡܥܒܕܢܘܬܐ)، ܠܘܚܐ 22.5 (ܡܨܥܝ̈ܬܐ ܕܟܢܦܩܝ ܡܢ ܡܘܕܝܠ) ܘܠܘܚܐ 22.6 (ܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܘܡܨܥܝ̈ܬܐ ܕܥܠ̈ܠܬܐ)؛ ܠܘܚܐ 7.11 ܕ-Brown (2015) – ܐܫܬܐ ܦܘܚ̈ܡܐ ܓܘ ܕܘܡܝܐ ܕ-375 ܓܒܪ̈ܐ ܘ-375 ܢܫ̈ܐ ܥܡ ܫܓܘܫܝ̈ܐ ܕܪܓܫܐ – ܒܩܘܪܒܐ ܕܡܢܬ̈ܐ ܡܢ ܥܣܪܐ ܓܘ χ² (ܟܬܒܐ ܟܛܒܥ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܬܠܬܐ ܡܢܝ̈ܢܐ) ܘܐܝܟ ܚܕ̈ܕܐ ܓܘ RMSEA، CFI ܘ-TLI؛ ܘܦܣܩܐ 6 ܕ-Rosseel (2012): χ²، AIC، BIC ܘ-Δχ²(12) = 48.251. ܩܘܒܠ lavaan 0.6-17 – 37 ܡܘܕܝ̈ܠܐ (ܥܡ ܐܪܒܥܐ ܓܘ̈ܕܐ، ܬܠܬܐ ܐܘܪ̈ܚܬܐ ܩܐ ܦܣܩܬܐ ܕܣܒܠܬܐ، ܫܪ̈ܝܐ ܘܒܘܚܪ̈ܢܐ ܕ-score)، ܐܠܦ̈ܐ ܕܒܘܚܪ̈ܢܐ. ܥܒܕܐ ܡܢ ܪܝܫ ܓܠܐ ܟܡܐ ܛܥܝ̈ܘܬܐ ܕܛܒܥܐ ܓܘ ܟܬܒ̈ܐ: ܓܘ ܠܘܚܐ 22.2 ܕ-Kline ܡܨܥܝܬܐ ܕ-LM3 ܓܘ ܨܝܢ ܛܒܝܥܐ ܝܠܗ 1.88، ܒܣ ܠܘ̈ܚܐ 22.3 ܘ-22.5 ܟܡܬܥܒܕܝ ܬܘܒ ܒܠܚܘܕ ܥܡ 1.86؛ ܘܓܘ ܚܘܫܒܢܐ ܕܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (ܦܐܬܐ 406-408) ܡܨܥܝܬܐ ܕܐܡܪܝܟܝ̈ܐ ܟܡܬܚܙܝܐ ܐܝܟ 1.106 ܒܕܘܟܬܐ ܕ-1.016 ܕܓܘ ܠܘܚܐ 22.6 – ܗܕܟܐ ܕ-d ܒܩܘܪܒܐ .40 ܝܠܗ ܘܠܐ .33. ܓܘ Brown، RMSEA ܕܫܘܝܘܬܐ ܕܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܓܘ ܠܘܚܐ 7.11 (.046) ܠܐ ܦܐܝܐ ܝܠܗ ܥܡ χ² ܕܓܘ ܗܘ ܣܕܪܐ ܓܘܦܗ (.043).

ܛܟܣܐ ܕܒܘܚܪ̈ܢܐ ܘܦܣܩ̈ܬܐ

ܡܢ ܬܚܬ ܠܥܠ. Brown (2015، ܦܐܬܐ 243-244) ܟܡܠܟ ܕܫܪܚ ܡܢ ܡܘܕܝܠ ܕܒܨܝܪ ܐܣܝܪܐ ܝܠܗ ܘܕܡܘܣܦܚ ܐܣܘܪ̈ܐ (constraints): (1) ܡܘܕܝܠ ܓܘ ܟܠ ܓܘܕܐ ܒܠܚܘܕܗ؛ (2) ܐܣܟܝܡܐ؛ (3) ܛܥ̈ܢܐ؛ (4) ܡܢܝ̈ܢܐ ܩܝ̈ܡܐ؛ (5) ܫܘܚܠ̈ܦܐ ܕܫܪ̈ܟܐ (ܒܨܒܝܢܐ)؛ ܘܐܢ ܐܝܬ ܨܒܝܢܐ ܬܐܘܪܝܐ – (6) ܫܘܚܠ̈ܦܐ ܕܥܠ̈ܠܬܐ، (7) ܫܘܚܠ̈ܦܐ ܡܫܘܬܦ̈ܐ ܘ-(8) ܡܨܥܝ̈ܬܐ. ܥܠܬܐ: ܐܡܢ ܕܡܘܕܝܠ ܥܡ ܟܠ ܐܣܘܪ̈ܐ ܠܐ ܝܠܗ ܦܐܝܐ ܥܣܩܐ ܝܠܗ ܠܝܕܥܐ ܡܘܕܝ ܝܠܗ ܥܘܩܬܐ، ܘ"ܒܘܚܪ̈ܢܐ ܕܓܒ̈ܐ ܡܢ ܠܐ ܡܫܬܚܠܦܢܘܬܐ ܟܡܣܬܡܟܝ ܥܠ ܣܒܪܐ ܕܓܒ̈ܐ ܐܚܪ̈ܢܐ ܩܝ̈ܡܐ ܝܢܐ". Kline (2023، ܦܐܬܐ 398) ܟܩܪܐ ܠܗ ܐܘܪܚܐ ܕ"ܫܬܐܣܐ ܚܐܪܐ" (free baseline)، ܩܘܒܠ ܐܘܪܚܐ ܗܦܝܟܬܐ ܕܟܫܪܐ ܐܣܘܪ̈ܐ ܡܢ ܡܘܕܝܠ ܓܡܝܪܐ. Vandenberg ܘ-Lance (2000، ܦܐܬܐ 12) ܟܡܘܣܦܝ ܩܕܡ ܟܠ ܡܕܡ ܒܘܚܪܢܐ ܟܠܢܝܐ ܩܐ ܫܘܝܘܬܐ ܕܡܐܛܪ̈ܝܟܣܐ ܕܫܘܚܠ̈ܦܐ ܡܫܘܬܦ̈ܐ؛ ܦܐܬܐ ܠܐ ܟܚܫܒܐ ܠܗ، ܡܛܠ ܕܡܫܕܝܢܘܬܐ ܕܝܠܗ "ܠܐ ܟܝܗܒܐ ܝܕܥܬܐ ܥܠ ܡܒܘܥܐ ܝܚܝܕܝܐ" ܕܠܐ ܫܘܝܘܬܐ (ܗܘ ܕܘܟܬܐ، ܦܐܬܐ 36؛ ܚܙܝܡܘܢ ܐܦ Kline، ܦܐܬܐ 395، ܘ-Brown، ܦܐܬܐ 244).

ܐܝܡܢ ܕܪܓܐ "ܢܛܝܪܐ" ܝܠܗ؟ ܐܟܐ ܠܝܬ ܫܠܡܘܬܐ، ܘܡܛܠ ܗܕܐ ܦܐܬܐ ܟܡܚܘܝܐ ܟܠ ܡܚܘ̈ܝܢܐ ܚܕ ܓܒ ܐܚܪܢܐ. ܒܘܚܪܢܐ ܩܠܣܝܩܝܐ – Δχ² ܒܝܢܝ ܬܪܝܢ ܡܘܕܝ̈ܠܐ ܡܩܢ̈ܢܐ؛ Vandenberg ܘ-Lance (2000، ܦܐܬܐ 46) ܡܠܟܠܗܘܢ ܕܦܝܫܚ ܥܡܗ ܐܝܟ ܐܘܪܚܐ ܪܫܝܬܐ. ܚܣܝܪܘܬܐ: ܥܡ ܕܘܡܝܐ ܪܒܐ ܟܦܪܫ ܐܦ ܦܘܪ̈ܫܢܐ ܙܥܘܪ̈ܐ ܛܒ (Putnick & Bornstein, 2016, pp. 9-10). ܡܢ ܐܟܐ ܫܢܝܬܐ ܠܫܘܢܝ̈ܐ ܓܘ ܡܚܘ̈ܝܢܐ: ΔCFI ≤ −.01 ܕ-Cheung ܘ-Rensvold (2002) – ܕܡܬܦܠܚ ܣܓܝ ܡܢ ܟܠ؛ Chen (2007) ܡܘܣܦܠܗ ΔRMSEA ≥ .015 ܘ-ΔSRMR ≥ .030 (ܡܝܛܪܝܬܐ) ܝܢ .015 (ܣܩܐܠܪܝܬܐ ܘܫܪܟܐ)؛ Meade ܘܐܚܪ̈ܢܐ (2008) ܡܩܪܒܠܗܘܢ ܬܚܘܡܐ ܚܪܝܦܐ ܕ-−.002 ܓܘ CFI؛ ܘ-Rutkowski ܘ-Svetina (2014) – ܬܚܘ̈ܡܐ ܪܟܝ̈ܟܐ ܒܝܫ ܩܐ ܛܥ̈ܢܐ ܐܡܢ ܕܦܚܡܚ 10-20 ܓܘ̈ܕܐ (ܟܠܗܘܢ ܐܝܟ ܕܡܬܚܙܝܢ ܓܒ Putnick ܘ-Bornstein, 2016، ܦܐܬܐ 9، ܘܓܒ Kline, 2023، ܦܐܬܐ 399). ܦܐܬܐ ܟܪܫܡ ܟܠܗܘܢ، ܘܓܘ ܥܡܘܕܐ ܕ"ܦܣܩܬܐ" ܟܡܚܝܕ Δχ² ܘ-ΔCFI – ܘܐܡܢ ܕܠܐ ܫܠܡܝ ܟܟܬܒ "ܚܠܝܛܐ". Kline (ܦܐܬܐ 399) ܡܦܠܓ ܪܥܝܢܐ ܝܠܗ: "ܐܝܬ ܣܒܪܐ ܙܥܘܪܐ" ܕܡܫܟܚܚ ܢܡܘ̈ܣܐ ܕܦܣܩܬܐ ܠܦܘܬ ܫܘܢܝ̈ܐ ܓܘ ܡܚܘ̈ܝܢܐ "ܕܦܠܚܝ ܒܟܠ ܕܘܟ̈ܝܬܐ"، ܘ"ܥܒܕܐ ܒܝܫܐ" ܝܠܗ ܕܒܛܠܚ ܫܪ̈ܟܐ ܘ-χ². ܓܘ ܡܬܠܐ ܕܝܠܗ (ܦܐܬܐ 404-405) Δχ² ܕܛܥ̈ܢܐ ܪܫܝܡܐ ܝܠܗ ܒܣ ΔCFI = .009، ܘܗܘ ܟܢܛܪ ܡܘܕܝܠ ܒܬܪ ܕܒܚܪܠܗ ܫܪ̈ܟܐ ܓܘ ܟܠ ܓܘܕܐ.

ܓܘ ܦܐܝܠ ܕܡܬܠܐ (ܕܠܐ ܫܪ̈ܝܐ): ܐܣܟܝܡܐ ܦܐܝܐ ܝܠܗ – χ²(102) = 118.87, p = .121، CFI .992، RMSEA .023؛ ܛܥ̈ܢܐ ܫܘ̈ܝܐ ܝܢܐ – Δχ²(9) = 2.87, p = .969؛ ܒܣ ܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܠܐ – Δχ²(9) = 71.57, p < .001، ΔCFI = −.029.

ܦܣܩܬܐ ܕܣܒܠܬܐ

ܠܥܠܬܐ ܠܝܬ ܚܕ̈ܝܘܬܐ ܕܝܠܗ، ܘܓܘ ܒܢܝܢܐ ܕܡܨܥܝ̈ܬܐ ܣܢܝܩܘܬܐ ܐܝܬ ܕܦܣܩܚ ܩܐܠܗ ܐܦ ܫܘܪܝܐ (Brown, 2015, p. 256; Kline, 2023, pp. 399-401). ܬܠܬܐ ܐܘܪ̈ܚܬܐ، ܥܡ ܗܝ ܦܐܝܘܬܐ ܓܘܦܗ ܒܚܬܝܬܘܬܐ ("ܠܐ ܟܡܫܢܐ ܡܕܡ ܓܘ ܦܐܝܘܬܐ ܟܠܢܝܬܐ"، Kline، ܦܐܬܐ 400) ܘܗܘ ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ d ܓܘܦܗ (ܦܐܬܐ 401):

marker (ܓܘܒܝܐ ܡܩܕܡܐ ܕ-lavaan): ܛܥܢܐ ܕܦܣܘܩܐ ܩܕܡܝܐ = 1 ܓܘ ܟܠ ܓܘ̈ܕܐ، ܘܡܨܥܝܬܐ ܕܥܠܬܐ = 0 ܓܘ ܓܘܕܐ ܕ-reference؛ ܓܘ ܦܘܫܐ ܕܓܘ̈ܕܐ ܡܨܥܝܬܐ ܟܡܫܬܥܪܐ ܡܢ ܪܦܦܐ ܕܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܫܘ̈ܝܐ ܝܢܐ – ܘܗܝ ܦܘܪܫܢܐ ܝܠܗ ܡܢ ܓܘܕܐ ܕ-reference (Brown، ܦܐܬܐ 256-257، ܐܘܪܚܐ ܕ-Mplus). ܓܘܕܐ ܕ-reference (std.lv): ܓܘ ܓܘܕܐ ܩܕܡܝܬܐ ܫܘܚܠܦܐ ܕܥܠܬܐ 1 ܘܡܨܥܝܬܐ ܕܝܠܗ 0، ܘܓܘ ܦܘܫܐ ܟܡܫܬܥܪܝ ܐܡܢ ܕܛܥ̈ܢܐ ܘܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܫܘ̈ܝܐ ܝܢܐ (Kline, p. 400) – ܦܘܪ̈ܫܢܐ ܟܦܝܫܝ ܒܚܕ̈ܝܘܬܐ ܕܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܓܘܕܐ ܕ-reference. ܪܡܙܢܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect coding) (Little ܘܐܚܪ̈ܢܐ, 2006، ܐܝܟ ܕܡܬܚܙܝܢ ܓܒ Kline، ܦܐܬܐ 400): ܡܨܥܝܬܐ ܕܛܥ̈ܢܐ ܕܟܠ ܥܠܬܐ = 1 ܘܓܘܡܪܐ ܕܡܢܝ̈ܢܐ ܩܝ̈ܡܐ = 0، ܗܕܟܐ ܕܥܠܬܐ ܐܝܬܝܐ ܓܘ ܣܒܠܬܐ ܕܦܣܘ̈ܩܐ – ܦܐܝܐ ܝܠܗ ܐܡܢ ܕܟܠ ܦܣܘ̈ܩܐ ܓܘ ܗܝ ܣܒܠܬܐ ܓܘܦܗ ܝܢܐ، ܐܝܟ Likert 1-7.

ܥܘܩܬܐ ܕܦܣܘܩܐ ܕ-reference. ܓܘ ܐܘܪܚܐ ܕ-marker ܛܥܢܐ ܕܦܣܘܩܐ ܩܕܡܝܐ ܩܝܡܐ ܘܫܘܝܐ ܝܠܗ ܓܘ ܟܠ ܓܘ̈ܕܐ، ܘܡܛܠ ܗܕܐ "ܣܢܝܩܘܬܐ ܐܝܬ ܕܡܣܒܚ" ܕܠܐ ܡܫܬܚܠܦܢܐ ܝܠܗ – ܠܐ ܡܨܝܚ ܕܒܚܪܚ ܠܗ (Kline, 2023, p. 400). ܐܢ ܗܘ ܓܘܦܗ ܝܠܗ ܦܣܘܩܐ ܕܐܝܬ ܓܘܗ ܥܘܩܬܐ، "ܟܠ ܦܘܫܐ ܕܦܣܘ̈ܩܐ ܓܘ ܥܠܬܐ ܡܨܝ ܕܡܬܚܙܝ ܡܫܬܚܠܦ̈ܢܐ" (Putnick & Bornstein, 2016, p. 7; Vandenberg & Lance, 2000, p. 46). ܦܘܫܪܐ ܓܘ ܦܐܬܐ: ܕܓܒܚ ܪܡܙܢܘܬܐ ܕܡܥܒܕܢܘܬܐ (ܗܝܓܝ ܡܨܝܚ ܕܫܪܚ ܟܠ ܛܥܢܐ)، ܝܢ ܕܡܫܢܚ ܦܣܘܩܐ ܐܚܪܢܐ ܠܪܫܐ ܕܥܠܬܐ. Putnick ܘ-Bornstein (ܗܘ ܕܘܟܬܐ) ܟܡܙܗܪܝ ܐܦ ܡܢ ܦܣܩܬܐ ܕܫܘܚܠܦܐ 1 ܘܡܨܥܝܬܐ 0 ܓܘ ܟܠ ܓܘ̈ܕܐ – ܗܝܓܝ ܒܘܚܪ̈ܢܐ ܕܛܥ̈ܢܐ ܘܕܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܛܥ̈ܝܐ ܝܢܐ ܐܢ ܓܘ̈ܕܐ ܫܪܝܪܐܝܬ ܦܪ̈ܝܫܐ ܝܢܐ ܒܫܘܚܠܦܐ ܘܒܡܨܥܝܬܐ؛ ܦܐܬܐ، ܐܝܟ lavaan، ܟܦܣܩܐ ܠܗܘܢ ܒܠܚܘܕ ܓܘ ܓܘܕܐ ܕ-reference.

ܠܐ ܡܫܬܚܠܦܢܘܬܐ ܡܢܬܢܝܬܐ

ܐܡܢ ܕܛܥ̈ܢܐ ܝܢ ܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܠܐ ܝܢܐ ܟܠܗܘܢ ܫܘ̈ܝܐ، ܡܨܝܚ ܕܫܪܚ ܐܣܘܪܐ (constraint) ܩܐ ܚܕ ܝܢ ܟܡܐ ܦܣܘ̈ܩܐ ܘܕܡܬܚܚ ܥܡ ܦܘܫܐ – ܠܐ ܡܫܬܚܠܦܢܘܬܐ ܡܢܬܢܝܬܐ (partial invariance) (Byrne ܘܐܚܪ̈ܢܐ, 1989، ܐܝܟ ܕܡܬܚܙܝܢ ܓܒ Kline, 2023، ܦܐܬܐ 401). ܐܗܐ ܣܓܝ ܡܬܚܙܐ: ܓܘ ܣܩܘܪܐ ܕ-Putnick ܘ-Bornstein (2016، ܦܐܬܐ 12) – 32% ܡܢ ܒܘܚܪ̈ܢܐ. ܕܟܝ ܟܡܫܟܚܚ ܡܘܕܝ ܕܫܪܚ: ܒܐܘܪܚܐ "ܠܒܣܬܪ" ܟܫܪܚ ܐܣܘܪܐ ܥܡ ܡܚܘܝܢܐ ܕܫܘܢܝܐ (ܒܘܚܪܢܐ ܕ-score) ܪܡܐ ܡܢ ܟܠ، ܟܡܪܗܛܚ ܡܢ ܪܝܫ ܘܟܬܢܚ، ܚܕ ܟܠ ܙܒܢܐ (Kline, p. 402; Putnick & Bornstein, p. 5)؛ ܠܦܘܬ Yoon ܘ-Kim (2014، ܐܝܟ ܕܡܬܚܙܝܢ ܓܒ Putnick ܘ-Bornstein، ܦܐܬܐ 14) ܩܐ ܫܪܝܐ ܕܚܕ ܒܬܪ ܚܕ ܐܝܬ ܒܨܝܪ ܛܥܝ̈ܘܬܐ ܕܙܢܐ ܩܕܡܝܐ ܡܢ ܫܪܝܐ ܕܟܠ ܐܣܘܪ̈ܐ ܕܐܝܬ ܓܘܝܗܝ ܥܘܩܬܐ ܒܚܕ ܙܒܢܐ، ܘ-Jung ܘ-Yoon (2016، ܐܝܟ ܕܡܬܚܙܝܢ ܐܟܡܐ) ܐܫܟܚܠܗܘܢ ܕܐܘܪܚܐ ܛܒ ܟܦܠܚܐ ܥܡ ܬܚܘܡܐ ܕ-6.635. ܓܘ ܦܐܬܐ – button ܕ"ܫܪܝܐ" ܓܘ ܠܘܚܐ ܕܒܘܚܪ̈ܢܐ ܕ-score. ܓܘ ܦܐܝܠ ܕܡܬܠܐ ܒܘܚܪܢܐ ܕ-score ܕܡܢܝܢܐ ܩܝܡܐ ܕ-השתתפות_3 ("ܐܢܐ ܟܐܬܝܢ/ܟܐܬܝܐ ܠܟܢܘܫܝ̈ܐ ܕܥܡܘܪ̈ܐ") ܝܠܗ χ²(1) = 62.86 – ܣܓܝ ܠܥܠ ܡܢ ܟܠ ܦܘܫܐ (השתתפות_1: 12.30)؛ ܒܬܪ ܫܪܝܐ ܕܝܠܗ ܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܐܚܪ̈ܢܐ ܡܢ ܩܕܡ ܫܘ̈ܝܐ ܝܢܐ (Δχ²(8) = 7.08, p = .528)، ܘܐܦ השתתפות_1 ܟܢܚܬ ܠܬܚܬ ܡܢ 3.84 – ܗܘ "ܡܢܓܕܐ ܗܘܐ" ܒܬܪ השתתפות_3 ܓܘ ܗܝ ܥܠܬܐ ܓܘܦܗ. ܐܗܐ ܝܠܗ ܥܠܬܐ ܕܟܫܪܚ ܚܕ ܟܠ ܙܒܢܐ. ܘܦܘܫܩܐ ܬܐܘܪܝܐ: ܓܘ ܫܒܒܘܬܐ ܚܕܬܐ ܡܕܝܢܬܐ ܟܟܢܫܐ ܟܢܘܫܝ̈ܐ ܕܬܘܩܢܐ، ܘܡܛܠ ܗܕܐ ܥܡܘܪ̈ܐ ܟܐܬܝ ܠܓܒܝܗܝ ܒܝܫ ܒܗܘ ܪܡܐ ܕܫܘܬܦܘܬܐ ܓܘܦܗ (ܗܕܟܐ ܒܢܝ̈ܐ ܝܢܐ ܝܗܝ̈ܒܬܐ ܕܡܬܠܐ).

ܟܡܐ ܫܠܝܛܐ ܝܠܗ ܕܫܪܚ؟ ܠܝܬ ܢܡܘܣܐ ܕܫܠܡܘܬܐ. Steenkamp ܘ-Baumgartner (1998) ܡܩܪܒܠܗܘܢ ܕܒܝܫ ܡܢ ܦܠܓܐ ܕܦܣܘ̈ܩܐ ܓܘ ܥܠܬܐ ܗܘܝ ܠܐ ܡܫܬܚܠܦ̈ܢܐ، ܘ-Vandenberg ܘ-Lance (2000) – ܪܘܒܐ ܕܝܗܝ؛ Byrne ܘܐܚܪ̈ܢܐ (1989) ܒܠܚܘܕ ܒܥܠܗܘܢ ܕܐܗܐ "ܗܘܐ ܡܠܝܐ ܡܢ ܓܒܐ ܬܐܘܪܝܐ" (ܟܠܗܘܢ ܐܝܟ ܕܡܬܚܙܝܢ ܓܒ Putnick ܘ-Bornstein, 2016، ܦܐܬܐ 9، ܕܟܡܥܗܕܝ ܕܐܦ ܚܕ ܡܢ ܦܘܩ̈ܕܢܐ ܠܐ ܟܡܣܬܡܟ ܥܠ ܒܘܨܝܐ ܡܢ ܢܣܝܢܐ). Vandenberg ܘ-Lance (2000، ܦܐܬܐ 38) ܟܡܠܟܝ ܕܫܪܚ ܛܥ̈ܢܐ "ܒܠܚܘܕ ܩܐ ܙܥܘܪܘܬܐ ܕܡܚܘ̈ܝܢܐ"، ܥܠ ܫܬܐܣܐ ܬܐܘܪܝܐ ܚܝܠܢܐ ܟܡܐ ܕܡܨܝܐ، ܘܐܡܢ ܕܐܝܬ ܫܘܪܪܐ ܡܚܠܦܢܐ (cross-validation)؛ Byrne (2016، ܦܐܬܐ 277) – ܕܗܘܐ ܒܝܫ ܡܢ ܚܕ ܡܢܝܢܐ ܩܝܡܐ ܠܐ ܡܫܬܚܠܦܢܐ "ܠܒܪ ܡܢ ܡܫܬܚܠܦܢܐ ܕ-reference". ܘܚܫܝܚܐ ܝܠܗ ܡܘܕܝ ܟܫܪܚ: ܠܦܘܬ Steinmetz (2013, as cited in Putnick & Bornstein, pp. 10, 14) ܛܥ̈ܢܐ ܠܐ ܫܘ̈ܝܐ ܩܪܝܒܐܝܬ ܠܐ ܟܡܨܠܝ ܦܘܚܡܐ ܕܡܨܥܝ̈ܬܐ، ܒܣ ܚܕ ܡܢܝܢܐ ܩܝܡܐ ܠܐ ܫܘܝܐ ܓܘ ܥܠܬܐ ܕ-4-6 ܦܣܘ̈ܩܐ ܡܒܪܝܠܗ ܠܦܘܪܫܢܐ "ܪܫܝܡܐ" ܕܓܠܐ ܓܘ 13% ܡܢ ܕܘ̈ܡܝܐ. ܘܡܐ ܕܬܠܝܐ ܝܠܗ ܒܫܪܝܐ: ܩܐ ܦܣܘܩܐ ܕܛܥܢܐ ܕܝܠܗ ܫܪܝܐ ܝܠܗ ܟܫܪܚ ܐܦ ܡܢܝܢܐ ܩܝܡܐ ܓܘ ܕܪܓܐ ܣܩܐܠܪܝܐ، "ܡܛܠ ܕܠܝܬ ܣܘܟܠܐ ܕܒܚܪܚ ܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܫܘ̈ܝܐ ܐܢ ܡܝܛܪܝܩܐ ܕܦܣܘ̈ܩܐ ܫܢܝܬܐ ܝܠܗ ܒܝܢܝ ܓܘ̈ܕܐ"، ܘܓܘ ܕܪܓܐ ܕܫܪܟܐ – ܐܦ ܫܘܚܠܦܐ ܕܫܪܟܐ ܕܦܣܘ̈ܩܐ ܥܡ ܛܥܢܐ ܝܢ ܡܢܝܢܐ ܩܝܡܐ ܫܪ̈ܝܐ (Putnick & Bornstein, pp. 5-6). ܦܐܬܐ ܟܥܒܕ ܐܗܐ ܡܢ ܓܢܗ (ܩܘܦܬܐ ܕܪܫܡܐ؛ lavaan ܠܐ ܟܥܒܕ ܐܗܐ ܡܢ ܓܢܗ، ܘܡܛܠ ܗܕܐ ܣܩܪܝܦܬ ܕ-R ܟܡܚܒܫ ܐܢܝ̈ ܫܪ̈ܝܐ ܓܠܝܐܝܬ).

ܦܘܚܡܐ ܕܥܠ̈ܠܬܐ: ܫܘܚܠ̈ܦܐ، ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܘܡܨܥܝ̈ܬܐ

"ܡܢ ܪܦܦܐ ܕܥܒܪܝ ܥܠ ܕܪ̈ܓܐ ܕܐܣܟܝܡܐ، ܡܝܛܪܝܐ ܘܣܩܐܠܪܝܐ، ܒܨܘܝܐ/ܒܨܘܝܬܐ ܚܐܪܐ/ܚܐܪܬܐ ܝܠܗ/ܝܠܗ̇ ܕܦܚܡ/ܕܦܚܡܐ ܡܨܥܝ̈ܬܐ ܕܓܘ̈ܕܐ ܥܠ ܥܠ̈ܠܬܐ ܟܣ̈ܝܬܐ" (Putnick & Bornstein, 2016, p. 7)، ܘ-Brown (2015، ܦܐܬܐ 243) ܟܡܘܣܦ ܕܐܗܐ ܡܨܝܢܐ ܝܠܗ ܐܦ ܐܡܢ ܕܒܠܚܘܕ ܡܢܬܐ ܡܢ ܛܥ̈ܢܐ ܘܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܫܘ̈ܝܐ ܝܢܐ. Vandenberg ܘ-Lance (2000، ܦܐܬܐ 40) ܟܡܢܝ ܝܘܬܪ̈ܢܐ ܥܠ ܒܘܚܪܢܐ t ܥܠ ܡܢܝ̈ܢܐ ܕܣܒ̈ܠܬܐ: ܦܘܚܡܐ ܙܕܝܩܐ ܝܠܗ ܒܠܚܘܕ ܐܢ ܡܫܘܚܬܐ ܫܘܝܐ ܝܠܗ، ܦܘܪ̈ܫܢܐ ܒܝܢܝ ܡܨܥܝ̈ܬܐ ܟܣ̈ܝܬܐ "ܡܬܘܪ̈ܨܐ ܝܢܐ ܩܐ ܛܥܝܘܬܐ ܕܡܫܘܚܬܐ"، ܘܡܨܝܚ ܕܫܠܛܚ ܥܠ ܠܐ ܡܫܬܚܠܦܢܘܬܐ ܡܢܬܢܝܬܐ. ܓܘ ܬܪܬܝܢ ܓܘ̈ܕܐ، ܒܘܚܪܢܐ ܕ-z ܕܡܨܥܝܬܐ ܕܥܠܬܐ (ܠܘܚܐ ܕܦܘܚܡܐ ܕܡܨܥܝ̈ܬܐ) ܘܒܘܚܪܢܐ ܟܠܢܝܐ ܕܫܘܝܘܬܐ ܕܡܨܥܝ̈ܬܐ ܟܝܗܒܝ ܩܪܝܒܐܝܬ ܗܘ ܡܕܡ ܓܘܦܗ (Brown، ܦܐܬܐ 261، 263: Δχ² = 1.91 ܩܘܒܠ z = 1.38)؛ ܓܘ ܒܝܫ ܡܢ ܬܪܬܝܢ ܓܘ̈ܕܐ – ܒܘܚܪܢܐ ܟܠܢܝܐ ܘܒܬܪܗ ܦܘܚ̈ܡܐ ܙܘܓܢ̈ܝܐ (pairwise comparisons)، ܥܡ ܬܘܪܨܐ ܕܪܡܐ ܕܪܫܝܡܘܬܐ (Vandenberg & Lance, p. 40; Brown, p. 263).

ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size). Kline (2023، ܦܐܬܐ 401، ܫܘܝܘܬܐ 22.2): d = (κ̂₁ − κ̂₂) / √((φ̂₁ + φ̂₂)/2) – ܦܘܪܫܢܐ ܕܡܨܥܝ̈ܬܐ ܦܠܝܓܐ ܥܠ ܫܪܫܐ ܡܪܒܥܐ ܕܡܨܥܝܬܐ ܕܫܘܚܠ̈ܦܐ ܕܥܠܬܐ؛ ܐܝܟ ܚܕ ܝܠܗ ܓܘ ܬܠܬܐ ܐܘܪ̈ܚܬܐ ܕܦܣܩܬܐ ܕܣܒܠܬܐ، ܘܟܡܣܒܐ ܫܘܚܠ̈ܦܐ ܫܘ̈ܝܐ ܘܓܘ̈ܕܐ ܫܘ̈ܝܐ. ܐܡܢ ܕܫܘܚܠ̈ܦܐ ܕܥܠܬܐ ܦܪ̈ܝܫܐ ܝܢܐ (ܒܘܚܪܢܐ M5)، Kline (ܦܐܬܐ 408) ܟܡܩܪܒ ܬܪܝܢ d، ܟܠ ܚܕ ܠܦܘܬ ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܚܕܐ ܓܘܕܐ – ܦܐܬܐ ܟܛܒܥ ܬܪܘܝܗܝ ܓܘ ܡܥܝܪܢܘܬܐ. Putnick ܘ-Bornstein (2016، ܦܐܬܐ 7) ܟܒܥܝ ܕܡܬܢܚ ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ ܐܝܟ ܐܗܐ ܒܟܠ ܡܐܪܐ. ܓܘ ܦܐܝܠ ܕܡܬܠܐ، ܓܘ ܡܘܕܝܠ ܣܩܐܠܪܝܐ ܡܢܬܢܝܐ: ܫܒܒܘܬܐ ܚܕܬܐ ܢܡܘܟܬܐ ܝܠܗ ܒܕܝܠܢܝܘܬܐ (d = −0.30، p < .001)، ܪܡܬܐ ܒܫܘܬܦܘܬܐ (d = 0.32) ܘܠܐ ܝܠܗ ܦܪܝܫܬܐ ܒܬܘܟܠܢܐ (d = 0.04، p = .669). ܓܘ ܡܢܝ̈ܢܐ ܕܣܒ̈ܠܬܐ ܚܙ̈ܝܐ ܦܘܪܫܢܐ ܒܫܘܬܦܘܬܐ ܪܒܐ ܝܠܗ ܒܝܫ (d = 0.46) – ܡܛܠ ܕ-השתתפות_3 ܢܦܝܚܐ ܝܠܗ ܓܘ ܫܒܒܘܬܐ ܚܕܬܐ؛ ܦܘܚܡܐ ܕܡܨܥܝ̈ܬܐ ܕܦܣܘ̈ܩܐ ܗܘܐ ܡܝܬܪ ܒܩܘܪܒܐ 40%.

ܫܘܚܠ̈ܦܐ ܘܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ. ܫܘܝܘܬܐ ܕܫܘܚܠ̈ܦܐ ܕܥܠ̈ܠܬܐ ܟܒܚܪܐ ܐܢ ܓܘ̈ܕܐ ܟܡܦܠܚܝ ܗܝ ܦܬܝܘܬܐ ܓܘܦܗ ܕܡܬܡܫܚܢܘܬܐ؛ ܦܘܚܡܐ ܐܝܟ ܐܗܐ ܐܝܬ ܠܗ ܣܘܟܠܐ ܒܠܚܘܕ ܐܡܢ ܕܛܥ̈ܢܐ ܫܘ̈ܝܐ ܝܢܐ، ܘܦܘܚܡܐ ܕܫܘܚܠ̈ܦܐ ܡܫܘܬܦ̈ܐ – ܒܠܚܘܕ ܐܡܢ ܕܐܦ ܫܘܚܠ̈ܦܐ ܫܘ̈ܝܐ ܝܢܐ (Brown, 2015, p. 262; Vandenberg & Lance, 2000, p. 39). ܦܐܬܐ ܟܒܚܪܐ ܫܘܚܠ̈ܦܐ ܩܘܒܠ ܡܘܕܝܠ ܣܩܐܠܪܝܐ (M5)، ܫܘܚܠ̈ܦܐ ܡܫܘܬܦ̈ܐ ܩܘܒܠ M5 (M6)، ܘܡܨܥܝ̈ܬܐ ܩܘܒܠ ܡܘܕܝܠ ܣܩܐܠܪܝܐ (M7) – ܥܝܕܐ ܕܣܐܝܛ (site convention)؛ Brown (ܠܘܚܐ 7.11) ܟܒܚܪ ܡܨܥܝ̈ܬܐ ܥܠ ܡܘܕܝܠ ܕܫܘܚܠ̈ܦܐ ܫܘ̈ܝܐ، ܘܐܡܢ ܕܫܘܚܠ̈ܦܐ ܫܘ̈ܝܐ ܝܢܐ ܦܘܪܫܢܐ ܙܥܘܪܐ ܛܒܐ ܝܠܗ.

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܘܚܐ 1 – ܪܒܘܬܐ ܕܟܠ ܓܘܕܐ، ܡܨܥܝ̈ܬܐ ܘܣܛܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܕܦܣܘ̈ܩܐ – ܝܗܝ̈ܒܬܐ ܕܟܢܘܫܝܐ ܕܟܡܨܝ ܐܚܪ̈ܢܐ ܕܥܒܕܝ ܬܘܒ ܦܘܫܩܐ. ܠܘܚܐ 2 – ܡܘܕܝܠ ܓܘ ܟܠ ܓܘܕܐ ܒܠܚܘܕܗ، ܥܡ ܫܪܟܐ ܪܒܐ؛ ܐܟܐ ܟܡܫܪܚ. ܠܘܚܐ 3 – ܠܒܐ: ܛܟܣܐ ܕܡܘܕܝ̈ܠܐ ܒܒܢܝܢܐ ܕܠܘܚܐ 3 ܕ-Putnick ܘ-Bornstein (2016، ܦܐܬܐ 29): ܦܐܝܘܬܐ ܕܟܠ ܡܘܕܝܠ، ܡܘܕܝܠ ܕܩܘܒܠܗ ܦܚܝܡܐ ܝܠܗ، Δχ²، Δdf، ܫܘܢܝ̈ܐ ܓܘ CFI، RMSEA ܘ-SRMR (ܬܚܝܬ ܨܦܪܐ ܓܘ CFI ܘܥܠ ܡܢ ܨܦܪܐ ܓܘ RMSEA ܘܓܘ SRMR – ܦܐܝܘܬܐ ܒܝܫܬܐ ܒܝܫ)، ܘܦܣܩܬܐ. ܠܘܚܐ ܕܒܘܚܪ̈ܢܐ ܕ-score (ܟܡܬܚܙܐ ܐܡܢ ܕܐܝܬ ܡܕܡ ܩܐ ܫܪܝܐ) – ܒܟܡܐ ܡܣܟܝܐ ܝܠܗ χ² ܕܢܚܬ ܐܢ ܚܕ ܐܣܘܪܐ ܫܪܐ، ܘ-EPC: ܛܝܡܐ ܡܣܟܝܐ ܕܦܪܡܝܛܪ ܓܘ ܟܠ ܓܘܕܐ ܒܬܪ ܫܪܝܐ؛ Kline (2023، ܦܐܬܐ 402): ܐܢ ܫܘܢܝܐ ܙܥܘܪܐ ܛܒܐ ܝܠܗ، "ܡܨܐ ܕܠܝܬ ܚܒܠܐ ܪܒܐ ܒܡܫܒܩܬܐ ܕܐܣܘܪܐ" ܐܦ ܐܡܢ ܕܒܘܚܪܢܐ ܪܫܝܡܐ ܝܠܗ. ܠܘܚܐ ܕܫܘܥܪ̈ܐ – ܛܥ̈ܢܐ، ܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܘܫܘܚܠ̈ܦܐ ܕܫܪ̈ܟܐ ܓܘ ܟܠ ܓܘܕܐ، ܓܘ ܡܘܕܝܠ ܕܓܒܝܐ ܝܠܗ (ܓܘܒܝܐ ܡܩܕܡܐ – ܕܪܓܐ ܪܡܐ ܕܠܐ ܡܫܬܕܐ ܝܠܗ)؛ = ܟܪܫܡ ܦܪܡܝܛܪ ܡܫܘܬܦܐ. ܠܘܚܐ ܕܥܠ̈ܠܬܐ – ܫܘܚܠ̈ܦܐ، ܡܨܥܝ̈ܬܐ ܘܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܓܘ ܟܠ ܓܘܕܐ. ܠܘܚܐ ܕܦܘܚܡܐ ܕܡܨܥܝ̈ܬܐ ܘܨܘܪܬܐ ܕ-d – ܥܠܬܐ ܟܣܝܬܐ ܩܘܒܠ ܡܢܝܢܐ ܕܣܒܠܬܐ ܚܙܝܐ. ܠܘܚܐ ܕܡܨܥܝ̈ܬܐ ܕܟܢܦܩܝ ܡܢ ܡܘܕܝܠ – ܐܝܟ ܠܘܚܐ 22.5 ܕ-Kline (ܦܐܬܐ 407): ܡܢ M3 ܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܡܫܘܬܦ̈ܐ ܝܢܐ، ܘܫܪܟܐ ܕܡܨܥܝܬܐ ܕܠܐ ܝܠܗ ܨܦܪܐ ܐܬܐ ܕܘܟܬܢܝܬܐ ܝܠܗ ܩܐ ܡܢܝܢܐ ܩܝܡܐ ܕܐܝܬ ܓܘܗ ܥܘܩܬܐ.

ܫܪ̈ܛܐ ܘܙܘܗܪ̈ܐ (Assumptions and warnings)

ܪܒܘܬܐ ܕܕܘܡܝܐ ܓܘ ܟܠ ܓܘܕܐ. Kline (2023، ܦܐܬܐ 403) ܟܡܝܬܐ ܕܘܡܝ̈ܐ ܕܡܕܡܝܢܘܬܐ (simulations) ܕ-Meade ܘ-Bauer (2007، ܐܝܟ ܕܡܬܚܙܝܢ ܓܒܗ): ܥܡ 400 ܓܘ ܟܠ ܓܘܕܐ ܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ (statistical power) ܣܓܝ ܙܒ̈ܢܐ ܪܡܐ ܗܘܐ، ܥܡ 200 – "ܣܓܝ ܟܫܚܠܦ"، ܘܠܝܬ ܦܘܚܡܐ ܦܫܝܛܐ ܕܡܫܬܘܬܦ̈ܢܐ ܠܦܣܘ̈ܩܐ ܕܟܡܫܪܪ ܚܝܠܐ. ܡܛܠ ܗܕܐ ܠܐ ܡܫܕܝܢܘܬܐ ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ ܠܐ ܝܠܗ ܣܗܕܘܬܐ ܚܝܠܢܬܐ ܩܐ ܠܐ ܡܫܬܚܠܦܢܘܬܐ، ܘܓܘ Δχ² ܓܘ ܕܘܡܝܐ ܪܒܐ – ܟܠ ܦܘܪܫܢܐ ܙܥܘܪܐ ܛܒܐ ܟܡܫܬܕܐ. ܓܘ̈ܕܐ ܠܐ ܫܘ̈ܝܐ: ܫܠܝܛܐ ܝܠܗ، ܒܣ ܛܒ ܒܝܫ ܡܫܘ̈ܝܐ – ܓܘܕܐ ܪܒܬܐ ܟܝܗܒܐ ܒܝܫ ܠ-χ²، ܠܡܚܘ̈ܝܢܐ ܘܠܒܘܚܪ̈ܢܐ ܕ-score (Brown, 2015, p. 251). ܦܣܘ̈ܩܐ ܕ-Likert: ܦܐܬܐ ܟܚܫܒܐ ܦܣܘ̈ܩܐ ܐܝܟ ܡܬܡܫܚ̈ܢܐ (ML)، ܘ-Kline (ܦܐܬܐ 409) ܟܐܡܪ ܕܐܗܐ "ܠܐ ܝܠܗ ܐܝܕܝܐܠ" ܥܡ 5 ܓܢ̈ܣܐ ܝܢ ܒܨܝܪ؛ ܓܘ ܦܘܫܩܐ ܕܓܢ̈ܣܐ ܐܝܬ thresholds ܒܕܘܟܬܐ ܕܡܢܝ̈ܢܐ ܩܝ̈ܡܐ، ܘܛܟܣܐ ܕܒܘܚܪ̈ܢܐ ܘ-identification ܦܪ̈ܝܫܐ ܝܢܐ (ܗܘ ܕܘܟܬܐ، ܦܐܬܐ 409-410) – ܓܘ R: ordered = ܓܘ lavaan. ܫܪܝܐ ܠܦܘܬ ܝܗܝ̈ܒܬܐ "ܬܚܘܬ ܡܦܠܚܢܘܬܐ ܕܓܕܫܐ ܝܠܗ" (Vandenberg & Lance, 2000, p. 37)؛ "ܥܡ ܒܘܚܪ̈ܢܐ ܘܫܪ̈ܝܐ ܣܦܝܩ̈ܐ، ܡܨܝܚ ܕܥܒܕܚ ܟܠ ܡܘܕܝܠ ܕܦܐܐ" (Kline, p. 402) – ܟܠ ܫܪܝܐ ܟܡܬܢܚ ܠܗ، ܘܛܒ ܒܝܫ ܕܫܪܪܚ ܓܘ ܕܘܡܝܐ ܚܕܬܐ. ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (missing values) – ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ ܓܘ ܟܠ ܓܘܕܐ (ܓܘܒܝܐ ܡܩܕܡܐ ܕ-lavaan).

ܡܘܕܝ ܠܐ ܟܚܫܒܐ ܐܗܐ ܦܐܬܐ. ܝܗܝ̈ܒܬܐ ܛܟܝ̈ܣܬܐ ܝܢ ܕܬܪܝܢ ܛܝ̈ܡܐ (thresholds، WLSMV)؛ ܠܐ ܡܫܬܚܠܦܢܘܬܐ ܥܠ ܐܘܪܟܐ ܕܙܒܢܐ ܓܘ ܗܝ ܓܘܕܐ ܓܘܦܗ (Kline, 2023, p. 394)؛ MIMIC – ܓܘܕܐ ܐܝܟ ܡܫܬܚܠܦܢܐ ܡܢܒܝܢܐ ܓܘ ܚܕ ܡܘܕܝܠ، ܕܟܒܚܪ ܒܠܚܘܕ ܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܘܡܨܥܝ̈ܬܐ (Brown, 2015, p. 242)؛ ܒܘܚܪܢܐ ܟܠܢܝܐ ܩܐ ܫܘܝܘܬܐ ܕܡܐܛܪ̈ܝܟܣܐ؛ ܒܘܚܪܢܐ factor-ratio ܕ-Cheung ܘ-Rensvold ܘܐܘܪܚܐ "ܠܩܕܡ" (Kline, p. 402)؛ ܠܐ ܡܫܬܚܠܦܢܘܬܐ ܩܪܝܒܬܐ (Bayesian) ܘ-alignment ܩܐ ܣܓܝ ܓܘ̈ܕܐ (Kline, p. 411)؛ ܡܚܘ̈ܝܢܐ ܕܡܥܒܕܢܘܬܐ ܕܠܐ ܠܐ ܡܫܬܚܠܦܢܘܬܐ ܐܝܟ d_MACS (Putnick & Bornstein, 2016, p. 17)؛ ܫܘܥܪܐ ܚܣܝܢܐ (MLR) ܘ-FIML؛ ܛܥ̈ܢܐ ܥܠ ܥܠ̈ܠܬܐ ܣܓܝ̈ܐܐ (cross-loadings).

ܘܕܟܝ ܟܥܒܕܚ ܐܗܐ ܒ-SPSS ܘ-AMOS؟

ܓܘ SPSS Statistics ܠܝܬ ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܡܫܪܪܢܐ؛ ܓܘ AMOS ܟܬܚܡܚ ܓܘ̈ܕܐ ܒܝܕ Analyze › Manage Groups – ܫܡܐ ܘܦܐܝܠ ܕܝܗܝ̈ܒܬܐ ܩܐ ܟܠ ܓܘܕܐ (Byrne, 2016, pp. 235-236). ܛܟܣܐ ܟܡܪܗܛܚ ܠܗ ܓܘ Analyze › Multiple-Group Analysis: AMOS ܟܡܩܪܒ ܡܘܕܝ̈ܠܐ ܡܛܝܒ̈ܐ – "measurement weights" (ܛܥ̈ܢܐ ܫܘ̈ܝܐ)، ܘܒܬܪܝܗܝ ܐܦ "structural covariances" ܘ-"measurement residuals" (ܦܐܬܐ 249). ܩܐ ܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܘܡܨܥܝ̈ܬܐ: ܓܘ Analysis Properties › Estimation ܟܪܫܡܚ Estimate means and intercepts، ܘܓܘ ܟܘܬܐ ܕ-Multiple-Group Analysis ܟܡܘܣܦܚ "measurement intercepts"؛ AMOS ܟܩܝܡ ܡܨܥܝ̈ܬܐ ܕܥܠ̈ܠܬܐ ܥܠ 0 ܓܘ ܟܠ ܓܘ̈ܕܐ، ܘܟܫܩܠܚ 0 ܓܘ ܚܕܐ ܓܘܕܐ ܩܐ ܕܡܨܥܝ̈ܬܐ ܕܝܠܗ̇ ܡܫܬܥܪܝ ܩܘܒܠ ܓܘܕܐ ܕ-reference (ܦܐܬܐ 277-278). Byrne (ܦܐܬܐ 249) ܟܡܥܝܪܐ ܕܐܣܘܪܐ ܕܫܘܚܠ̈ܦܐ ܕܫܪ̈ܟܐ "ܟܡܬܚܫܒ ܒܘܚܪܢܐ ܚܪܝܦܐ ܝܬܝܪ" ܘܡܛܠ ܗܕܐ ܩܠܝܠ ܟܡܬܚܙܐ.

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

ܓܘ lavaan: group = ܩܐ ܥܡܘܕܐ ܕܓܘܕܐ، group.equal = ܩܐ ܙܢ̈ܐ ܕܐܣܘܪ̈ܐ ("loadings", "intercepts", "residuals", "lv.variances", "lv.covariances", "means") ܘ-group.partial = ܩܐ ܫܪ̈ܝܐ (Rosseel, 2012, Section 6)؛ lavTestLRT ܟܦܚܡ ܡܘܕܝ̈ܠܐ ܡܩܢ̈ܢܐ، ܘ-lavTestScore ܟܝܗܒ ܒܘܚܪ̈ܢܐ ܕ-score ܩܐ ܟܠ ܐܣܘܪܐ ܕܫܘܝܘܬܐ. ܚܙܝܡܘܢ: ܓܘ lavaan 0.6-17 effect.coding = TRUE ܠܐ ܟܚܫܒ group.partial ܘ-group.equal = "means" – ܥܡ ܪܡܙܢܘܬܐ ܕܡܥܒܕܢܘܬܐ ܘܫܪ̈ܝܐ، ܝܢ ܐܡܢ ܕܒܚܪܚ ܫܘܝܘܬܐ ܕܡܨܥܝ̈ܬܐ، ܣܢܝܩܘܬܐ ܐܝܬ ܕܟܬܒܚ ܐܣܘܪ̈ܐ ܒܐܝܕܐ، ܐܝܟ ܓܘ ܣܩܪܝܦܬ ܕ-Kline (2023، ܨܚܚܐ 22). button ܕ"ܡܚܬܬܐ ܕܣܩܪܝܦܬ ܕ-R" ܓܘ ܡܦܩܢܐ ܟܟܬܒ ܛܟܣܐ ܕܪܗܛܠܘܟܘܢ، ܥܡ ܫܪ̈ܝܐ. ܣܩܪܝܦܬ ܕܠܬܚܬ ܪܗܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ (lavaan 0.6-17).

# ܦܘܚܡܐ ܕܓܘ̈ܕܐ ܘܠܐ ܡܫܬܚܠܦܢܘܬܐ ܕܡܫܘܚܬܐ – ܦܪܘܦܣܘܪ ܣܛܐܛ. ܐܗܐ ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8؛ ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܡܫܪܐ ܒܚܕܐ ܡܠܬܐ ܕܣܘܪܝܬ
library(readxl)   # ܩܪܝܢܐ ܕܐܩܣܠ
library(lavaan)   # ܦܘܢܩܣܝ̈ܘܢܐ: cfa, lavTestLRT, lavTestScore

# ܛܥܢܐ: ܛܘܦܣܐ ܬܩܝܢܐ – ܣܕܪܐ = ܡܫܬܘܬܦܢܐ؛ ܓܠܝܘܢܐ "נתונים"
d <- read_excel("C:/Rdata/DATA_invariance_example_heb.xlsx", sheet = "נתונים")
items <- c(paste0("שייכות_", 1:4), paste0("אמון_", 1:4), paste0("השתתפות_", 1:4))
d <- as.data.frame(d[, c("שכונה", items)])
names(d) <- c("grp", paste0("b", 1:4), paste0("t", 1:4), paste0("p", 1:4))   # ܫܡܗ̈ܐ ܩܨܝܪ̈ܐ ܒܐܢܓܠܝܙܝܐ ܩܐ ܡܘܕܝܠ
labs <- c("ותיקה", "חדשה")   # ܩܕܡܝܬܐ – ܓܘܕܐ ܕ-reference

model <- "
  belong =~ b1 + b2 + b3 + b4
  trust  =~ t1 + t2 + t3 + t4
  partic =~ p1 + p2 + p3 + p4
"
fit <- function(...) cfa(model, data = d, group = "grp", group.label = labs, ...)
m1 <- fit()                                                  # ܐܣܟܝܡܐ
m2 <- fit(group.equal = "loadings")                          # ܡܝܛܪܝܬܐ
m3 <- fit(group.equal = c("loadings", "intercepts"))         # ܣܩܐܠܪܝܬܐ
lavTestLRT(m1, m2, m3)
# ܦܐܪ̈ܐ: χ²(102) = 118.87; Δχ²(9) = 2.875, p = .969; Δχ²(9) = 71.567, p < .001

# ܒܘܚܪ̈ܢܐ ܕ-score ܩܐ ܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܓܘ ܡܘܕܝܠ ܣܩܐܠܪܝܐ – ܡܘܕܝ ܕܫܪܚ
st <- lavTestScore(m3)$uni; pt <- parTable(m3)
st$param <- paste(pt$lhs, pt$op, pt$rhs)[match(st$lhs, pt$plabel)]
head(st[order(-st$X2), c("param", "X2", "p.value")], 3)    # ܦܐܪ̈ܐ: p3 ~1: 62.864; p1 ~1: 12.296; p2 ~1: 5.113

# ܣܩܐܠܪܝܬܐ ܡܢܬܢܝܬܐ: ܡܢܝܢܐ ܩܝܡܐ ܕ-p3 ܚܐܪܐ ܓܘ ܟܠ ܓܘܕܐ
m3p <- fit(group.equal = c("loadings", "intercepts"), group.partial = "p3 ~ 1")
lavTestLRT(m2, m3p)                                          # ܦܐܪܐ: Δχ²(8) = 7.082, p = .528
pe <- parameterEstimates(m3p)
pe[pe$op == "~1" & pe$lhs %in% c("belong", "trust", "partic") & pe$group == 2, c("lhs", "est", "se", "z", "pvalue")]
# ܦܐܪ̈ܐ: belong -0.299 (SE 0.090, z = -3.311); trust 0.041 (0.097); partic 0.393 (0.111, z = 3.549)
m7 <- fit(group.equal = c("loadings", "intercepts", "means"), group.partial = "p3 ~ 1")
lavTestLRT(m3p, m7)                                          # ܒܘܚܪܢܐ ܟܠܢܝܐ ܩܐ ܡܨܥܝ̈ܬܐ: Δχ²(3) = 40.868

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

Putnick ܘ-Bornstein (2016، ܦܐܬܐ 16) ܐܫܟܚܘ ܕܓܘ ܩܪܝܒ ܚܕ ܡܢ ܚܡܫܐ ܡܢ ܒܘܨ̈ܝܐ ܐܦܠܐ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom) ܠܐ ܬܢܝ̈ܐ ܝܢܐ ܗܘܘ، ܘܟܡܩܪܒܝ ܛܝܡܐ ܬܚܬܝܐ (minimum) ܫܘܝܐ ܠܟܠ: (1) ܪܒܘܬܐ ܕܕܘܡܝܐ (sample size) ܓܘ ܡܘ̈ܕܝܠܐ، ܐܢ ܦܪܝܫܐ ܝܠܗ ܡܢ ܕܘܡܝܐ ܟܠܗ؛ (2) ܦܘܠܚܢܐ ܥܡ ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (missing values)؛ (3) ܡܢܝܢܐ ܕܓܘ̈ܕܐ ܘܪܒܘܬܐ ܕܟܠ ܚܕܐ؛ (4) ܢܡܘ̈ܣܐ ܕܦܐܝܘܬܐ ܩܐ ܡܘܕܝܠ ܐܣܟܝܡܝܐ (configural model) ܘܩܐ ܦܘܚܡ̈ܐ؛ ܘ-(5) ܠܘܚܐ (table) ܕܟܠ ܡܘ̈ܕܝܠܐ – df، ܡܚܘ̈ܝܢܐ ܕܦܐܝܘܬܐ (fit indices)، ܐܝܢܐ ܡܘܕܝܠ ܦܘܚܡܐ ܝܠܗ ܥܡ ܐܝܢܐ، Δdf، ܦܘܪ̈ܫܢܐ ܘܦܘܣܩܢܐ – ܐܝܟ ܠܘܚܐ 3 ܓܘ ܦܐܬܐ. Kline (2023، ܦܐܬܐ 408-409) ܟܡܘܣܦ: ܠܡܦܫܩܐ ܥܠܬܐ ܕܟܠ ܫܘܢܝܐ ܓܘ ܡܘܕܝܠ، ܠܡܒܚܪܐ ܪܡܙܐ ܬܠܬܐ ܓܗ̈ܐ، ܠܡܝܕܥܐ ܓܘܒ̈ܝܐ ܡܩܕ̈ܡܐ (defaults) ܕܦܪܘܓܪܡ (ܓܘ Mplus، ܡܬܠܐ، ܛܥ̈ܢܐ (loadings) ܘܡܢܝ̈ܢܐ ܩܝ̈ܡܐ (intercepts) ܫܘ̈ܝܐ ܝܢܐ ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ)، ܠܡܟܬܒܐ ܬܘܩܢܐ ܡܢ ܩܕܡ ܘܠܡܦܪܣܐ ܝܗܝ̈ܒܬܐ ܘܪܡܙܐ، ܘܠܡܬܚܘܝܐ ܫܪ̈ܟܐ (residuals) ܓܘ ܟܠ ܓܘܕܐ. ܡܢ ܦܐܬܐ: ܠܘܚܐ 3، ܫܪ̈ܝܐ (releases) ܘܥܠ̈ܠܬܐ ܕܝܗܘܢ، ܠܘܚܐ ܕܦܘܚܡܐ ܕܡܨܥܝ̈ܬܐ ܥܡ d، ܘܦܣܩܐ ܕܡܫܟܚ̈ܢܘܬܐ (results paragraph). APA (2020، ܦܣܩܐ 6.44) – ܠܡܦܪܫܐ ܫܡܗ̈ܐ ܩܛܝ̈ܢܐ (CFA, CFI, RMSEA) ܓܘ ܡܬܚܙܝܢܘܬܐ ܩܕܡܝܬܐ؛ ܦܣܩܐ 6.36 – ܕܠܐ ܨܦܪܐ ܩܕܡ ܢܘܩܙܐ ܩܐ p، CFI ܘ-RMSEA.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܠܡܦܚܡܐ ܡܨܥܝ̈ܬܐ ܕܡܢܝ̈ܢܐ ܕܣܒܠܬܐ ܕܠܐ ܒܘܚܪܢܐ. ܒܘܚܪܢܐ t ܥܠ ܡܨܥܝܬܐ (mean) ܕܦܣܘ̈ܩܐ (items) ܟܣܐܡ – ܕܠܐ ܒܘܚܪܢܐ – ܠܐ ܡܫܬܚܠܦܢܘܬܐ ܣܩܐܠܪܝܬܐ (scalar invariance) ܓܡܝܪܬܐ. ܓܘ ܦܐܝܠ ܕܡܬܠܐ (sample data file) ܗܘ ܟܡܪܒܐ ܦܘܪܫܢܐ ܓܘ ܫܘܬܦܘܬܐ ܒܩܪܝܒ 40%.

ܠܡܦܚܡܐ ܛܥ̈ܢܐ ܡܬܩ̈ܢܐ ܒܝܢܝ ܓܘ̈ܕܐ. ܐܢܝ̈ ܬܠܝ̈ܐ ܝܢܐ ܒܫܘܚܠ̈ܦܐ (variances) ܕܟܠ ܓܘܕܐ، ܘܦܪ̈ܝܫܐ ܝܢܐ ܐܦ ܐܡܬܝ ܕܕܠܐ ܡܬܩ̈ܢܐ ܫܘ̈ܝܐ ܝܢܐ (Kline, 2023, p. 405; Brown, 2015, p. 262) – ܟܦܚܡܚ ܕܠܐ ܡܬܩ̈ܢܐ.

ܠܡܦܚܡܐ ܡܨܥܝ̈ܬܐ ܕܥܠ̈ܠܬܐ ܐܡܬܝ ܕܕܪܓܐ ܣܩܐܠܪܝܐ ܡܣܠܝܐ ܝܠܗ. ܩܕܡ ܟܫܪܚ ܡܢܝ̈ܢܐ ܩܝ̈ܡܐ (intercepts) ܕܐܝܬ ܠܗܘܢ ܥܘܩܬܐ (ܐܢ ܐܝܬ ܥܠܬܐ ܬܪܝܨܬܐ ܩܐ ܗܕܐ)، ܘܒܣ ܒܬܪ ܗܕܐ ܟܦܚܡܚ.

ܠܡܫܪܝܐ ܐܣܘܪ̈ܐ ܣܓܝ̈ܐܐ ܒܚܕ ܓܗܐ، ܝܢ ܗܠ ܕܦܐܝܐ. ܚܕ ܚܕ، ܥܡ ܥܠܬܐ، ܘܟܬܢܚ ܟܠ ܫܪܝܐ؛ ܐܡܬܝ ܕܪܘܒܐ ܕܦܣܘ̈ܩܐ ܓܘ ܥܠܬܐ (factor) ܠܐ ܝܢܐ ܠܐ ܡܫܬܚܠ̈ܦܢܐ – ܥܠܬܐ ܠܝܬܝܗ ܗܝ ܥܠܬܐ.

ܠܡܦܣܩܐ ܒܣ ܠܦܘܬ ΔCFI، ܝܢ ܒܣ ܠܦܘܬ Δχ². ܟܬܢܚ ܬܪܘܝܗܘܢ، ܘܟܒܚܪܚ ܫܪ̈ܟܐ (residuals) ܓܘ ܟܠ ܓܘܕܐ (Kline, 2023, pp. 399, 409).

ܠܡܬܒܥܐ ܫܘܚܠ̈ܦܐ ܕܫܪ̈ܟܐ ܫܘ̈ܝܐ ܐܝܟ ܫܪܛܐ. ܠܐ ܡܫܬܚܠܦܢܘܬܐ ܕܫܪ̈ܟܐ ܠܐ ܝܠܗ ܣܢܝܩܬܐ ܩܐ ܦܘܚܡܐ ܕܡܨܥܝ̈ܬܐ ܕܥܠ̈ܠܬܐ (Putnick & Bornstein, 2016, p. 6).

marker ܕܠܐ ܝܠܗ ܠܐ ܡܫܬܚܠܦܢܐ. ܐܢ ܟܠ ܛܥ̈ܢܐ "ܟܢܦܠܝ"، ܒܠܟܝ ܥܘܩܬܐ ܓܘ ܦܣܘܩܐ ܕ-reference ܝܠܗ – ܡܢܣܝܡܘܢ ܪܡܙܢܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect coding) ܝܢ marker ܐܚܪܢܐ.

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.

Putnick, D. L., & Bornstein, M. H. (2016). Measurement invariance conventions and reporting: The state of the art and future directions for psychological research. Developmental Review, 41, 71-90. https://doi.org/10.1016/j.dr.2016.06.004

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

Vandenberg, R. J., & Lance, C. E. (2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods, 3(1), 4-70. https://doi.org/10.1177/109442810031002

Byrne ܘܐܚܪ̈ܢܐ (1989)، Chen (2007)، Cheung ܘ-Rensvold (2002)، Jung ܘ-Yoon (2016)، Meade ܘܐܚܪ̈ܢܐ (2008)، Rutkowski ܘ-Svetina (2014)، Steenkamp ܘ-Baumgartner (1998)، Steinmetz (2013)، Widaman ܘ-Reise (1997) ܘ-Yoon ܘ-Kim (2014) – ܐܝܟ ܕܡܬܡܠܠܝ ܓܘ Putnick ܘ-Bornstein (2016)؛ Byrne ܘܐܚܪ̈ܢܐ (1989)، Guo ܘܐܚܪ̈ܢܐ (2021)، Little ܘܐܚܪ̈ܢܐ (2006) ܘ-Meade ܘ-Bauer (2007) – ܐܝܟ ܕܡܬܡܠܠܝ ܓܘ Kline (2023)؛ Horn ܘ-McArdle (1992) – ܐܝܟ ܕܡܬܡܠܠܝ ܓܘ Vandenberg ܘ-Lance (2000). ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ (site rule)، ܓܘ ܪܫܝܡܬܐ ܕܡܒܘ̈ܥܐ (reference list) ܟܡܬܚܙܝ ܒܣ ܡܒܘ̈ܥܐ ܕܩܪܝ̈ܐ ܝܢܐ ܒܢܘܣܚܐ ܫܪܫܝܐ. ܡܢܝ̈ܢܐ ܕܦܐܬ̈ܐ ܕ-Putnick ܘ-Bornstein (2016) – ܠܦܘܬ ܟܬܒܐ ܕܐܝܕܐ ܕܡܟܬܒ̈ܢܐ ܓܘ PubMed Central. ܥܝ̈ܕܐ ܕܣܐܝܛ (site conventions): ܥܡܘܕܐ ܕ"ܦܘܣܩܢܐ" (Δχ² ܘ-ΔCFI ܚܕ ܓܗܐ، "ܡܚܠܛܐ" ܐܡܬܝ ܕܦܠܝܓܝ ܝܢܐ)، ܬܚܘܡܐ ܩܐ ܡܚܘܝܐ ܕܒܘܚܪ̈ܢܐ ܕ-score (score tests)، ܫܪܝܐ ܡܢ ܓܢܗ ܕܡܢܝ̈ܢܐ ܩܝ̈ܡܐ ܘܫܪ̈ܟܐ ܒܬܪ ܫܪܝܐ، d ܕܡܢܝܢܐ ܕܣܒܠܬܐ (scale score) ܚܙܝܐ، ܛܠܠܐ ܕܫܪ̈ܟܐ ܕܡܨܥܝ̈ܬܐ ܠܥܠ ܡܢ .10 ܣܛܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ، ܦܘܚܡܐ ܕܫܘܚܠ̈ܦܐ ܘܕܡܨܥܝ̈ܬܐ ܩܘܒܠ ܡܘܕܝܠ ܣܩܐܠܪܝܐ، ܘܦܐܝܠ ܕܡܬܠܐ (ܝܗܝ̈ܒܬܐ ܕܡܘ̈ܝܬܐ، ܥܡ ܦܣܘܩܐ ܚܕ ܕܠܐ ܝܠܗ ܠܐ ܡܫܬܚܠܦܢܐ ܒܨܒܝܢܐ). ܚܘܫܒܢܐ ܓܘ ܦܐܬܐ ܫܪܝܪܐ ܝܠܗ ܩܘܒܠ ܚܙܡܐ lavaan 0.6-17 ܓܘ R ܘܩܘܒܠ ܡܦܩܢܐ (output) ܛܒܝܥܐ ܕ-Kline (2023)، Brown (2015) ܘ-Rosseel (2012).