ܦܘܫܩܐ ܕܫܒ̈ܝܠܐ ܘܡܨܥܝܘܬܐ

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)؟

ܐܡܬܝ ܕܫܘܐܠܐ ܠܐ ܝܠܗ "ܐܝܢܐ X ܟܡܢܒܐ Y" ܐܠܐ "ܒܐܝܢܐ ܐܘܪܚܐ": X ܟܡܥܒܕ ܥܠ M، ܘ-M ܟܡܥܒܕ ܥܠ Y. Field (2024، ܦܣܩܐ 11.4.1) ܟܡܚܘܐ ܡܨܥܝܘܬܐ (mediation) ܐܝܟ ܡܢܝܘܬܐ ܕܓܘܗ̇ "ܐܣܘܪܐ ܒܝܢܝ ܡܢܒܝܢܐ ܘܡܫܬܚܠܦܢܐ ܡܢܒܝܐ ܡܦܫܩܐ ܝܠܗ ܒܐܘܪܚܐ ܕܐܣܘܪܐ ܕܬܪܘܝܗܝ ܥܡ ܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ، ܡܨܥܝܐ": ܡܥܒܕܢܘܬܐ ܟܠܢܝܬܐ ܕ-X ܥܠ Y ܟܡܬܦܠܓܐ ܠܡܥܒܕܢܘܬܐ ܬܪܝܨܬܐ (c) ܘܠܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܒܐܘܪܚܐ ܕܡܨܥܝܐ (ܫܒ̈ܝܠܐ a ܘ-b). ܡܬܠܐ ܕܝܠܗ (Lambert et al., 2012): ܚܙܝܬܐ ܕܦܘܪܢܘܓܪܐܦܝܐ ← ܢܚܬܬܐ ܓܘ ܩܝܡܐ ܕܙܘܘܓܐ ← ܢܟܠܐ – "ܠܐ ܡܣܬܟܠܢܐ ܝܠܗ ܕܟܠ ܐܢܫܐ ܕܟܚܙܐ ܦܘܪܢܘܓܪܐܦܝܐ ܟܪܗܛ ܡܚܕܐ ܠܢܟܠܐ؛ ܒܠܟܝ ܐܗܐ ܟܡܛܝܐ ܠܫܘܢܝܐ ܕܪܓܫܐ ܝܢ ܕܗܘܢܐ" ܕܝܠܗ ܡܟܢܘܬܐ. ܦܘܫܩܐ ܕܫܒ̈ܝܠܐ (path analysis) ܝܠܗ ܓܘܢܝܘܬܐ: ܟܡܐ ܡܫܬܚܠܦ̈ܢܐ ܡܢܒ̈ܝܐ، ܟܡܐ ܡܨܥ̈ܝܐ (Field، ܦܣܩܐ 11.4.7 – ܬܪܝܢ ܡܨܥ̈ܝܐ ܒܓܢܒ ܚܕ̈ܕܐ)، ܫܫ̈ܠܬܐ ܐܪ̈ܝܟܬܐ ܝܬܝܪ، ܘܡܢܒ̈ܝܢܐ ܕܟܡܥܒܕܝ ܥܠ ܡܢܬܐ ܡܢ ܡܫܬܚܠܦ̈ܢܐ ܘܠܐ ܥܠ ܐܚܪ̈ܢܐ – ܟܠ ܫܘܝ̈ܘܬܐ ܡܫܘܥܪ̈ܐ ܝܢܐ ܐܟܚܕܐ، ܘܡܘܕܝܠ ܟܠܗ ܒܚܝܪܐ ܝܠܗ ܩܘܒܠ ܝܗܝ̈ܒܬܐ. ܐܗܐ ܝܠܗ ܓܕܫܐ ܝܚܝܕܝܐ ܕܡܘܕܝ̈ܠܐ ܕܫܘܝ̈ܘܬܐ ܒܢܝܢܝ̈ܬܐ (SEM) ܕܓܘܗ ܟܠ ܡܫܬܚܠܦ̈ܢܐ ܚܙܝ̈ܐ ܝܢܐ: Pallant (2020، ܨܚܚܐ 10) ܟܡܚܘܝܐ SEM ܐܝܟ ܐܘܡܢܘܬܐ "ܕܒܢܝܬܐ ܝܠܗ̇ ܥܠ ܪܝܓܪܫܢ ܣܓܝܐܐ ܘܦܘܫܩܐ ܕܥܠ̈ܠܬܐ، ܕܟܡܫܒܩܐ ܠܫܘܥܪܐ ܕܚܫܝܚܘܬܐ ܕܟܠ ܚܕ ܡܢ ܡܫܬܚܠܦ̈ܢܐ ܠܐ ܬܠܝ̈ܐ ܓܘ ܡܘܕܝܠ، ܠܒܘܚܪܢܐ ܕܦܐܝܘܬܐ ܟܠܢܝܬܐ ܕܡܘܕܝܠ ܠܝܗܝ̈ܒܬܐ، ܘܠܦܘܚܡܐ ܕܡܘܕܝ̈ܠܐ ܐܚܪ̈ܢܐ" – ܘܟܡܘܣܦܐ ܕ-SPSS ܓܢܣܗ ܠܐ ܟܐܚܕ ܠܗ̇ (ܣܢܝܩ ܝܠܗ AMOS).

ܫܘܝܘܬܐ ܚܕܐ ܒܠܚܘܕ – ܦܐܬܐ ܪܝܓܪܫܢ ܣܪܛܢܝܐ (ܗܢ ܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ، ܥܡ ܒܘܚܪܢܐ ܕܫܪ̈ܟܐ)؛ ܐܣܘܪܐ ܒܝܢܝ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܕܠܐ ܐܘܪܚܐ – ܦܐܬܐ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ؛ ܡܫܬܚܠܦܢܐ ܡܢܒܝܐ ܕܬܪܝܢ ܛܝ̈ܡܐ – ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ (ܦܘܫܩܐ ܕܫܒ̈ܝܠܐ ܟܣܐܡ ܡܫܬܚܠܦ̈ܢܐ ܡܢܒ̈ܝܐ ܟܡܝ̈ܝܐ)؛ ܥܠ̈ܠܬܐ ܟܣ̈ܝܬܐ – ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܡܫܪܪܢܐ (ܡܘܕܝܠ ܕܡܫܘܚܬܐ) ܘ-ܡܘܕܝܠ ܕܫܘܝ̈ܘܬܐ ܒܢܝܢܝ̈ܬܐ (ܫܒ̈ܝܠܐ ܒܝܢܝ ܥܠ̈ܠܬܐ ܟܣ̈ܝܬܐ) ܘ-ܡܨܥܝܘܬܐ ܒܝܢܝ ܥܠ̈ܠܬܐ ܟܣ̈ܝܬܐ (bootstrap ܐܝܟ lavaan)؛ ܡܘܕܝ̈ܠܐ ܠܐ ܪܩܘܪܣܝܒܝ̈ܐ (non-recursive؛ ܡܥܒ̈ܕܢܘܝܬܐ ܕܚܕ̈ܕܐ) – ܠܐ ܓܘ ܦܐܬܐ؛ ܡܪܟܟܢܘܬܐ (ܥܒܕܐ ܕܚܕ̈ܕܐ؛ Field، ܦܣܩܐ 11.3)، ܡܨܥܝܘܬܐ ܐܝܟ PROCESS ܘܡܨܥܝܘܬܐ ܡܪܟܟܬܐ – ܦܐܬܐ ܡܪܟܟܢܘܬܐ ܘܡܨܥܝܘܬܐ. ܡܢܝܢܐ ܕܣܒܠܬܐ ܕܦܣܘ̈ܩܐ ܣܓܝ̈ܐܐ (ܦܐܬܐ ܐܠܦܐ ܕ-Cronbach ܘܡܢܝܢܐ ܕܣܒܠܬܐ) ܡܬܚܫܒܐ ܝܠܗ ܐܝܟ ܡܫܬܚܠܦܢܐ ܕܪ̈ܘܚܩܐ ܫܘ̈ܝܐ (interval variable) ܠܦܘܬ ܥܝܕܐ ܕܣܐܝܛ (ܦܐܬܐ ܡܫܬܚܠܦ̈ܢܐ ܘܕܪ̈ܓܐ ܕܡܫܘܚܬܐ)؛ ܦܣܘܩܐ ܕ-Likert ܝܚܝܕܝܐ – ܠܐ.

ܣܘܟܠܐ: ܡܢ ܡܘܕܝܠ ܠܡܐܛܪܝܟܣ ܕܫܘܚܠ̈ܦܐ ܡܫܘܬ̈ܦܐ ܘܠܕܥܪܬܐ

ܡܘܕܝܠ ܝܠܗ ܣܕܪܐ ܕܫܘܝ̈ܘܬܐ ܕܪܝܓܪܫܢ. Field (2024، ܦܣܩܐ 11.4.2): "ܐܬܘ̈ܬܐ ܕܟܡܚܘܝ̈ܢ ܫܒ̈ܝܠܐ ܟܡܚܘܝ̈ܢ ܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ ܠܐ ܡܬܩ̈ܢܐ" – ܫܒܝܠܐ a ܝܠܗ B ܕ-X ܓܘ ܫܘܝܘܬܐ ܕ-M، ܫܒ̈ܝܠܐ b ܘ-c ܝܢܐ B ܕ-M ܘܕ-X ܓܘ ܫܘܝܘܬܐ ܕ-Y. ܓܘ ܬܫܥܝܬܐ (Baron & Kenny, 1986، ܓܘ Field) ܫܥܪܘܠܗܘܢ ܒܬܠܬܐ ܪܝܓܪܫ̈ܢܐ ܦܪ̈ܝܫܐ؛ ܦܘܫܩܐ ܕܫܒ̈ܝܠܐ ܟܡܫܥܪ ܟܠܗܝܢ ܒܚܕ ܙܒܢܐ ܒܐܘܪܚܐ ܕܡܬܚܙܝܢܘܬܐ ܥܠܝܬܐ (ML)، ܐܝܟ ܚܘܫܒܢܐ lavaan ܓܘ R: ܓܘ ܡܘܕܝܠ ܪܩܘܪܣܝܒܝܐ (recursive؛ ܕܠܐ ܚܘܕܪ̈ܐ) ܫܘ̈ܥܪܐ ܕܡ̈ܝܐ ܝܢܐ ܠܐܢܝ ܕܪܝܓܪܫܢ ܪܓܝܠܐ ܩܐ ܟܠ ܫܘܝܘܬܐ، ܘܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܙܥܘܪ̈ܬܐ ܝܢܐ ܩܠܝܠ (ܡܦܠܓܢܐ N ܒܕܘܟܬܐ ܕ-N − k − 1). ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܝܠܗ̇ product ܕܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ ܒܐܘܪܟܐ ܕܫܒܝܠܐ، ab (Field, Equation 11.6)؛ ܟܠܢܝܬܐ – c + ab. ܓܘ ܐܗܐ ܦܐܬܐ، ܥܡ ܟܡܐ ܫܒ̈ܝܠܐ ܠܐ ܬܪ̈ܝܨܐ ܒܝܢܝ ܙܘܓܐ ܕܡܫܬܚܠܦ̈ܢܐ، ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܝܠܗ̇ ܓܘܡܪܐ ܕ-products ܥܠ ܟܠ ܫܒ̈ܝܠܐ، ܘܡܥܒܕܢܘܬܐ ܟܠܢܝܬܐ ܚܫܝܒܬܐ ܝܠܗ̇ ܡܢ ܡܐܛܪܝܟܣ (I − A)⁻¹ ܕܟܠ ܫܒ̈ܝܠܐ.

ܡܘܕܝ ܒܚܝܪܐ ܝܠܗ ܓܘ χ². ܡܢ ܡܘܕܝܠ (ܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ ܘܫܘܚܠ̈ܦܐ ܕܛܥܝܘܬܐ) ܡܨܝܚ ܕܚܫܒܚ ܐܝܢܐ ܡܐܛܪܝܟܣ ܕܫܘܚܠ̈ܦܐ ܡܫܘܬ̈ܦܐ (covariance matrix) ܗܘ "ܟܡܣܟܐ" ܕܚܙܐ ܒܝܢܝ ܟܠ ܡܫܬܚܠܦ̈ܢܐ؛ ܟܦܚܡܚ ܠܗ̇ ܥܡ ܡܐܛܪܝܟܣ ܕܚܙܝܬܐ ܝܠܗ̇ ܒܥܒܕܐ. χ² ܟܡܫܚ ܦܘܪܫܢܐ، ܘܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom) ܝܢܐ ܡܢܝܢܐ ܕܫܘܚܠ̈ܦܐ ܘܫܘܚܠ̈ܦܐ ܡܫܘܬ̈ܦܐ ܓܘ ܝܗܝ̈ܒܬܐ ܒܨܝܪ ܡܢܝܢܐ ܕܦܪܡܝ̈ܛܪܐ ܕܡܘܕܝܠ ܟܡܫܥܪ. ܡܘܕܝܠ ܕܓܘܗ ܟܠ ܓܐܪܐ ܕܡܨܐ ܕܗܘܐ ܐܝܬܘܗܝ (ܠܡܬܠܐ ܡܨܥܝܘܬܐ ܦܫܝܛܬܐ X → M → Y ܥܡ ܫܒܝܠܐ ܬܪܝܨܐ) ܝܠܗ ܡܠܝܐ (saturated): df = 0، ܦܐܝܘܬܐ ܓܡܝܪܬܐ ܡܢ ܬܚܘܡܐ، ܘܠܝܬ ܡܕܡ ܕܒܚܪܚ ܠܒܪ ܡܢ ܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ. ܒܣ ܐܡܬܝ ܕܡܘܕܝܠ ܟܫܩܠ ܐܣܘܪܐ (ܠܡܬܠܐ: ܠܝܬ ܫܒܝܠܐ ܬܪܝܨܐ ܡܢ "קבוצה" ܠ-"שימוש_יומי" ܓܘ ܦܐܝܠ ܕܡܬܠܐ) ܐܝܬ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ، ܘ-χ² ܟܒܚܪ ܐܢ ܫܩܠܬܐ ܫܠܝܡܬܐ ܝܠܗ̇ ܥܡ ܝܗܝ̈ܒܬܐ – ܗܪܟܐ p ܪܒܐ ܡܢ .05 ܝܠܗ ܦܐܪܐ ܕܒܥܝܚ. ܡܚܘ̈ܝܢܐ ܐܚܪ̈ܢܐ ܕܦܐܝܘܬܐ (CFI, TLI, RMSEA, SRMR) ܟܡܦܫܩܝ ܗܘ ܦܘܪܫܢܐ ܠܣܒ̈ܠܬܐ ܕܬܠܝ̈ܐ ܒܨܝܪ ܝܢܐ ܥܠ ܪܒܘܬܐ ܕܕܘܡܝܐ، ܘ-AIC ܘ-BIC ܡܦܠܚ̈ܐ ܝܢܐ ܩܐ ܦܘܚܡܐ ܕܡܘܕܝ̈ܠܐ ܐܚܪ̈ܢܐ ܥܠ ܗܢ ܝܗܝ̈ܒܬܐ (American Psychological Association [APA], 2020، ܠܘܚܐ 7.19 – ܠܘܚܐ ܕܦܘܚܡܐ ܕܡܘܕܝ̈ܠܐ ܥܡ χ²، RMSEA، AIC ܘ-BIC). ܦܐܬܐ ܟܚܫܒ ܟܠ ܐܢܝ ܚܬܝܬܐܝܬ ܐܝܟ lavaan (ܕܡܝܘܬܐ ܥܕܡܐ ܡܢܝܢܐ ܫܬܝܬܝܐ ܓܘ ܡܚܘ̈ܝܢܐ، ܓܘ ܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ، ܓܘ ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܘܓܘ ܡܥܒ̈ܕܢܘܝܬܐ ܬܚܘܡ̈ܬܐ).

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܘܚܐ 1 – ܦܐܝܘܬܐ. ܩܕܡܝܬ df: ܐܢ 0 – ܡܘܕܝܠ ܡܠܝܐ ܝܠܗ ܘܠܘܚܐ 1 ܣܦܝܩܐ ܝܠܗ ܡܢ ܝܕܥܬܐ. ܐܢ ܠܐ: χ² ܥܡ p (ܟܒܥܝܚ ܠܐ ܪܫܝܡܐ)، ܘܒܬܪ ܗܕܐ ܡܚܘ̈ܝܢܐ ܠܦܘܬ Hu ܘ-Bentler (1999، ܦܐܬܐ 27): ܛܝܡܐ "ܩܪܝܒܐ ܠ-.95" ܩܐ CFI ܘ-TLI، "ܩܪܝܒܐ ܠ-.06" ܩܐ RMSEA ܘ"ܩܪܝܒܐ ܠ-.08" ܩܐ SRMR ܟܡܚܘܝ ܦܐܝܘܬܐ ܛܒܬܐ ܒܡܫܘܚܬܐ؛ Brown (2015، ܦܐ̈ܬܐ 74-75) ܟܡܘܣܦ ܦܬܝ̈ܘܬܐ ܡܩܒ̈ܠܬܐ – CFI ܘ-TLI ܒܝܢܝ .90 ܘ-.95 (Bentler, 1990، ܐܝܟ ܕܡܬܡܠܠܐ ܓܘܗ)، RMSEA ܥܕܡܐ .08 (Browne & Cudeck, 1993، ܐܝܟ ܕܡܬܡܠܠܝ ܓܘܗ) – ܘܟܡܚܝܠ ܕ"ܩܪܝܒܐ ܠ-" ܠܐ ܝܠܗ ܡܢ ܓܕܫܐ: ܬܚܘ̈ܡܐ ܫܚܠܦܠܗܘܢ ܠܦܘܬ ܫܪ̈ܛܐ ܕܡܘܕܝܠ. simulations ܕ-Hu ܘ-Bentler ܥܒܝܕ̈ܐ ܝܢܐ ܥܠ ܡܘܕܝ̈ܠܐ ܥܡ ܡܫܬܚܠܦ̈ܢܐ ܟܣ̈ܝܐ، ܘܡܛܠ ܗܕܐ ܓܘ ܡܘܕܝܠ ܕܫܒ̈ܝܠܐ ܕܡܫܬܚܠܦ̈ܢܐ ܚܙ̈ܝܐ ܬܚܘ̈ܡܐ ܩܘܪܒܐ ܝܢܐ. ܩܠ̈ܝܬܐ ܠܒܪ ܡܢ ܦܬܝܘܬܐ ܡܩܒܠܬܐ ܡܛܠ̈ܠܬܐ ܝܢܐ. χ² ܪܓܝܫܐ ܝܠܗ ܠܪܒܘܬܐ ܕܕܘܡܝܐ: ܓܘ ܕܘܡܝܐ ܪܒܐ ܟܠ ܦܘܪܫܢܐ ܙܥܘܪܐ ܟܢܦܩ ܪܫܝܡܐ، ܘܓܘ ܕܘܡܝܐ ܙܥܘܪܐ ܠܒܘܚܪܢܐ ܠܝܬ ܚܝܠܐ – ܡܛܠ ܗܕܐ ܟܩܪܚ ܟܠ ܡܚܘ̈ܝܢܐ ܐܟܚܕܐ، ܘܩܘܦܣܐ ܕ"ܩܪܝܢܐ ܕܦܐܪܐ" ܟܐܡܪܐ ܐܢ ܫܠܝܡ̈ܐ ܝܢܐ.

ܠܘܚܐ 2 – ܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ ܕܫܒ̈ܝܠܐ. ܩܐ ܟܠ ܓܐܪܐ: B (ܠܐ ܡܬܩܢܐ – "ܫܘܢܝܐ ܓܘ ܡܢܒܝܐ ܩܐ ܟܠ ܡܫܘܚܬܐ ܓܘ ܡܢܒܝܢܐ، ܐܡܬܝ ܕܐܚܪ̈ܢܐ ܩܝܡ̈ܐ ܝܢܐ"؛ Field, 2024، ܦܣܩܐ 9.11.3)، ܛܥܝܘܬܐ ܬܩܝܢܬܐ، z ܘ-p (ܫܘܥܪܐ ML – ܦܘܠܓܐ ܢܘܪܡܠܝܐ، ܠܐ t)، ܬܚܘܡܐ ܕܬܘܟܠܢܐ 95%، ܘ-β ܡܬܩܢܐ ܩܐ ܦܘܚܡܐ ܒܝܢܝ ܫܒ̈ܝܠܐ ܘܒܝܢܝ ܒܘܨ̈ܝܐ. Field (ܦܣܩܐ 11.4.5) ܟܩܪܐ ܡܦܩܢܐ ܫܒܝܠܐ ܒܬܪ ܫܒܝܠܐ: "ܚܙܝܬܐ ܕܦܘܪܢܘܓܪܐܦܝܐ ܟܡܢܒܝܐ ܪܫܝܡܐܝܬ ܩܝܡܐ ܕܙܘܘܓܐ، B = −0.47, 95% CI [−0.94, −0.00], p = .048؛ ܪܘܫܡܐ ܣܠܝܒܐ ܟܐܡܪ ܕܟܡܐ ܕܚܙܝܬܐ ܟܣܠܩܐ، ܩܝܡܐ ܟܢܚܬ".

ܠܘܚܐ 3 – R² ܘܫܘܚܠܦܐ ܕܛܥܝܘܬܐ ܩܐ ܟܠ ܡܫܬܚܠܦܢܐ ܡܢܒܝܐ: ܟܡܐ ܡܢ ܫܘܚܠܦܐ (variance) ܕܝܠܗ ܫܘܝܘܬܐ ܕܝܠܗ ܟܡܦܫܩܐ (Field ܟܡܘܕܥ ܓܘ ܡܬܠܐ ܕܝܠܗ 2% ܩܐ ܩܝܡܐ ܘ-11.4% ܩܐ ܢܟܠܐ).

ܠܘܚܐ 4 – ܡܥܒ̈ܕܢܘܝܬܐ. ܩܐ ܟܠ ܙܘܓܐ ܕܐܝܬ ܒܝܢܝܗܘܢ ܫܒܝܠܐ ܠܐ ܬܪܝܨܐ: ܡܥܒܕܢܘܬܐ ܬܪܝܨܬܐ، ܠܐ ܬܪܝܨܬܐ (ab) ܥܡ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܒܐܘܪܚܐ ܕ-delta (ܒܘܚܪܢܐ ܕ-Sobel) ܘ-p، ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܒ-delta، ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܒ-bootstrap، ܡܥܒܕܢܘܬܐ ܟܠܢܝܬܐ ܥܡ ܬܚܘܡܐ ܕ-bootstrap، ܘܡܚܘܝܢܐ ܕܡܨܥܝܘܬܐ. ܐܝܢܐ ܬܚܘܡܐ ܟܩܪܚ؟ ܗܪܟܐ ܡܒܘ̈ܥܐ ܫܠܝܡ̈ܐ ܝܢܐ: Field (ܦܣ̈ܩܐ 11.4.2 ܘ-11.4.6) – "ܓܒܐܠܝ ܙܒܢ̈ܐ ܣܓܝ̈ܐܐ ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܕ-bootstrap، ܘܡܛܠ ܗܕܐ ܡܘܕܥܘܢ ܠܗܘܢ"؛ ܥܠܬܐ: ܦܘܠܓܐ ܕ-product ab ܠܐ ܝܠܗ ܢܘܪܡܠܝܐ ܘܠܐ ܫܘܐ ܠܬܪܝܢ ܓܢ̈ܒܐ، ܘܬܚܘܡܐ ܫܘܐ ܕ-delta ܚܬܝܬܐ ܒܨܝܪ ܝܠܗ ܓܘ ܕܘ̈ܡܝܐ ܙܥܘܪ̈ܐ. ܦܣܩܐ: ܬܚܘܡܐ ܕ-bootstrap ܕܠܐ ܟܐܚܕ ܨܦܪܐ – "ܟܡܝܠܚ ܕܫܠܡܚ ܕܗܘܝܠܗ̇ ܡܨܥܝܘܬܐ" (Field، ܡܠܟ̈ܐ ܕ-Sam). bootstrap ܓܘ ܦܐܬܐ ܥܡ ܙܪܥܐ ܝܠܗ (ܗܘ ܙܪܥܐ – ܗܘ ܬܚܘܡܐ ܓܘ ܟܠ ܪܗܛܐ، ܓܘ ܟܠ ܡܚܫܒܢܐ؛ ܫܚܠܦܘܢ ܙܪܥܐ ܕܚܙܝܬܘܢ ܟܡܐ ܬܚܘܡܐ ܓܢܣܗ ܟܫܢܐ)، ܘܡܘܠܕܢܐ (generator) ܝܠܗ ܡܘܠܕܢܐ ܕ-R: ܙܪܥܐ 2026 ܓܘ ܦܐܬܐ ܘ-iseed = 2026 ܓܘ lavaan ܟܝܗܒܝ ܗܢ ܕܘܡ̈ܝܐ ܘܗܘ ܬܚܘܡܐ ܕܕܪ̈ܓܐ ܡܢ ܡܐܐ (ܡܕܒܪܢܐ ܕ-R ܠܬܚܬ)؛ PROCESS ܕ-Hayes ܟܛܒܥ ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ ܬܚܘܡܐ BCa (ܡܬܘܪܨܐ ܡܢ ܡܣܒ ܒܐܦ̈ܐ)، ܩܪܝܒܐ ܐܠܐ ܠܐ ܕܡܝܐ.

ܨܘܪܬܐ ܕܫܒ̈ܝܠܐ – ܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ ܡܬܩ̈ܢܐ ܥܠ ܓܐܪ̈ܐ، ܓܐܪܐ ܡܢܩܛܐ ܩܐ ܫܒܝܠܐ ܠܐ ܪܫܝܡܐ؛ Field (ܦܣܩܐ 11.4.6، ܨܘܪܬܐ 11.12) ܟܡܪܚܩ ܕܡܚܘܝܚ ܡܘܕܝܠ ܗܟܢܐ ܓܘ ܬܘܢܝܐ. ܦܣܩܐ ܕܡܫܟܚ̈ܢܘܬܐ – ܦܐܝܘܬܐ، ܫܒ̈ܝܠܐ، ܡܥܒ̈ܕܢܘܝܬܐ ܠܐ ܬܪ̈ܝܨܬܐ ܘ-R²، ܒܣܘܪܝܬ ܘܒܐܢܓܠܝܙܝܐ. ܩܘܦܣܐ ܕ"ܩܪܝܢܐ ܕܦܐܪܐ" – ܐܝܢܐ ܡܚܘ̈ܝܢܐ ܫܠܝܡ̈ܐ ܝܢܐ؟، ܦܘܚܡܐ ܕܡܫܬܘܬܦ̈ܢܐ ܠܦܪܡܝ̈ܛܪܐ، delta ܩܘܒܠ bootstrap، ܡܨܥܝܘܬܐ ܡܢܬܢܝܬܐ/ܓܡܝܪܬܐ ܘܡܨܥܝܘܬܐ ܠܐ ܫܠܝܡܬܐ (inconsistent mediation)، ܘܡܥܗܕܢܘܬܐ ܕܡܘܕܝܠ ܩܕܡ ܝܠܗ ܡܢ ܝܗܝ̈ܒܬܐ.

ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size)

Field (2024، ܦܣܩܐ 11.4.3): "ܦܫܝܛܐ ܝܬܝܪ ܝܠܗ ܕܚܙܝܚ B ܕܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕܝܠܗ" – ab ܝܠܗ ܡܢܝܢܐ ܡܫܘܬܦܐ ܕܪܝܓܪܫܢ ܓܡܝܪܐܝܬ، ܓܘ ܡܫܘ̈ܚܬܐ ܕܡܫܬܚܠܦܢܐ ܡܢܒܝܐ. ܩܐ ܦܘܚܡܐ ܒܝܢܝ ܒܘܨ̈ܝܐ ܟܡܬܩܢܚ: ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܡܬܩܢܬܐ ܡܢܬܢܐܝܬ – ab ܡܦܠܓܐ ܥܠ ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܡܢܒܝܐ (MacKinnon, 2008، ܓܘ Field، ܫܘܝܘܬܐ 11.7)، ܘܡܚܘܝܢܐ ܕܡܨܥܝܘܬܐ (index of mediation) – ܡܣܘܓܐܐ ܐܦ ܥܠ ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܡܢܒܝܢܐ (Preacher & Hayes, 2008، ܓܘ Field، ܫܘܝܘܬܐ 11.8)، ܗܢܘ ܕܐܡܪ ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܡܬܩܢܬܐ ܓܡܝܪܐܝܬ؛ Field ܟܡܘܕܥ ܠܗ ܓܘ ܡܬܠܐ ܕܝܠܗ: "0.04 – ܙܥܘܪܐ ܣܓܝ". ܠܘܚܐ 4 ܟܛܒܥ ܡܚܘܝܢܐ ܕܡܨܥܝܘܬܐ، ܘܩܘܦܣܐ ܕܩܪܝܢܐ ܐܦ ܡܬܩܢܐ ܡܢܬܢܐܝܬ. ܩܐ ܟܠ ܫܘܝܘܬܐ R² ܝܠܗ ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size) ܟܠܢܝܬܐ (ܡܫܘܚܬܐ ܕ-Cohen, 1988، ܦܐ̈ܬܐ 413-414: .02 / .13 / .26)، ܘ-β ܕܟܠ ܫܒܝܠܐ – ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ ܕܫܒܝܠܐ ܝܚܝܕܝܐ. ܦܘܚܡܐ "ܠܐ ܬܪܝܨܬܐ ܡܦܠܓܐ ܥܠ ܟܠܢܝܬܐ" (P_M) ܠܐ ܝܠܗ ܛܒܝܥܐ: ܠܐ ܝܠܗ ܟܪܝܐ ܠ-0-1 ܘܟܦܩܥ ܐܡܬܝ ܕܡܥܒܕܢܘܬܐ ܟܠܢܝܬܐ ܙܥܘܪܬܐ ܝܠܗ̇ (ܡܨܥܝܘܬܐ ܠܐ ܫܠܝܡܬܐ).

ܫܪ̈ܛܐ ܘܙܘܗܪ̈ܐ (Assumptions and warnings)

ܡܘܕܝܠ ܩܕܡ ܝܠܗ ܡܢ ܝܗܝ̈ܒܬܐ. ܛܘܟܣܐ ܕܓܐܪ̈ܐ ܟܦܣܩܐ ܠܗ ܬܐܘܪܝܐ – ܠܐ ܚܘܫܒܢܐ ܘܠܐ ܦܐܝܘܬܐ. Field (2024، ܦܣܩܐ 11.4.1) ܟܟܬܒ ܫܪ̈ܛܐ ܕܡܨܥܝܘܬܐ ܐܝܟ ܗܘܦܘܬܣ̈ܝܣ ܡܢ ܩܕܡ ("ܩܐ ܕܗܘܦܘܬܣܝܣ ܗܘܝܐ ܬܪܝܨܬܐ: (1)… (4)…")؛ ܦܘܫܩܐ ܕܫܒ̈ܝܠܐ ܟܒܚܪ ܐܢ ܡܘܕܝܠ ܝܗܝܒܐ ܫܠܝܡܐ ܝܠܗ ܥܡ ܝܗܝ̈ܒܬܐ، ܠܐ ܐܢ ܬܪܝܨܐ ܝܠܗ – ܡܘܕܝ̈ܠܐ ܐܚܪ̈ܢܐ (ܓܐܪ̈ܐ ܗܦܝ̈ܟܐ، ܡܨܥܝܐ ܕܠܐ ܡܫܘܚܐ ܝܠܗ) ܡܨܝܝ ܕܦܐܝܝ ܒܗܝ ܡܫܘܚܬܐ، ܘ-Pallant (2020، ܨܚܚܐ 10) ܟܡܚܘܝܐ ܕ-SEM "ܟܡܫܒܩ ܠܦܘܚܡܐ ܕܡܘܕܝ̈ܠܐ ܐܚܪ̈ܢܐ". ܡܘܕܝܠ ܕܫܘܚܠܦܐ ܝܠܗ ܒܬܪ ܚܙܝܬܐ ܕܡܫܟܚ̈ܢܘܬܐ (ܐܘܣܦܬܐ ܕܓܐܪܐ "ܕܦܐܝܐ") ܦܘܫܩܐ ܡܒܨܝܢܐ (exploratory) ܝܠܗ ܘܟܡܘܕܥܚ ܠܗ ܗܟܢܐ.

ܪܩܘܪܣܝܒܝܘܬܐ (recursiveness). ܦܐܬܐ ܟܡܩܒܠ ܡܘܕܝ̈ܠܐ ܕܠܐ ܚܘܕܪ̈ܐ (DAG): ܡܫܬܚܠܦܢܐ ܠܐ ܡܨܐ ܕܡܥܒܕ ܥܠ ܓܢܣܗ، ܬܪܝܨܐܝܬ ܝܢ ܒܐܘܪܚܐ ܕܐܚܪ̈ܢܐ. ܡܥܒ̈ܕܢܘܝܬܐ ܕܚܕ̈ܕܐ ܕܡܘܕܝ̈ܠܐ ܠܐ ܪܩܘܪܣܝܒܝ̈ܐ ܣܢܝܩ̈ܐ ܝܢܐ ܠܡܫܬܚܠܦ̈ܢܐ instrumental – ܠܐ ܓܘ ܦܐܬܐ.

ܫܪ̈ܛܐ ܕܪܝܓܪܫܢ ܩܐ ܟܠ ܫܘܝܘܬܐ (Field, Section 9.4.1): ܣܪܛܢܝܘܬܐ (linearity) ܘ-additivity، ܠܐ ܬܠܝܘܬܐ ܕܫܪ̈ܟܐ (independence of residuals)، ܫܘܝܘܬܐ ܕܫܘܚܠ̈ܦܐ (homoscedasticity) ܘܢܘܪܡܠܝܘܬܐ (normality). ܫܘܥܪܐ ܕ-ML ܟܣܒܪ ܢܘܪܡܠܝܘܬܐ ܕܡܫܬܚܠܦ̈ܢܐ ܣܓܝ̈ܐܐ (multivariate normality) ܕܡܫܬܚܠܦ̈ܢܐ ܕܦܐܪܐ (outcome variables)؛ ܬܒܪܐ ܕܝܗ̇ ܟܡܥܩܡ χ² ܘܛܥܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ (standard errors). ܒܘܚܪܢܐ ܕܫܪ̈ܟܐ ܕܟܠ ܫܘܝܘܬܐ – ܓܘ ܦܐܬܐ ܪܝܓܪܫܢ ܣܪܛܢܝܐ (ܠܘܚܐ ܕܒܘܚܪܢܐ ܘܨܘܪܬܐ ZRESID)، ܘܕܡܫܬܚܠܦ̈ܢܐ ܒܓܢܣܗܘܢ – ܓܘ ܦܐܬܐ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܫܪ̈ܛܐ. Field (ܦܣܩܐ 11.4.4) ܟܡܩܪܒ ܓܘ PROCESS ܛܥܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ ܚܣܝ̈ܢܬܐ ܩܐ heteroscedasticity (HC4) – ܠܐ ܓܘ ܦܐܬܐ.

ܪܒܘܬܐ ܕܕܘܡܝܐ. ܢܡܘܣܐ ܕܨܒܥܐ (rule of thumb) ܥܬܝܩܐ: ܥܣܪܐ ܡܫܬܘܬܦ̈ܢܐ (participants) ܩܐ ܟܠ ܦܪܡܝܛܪ (parameter) ܡܫܘܥܪܐ (ܫܒ̈ܝܠܐ ܘܫܘܚܠ̈ܦܐ ܕܛܥܝܘܬܐ)؛ ܦܐܬܐ ܟܡܙܗܪܐ ܐܢ ܒܨܝܪ ܝܠܗ. ܢܡܘ̈ܣܐ ܕܪܝܓܪܫܢ ܕ-Pallant (2020، ܨܚܚܐ 13: N > 50 + 8m، 15 ܩܐ ܟܠ ܡܢܒܝܢܐ) ܥܠ ܟܠ ܫܘܝܘܬܐ ܒܦܪܝܫܘܬܐ ܝܢܐ. Field (ܦܣܩܐ 11.4.7) ܟܐܡܪ ܕܓܘ ܕܘܡܝܐ ܪܒܐ ܒܣܓܝ (947) "ܠܝܬ ܛܝܡܐ ܓܘ bootstrap" – ܘܓܘ ܕܘܡܝܐ ܙܥܘܪܐ ܐܝܬܘܗܝ ܣܢܝܩܐ ܝܬܝܪ.

ܙܢ̈ܐ ܕܡܫܬܚܠܦ̈ܢܐ. ܡܫܬܚܠܦ̈ܢܐ ܕܦܐܪܐ (outcome variables) ܟܡܝ̈ܐ ܘܡܬܡܫܚ̈ܢܐ (continuous) ܝܢܐ؛ ܡܢܒ̈ܝܢܐ (predictors) ܟܡܝ̈ܐ ܝܢ ܕܬܪܝܢ ܛܝ̈ܡܐ (ܓܘܕܐ 1/2 – B ܕܝܠܗ ܝܠܗ ܦܘܪܫܢܐ ܕܡܨܥܝ̈ܬܐ)؛ ܡܫܬܚܠܦܢܐ ܕܓܢ̈ܣܐ (categorical variable) ܥܡ ܬܠܬܐ ܕܪ̈ܓܐ ܘܝܬܝܪ ܣܢܝܩ ܝܠܗ ܠܪܡܙܢܘܬܐ ܕܡܫܬܚܠܦ̈ܢܐ ܕܓܠܐ (dummy coding؛ Field, Section 9.4.1)، ܕܠܐ ܐܝܬ ܓܘ ܦܐܬܐ؛ ܡܫܬܚܠܦܢܐ ܕܛܟܣܐ (ordinal variable) ܟܥܐܠ ܐܝܟ ܡܢܝܢܐ ܥܡ ܙܘܗܪܐ. ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (missing values) – ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (listwise deletion) ܥܠ ܟܠ ܡܫܬܚܠܦ̈ܢܐ ܕܡܘܕܝܠ (ܦܐܬܐ ܟܡܘܕܥܐ ܟܡܐ ܫܒܝܩ̈ܐ ܝܢܐ)؛ FIML، ܐܘܪܚܐ ܡܩܒܠܬܐ ܓܘ SEM ܩܐ ܚܣܝ̈ܪܐ، ܠܐ ܐܝܬ ܓܘ ܦܐܬܐ – ܚܙܝܡܘܢ ܦܐܬܐ ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ. ܡܫܬܚܠܦ̈ܢܐ exogenous ܡܚܫ̈ܒܐ ܝܢܐ ܩܝ̈ܡܐ (fixed.x، ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ (default) ܕ-lavaan): ܫܘܚܠ̈ܦܐ ܘܫܘܚܠ̈ܦܐ ܡܫܘܬܦ̈ܐ (covariances) ܒܝܢܝܗܝ ܫܩܝ̈ܠܐ ܝܢܐ ܡܢ ܕܘܡܝܐ ܘܠܐ ܡܫܘܥܪ̈ܐ ܝܢ ܡܢܝ̈ܐ ܝܢܐ ܐܝܟ ܦܪܡܝ̈ܛܪܐ.

ܡܨܥܝܘܬܐ ܠܐ ܫܠܡܬܐ (inconsistent mediation). ܐܝܡܢ ܕܡܥܒܕܢܘܬܐ ܬܪܝܨܬܐ (direct effect) ܘܠܐ ܬܪܝܨܬܐ (indirect effect) ܒܪ̈ܘܫܡܐ ܗܦܝ̈ܟܐ ܝܢܐ، ܡܥܒܕܢܘܬܐ ܟܠܢܝܬܐ (total effect) ܙܥܘܪܬܐ ܝܠܗ̇ ܡܢ ܬܪܘܝܗܝ – ܘܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation) ܦܫܝܛܐ ܒܝܢܝ X ܘ-Y ܡܨܐ ܕܗܘܐ ܣܦܪ ܐܦܢ ܕܐܝܬ ܡܨܥܝܘܬܐ (mediation) ܫܪܝܪܬܐ. ܐܗܐ ܝܠܗ ܥܠܬܐ ܕ-Field (ܦܣܩܐ 11.4.2) ܟܡܣܠܐ ܫܪܛܐ ܩܕܡܝܐ ܕ-Baron ܘ-Kenny ("X ܣܢܝܩ ܝܠܗ ܠܡܢܒܝܐ Y ܩܕܡ") ܐܝܟ ܫܪܛܐ ܕܠܐ ܡܨܐ ܕܠܐ ܗܘܐ؛ ܩܘܛܝܐ ܕܩܪܝܢܐ ܟܡܪܫܡ ܚܠܬܐ ܐܝܟ ܗܕܐ. "ܡܨܥܝܘܬܐ ܓܡܝܪܬܐ" ܘ"ܡܢܬܢܝܬܐ" – ܠܫܢܐ ܕ-Baron ܘ-Kenny: ܐܢ ܫܒܝܠܐ ܬܪܝܨܐ ܠܐ ܝܠܗ ܪܫܝܡܐ ܣܛܐܛܝܣܛܝܩܐܝܬ (statistically significant) ܥܡ ܠܐ ܬܪܝܨܐ، "ܓܡܝܪܬܐ". Field ܟܡܙܗܪ ܡܢ "ܚܘܫܒܐ ܕܐܘܟܡܐ-ܚܘܪܐ": p ܕܥܒܪ ܡܢ .049 ܠ-.051 ܠܐ ܝܠܗ ܫܘܢܝܐ، ܘ-B ܕܢܚܬ ܡܢ .46 ܠ-.18 ܝܠܗ ܫܘܢܝܐ ܐܦܢ ܬܪܘܝܗܝ ܪ̈ܫܝܡܐ ܝܢܐ – ܟܡܘܕܥܚ ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܕܝܠܗ̇.

ܡܘܕܝ ܠܐ ܟܚܫܒܐ ܐܗܐ ܦܐܬܐ. ܥܠ̈ܠܬܐ ܟܣ̈ܝܬܐ (latent factors) ܘ-CFA، ܡܘܕܝ̈ܠܐ ܠܐ recursive، ܦܘܚܡܐ ܕܡܘܕܝ̈ܠܐ (Δχ²) ܘܡܘܕܝ̈ܠܐ ܕܓܘ̈ܕܐ ܣܓܝ̈ܐܐ، ܡܚܘ̈ܝܢܐ ܕܫܘܢܝܐ (modification indices)، FIML ܩܐ ܚܣܝ̈ܪܐ، ܛܥܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ ܚܣܝ̈ܢܬܐ (MLR, HC4)، ܬܚܘܡܐ ܕ-bootstrap ܕܙܢܐ BCa، ܡܫܬܚܠܦ̈ܢܐ ܕܓܠܐ (dummy variables) ܐܘܛܘܡܛܝ̈ܐ، ܡܪܟܟܢܘܬܐ (moderation) ܘܡܨܥܝܘܬܐ ܡܪܟܟܬܐ (moderated mediation؛ Field, Section 11.3)، P_M ܘ-κ² (Preacher & Kelley, 2011، ܓܘ Field).

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

ܓܘ SPSS ܠܝܬ ܦܘܫܩܐ ܕܫܒ̈ܝܠܐ (path analysis): Pallant (2020، ܨܚܚܐ 10) – "ܓܘ IBM SPSS Statistics ܠܝܬ ܡܢܬܐ ܩܐ ܡܘܕܝ̈ܠܐ ܕܫܘܝ̈ܘܬܐ ܒܢܝܢܝ̈ܬܐ، ܐܠܐ ܟܡܣܡܟ ܠܬܘܣܦܬܐ AMOS". ܬܪܝܢ ܐܘܪ̈ܚܬܐ ܡܩܒ̈ܠܬܐ: (1) AMOS – ܟܨܝܪܚ ܡܘܕܝܠ ܘܟܫܩܠܚ ܗܢܝ ܠܘ̈ܚܐ (ܫܘܥܪ̈ܐ ܕ-ML، ܡܚܘ̈ܝܢܐ ܕܦܐܝܘܬܐ (fit indices)، ܡܥܒܕ̈ܢܘܝܬܐ ܬܪ̈ܝܨܬܐ/ܠܐ ܬܪ̈ܝܨܬܐ/ܟܠܢ̈ܝܬܐ، bootstrap)؛ (2) PROCESS ܕ-Hayes (ܬܘܣܦܬܐ ܡܓܢ) ܩܐ ܡܘܕܝ̈ܠܐ ܕܡܨܥܝܘܬܐ ܘܡܪܟܟܢܘܬܐ – ܐܘܪܚܐ ܕ-Field (2024، ܦܣ̈ܩܐ 11.4.4-11.4.5): Analyze › Regression › PROCESS، ܡܫܬܚܠܦܢܐ ܕܦܐܪܐ ܠ-Y، ܡܢܒܝܢܐ ܠ-X، ܡܨܥܝܐ (mediator؛ ܝܢ ܟܡܐ) ܠ-Mediator(s) M، ܡܘܕܝܠ 4، Bootstrap inference for model coefficients، ܘܓܘ ܓܘܒ̈ܝܐ Effect size ܘ-Total effect model؛ ܡܦܩܢܐ (output) – ܟܬܒܐ: ܫܘܝܘܬܐ ܕ-M (ܫܒܝܠܐ a)، ܫܘܝܘܬܐ ܕ-Y (b ܘ-c)، ܡܥܒܕܢܘܬܐ ܟܠܢܝܬܐ، ܘ"Indirect effect of X on Y" ܥܡ ܬܚܘܡܐ ܕ-bootstrap (BCa) ܘܡܚܘܝܢܐ ܕܡܨܥܝܘܬܐ. PROCESS ܟܪܝܐ ܝܠܗ ܠܛܘܦ̈ܣܐ ܕܡܘܕܝ̈ܠܐ ܕܝܠܗ (ܡܨܥܝ̈ܐ ܒܓܢܒ ܚܕ̈ܕܐ، ܠܐ ܫܫܠܬܐ ܐܪܝܟܬܐ ܘܠܐ ܟܡܐ ܡܫܬܚܠܦ̈ܢܐ ܕܦܐܪܐ)؛ ܡܘܕܝܠ ܓܘܢܝܐ – AMOS ܝܢ lavaan.

ܣܝܢܬܐܟܣ (syntax) ܕܦܐܬܐ ܟܒܢܐ ܟܪܗܛ ܫܘܝ̈ܘܬܐ ܕܡܘܕܝܠ ܐܝܟ ܪܝܓܪ̈ܫܢܐ ܦܪ̈ܝܫܐ ܓܘ SPSS (ܐܘܪܚܐ ܕ-Baron ܘ-Kenny، Field، ܦܣܩܐ 11.4.2)، ܒܬܪ SELECT IF ܕܟܡܬܢܐ ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ: B، Beta ܘ-R Square ܫܘ̈ܝܐ ܝܢܐ ܠܠܘ̈ܚܐ 2-3؛ ܛܥܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ، t ܘ-p ܦܪ̈ܝܫܐ ܝܢܐ ܩܠܝܠ (OLS ܩܘܒܠ ML)؛ ܡܚܘ̈ܝܢܐ ܕܦܐܝܘܬܐ ܘܡܥܒܕ̈ܢܘܝܬܐ ܠܐ ܬܪ̈ܝܨܬܐ ܠܐ ܦܠܛܝ – ܩܐ ܐܢܝ PROCESS ܝܢ AMOS. ܩܐ ܡܘܕܝܠ ܕܡܬܠܐ:

SELECT IF (NOT MISSING(גיל) AND NOT MISSING(קבוצה) AND NOT MISSING(עמדות_ציון) AND NOT MISSING(שימוש_יומי)).
EXECUTE.
REGRESSION
  /MISSING LISTWISE
  /STATISTICS COEFF OUTS CI(95) R ANOVA
  /NOORIGIN
  /DEPENDENT עמדות_ציון
  /METHOD=ENTER קבוצה גיל.
REGRESSION
  /MISSING LISTWISE
  /STATISTICS COEFF OUTS CI(95) R ANOVA
  /NOORIGIN
  /DEPENDENT שימוש_יומי
  /METHOD=ENTER עמדות_ציון גיל.

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

ܚܒܝܫܘܬܐ lavaan ܝܠܗ̇ ܬܩܢܐ: ܟܟܬܒܚ ܡܘܕܝܠ ܐܝܟ ܫܘܝ̈ܘܬܐ (~ ܩܐ ܪܝܓܪܫܢ)، ܟܝܗܒܚ ܪܘ̈ܫܡܐ (labels) ܠܫܒ̈ܝܠܐ ܘܟܡܚܕܕܚ ܡܥܒܕ̈ܢܘܝܬܐ ܠܐ ܬܪ̈ܝܨܬܐ ܘܟܠܢ̈ܝܬܐ ܒ-:=؛ sem() ܟܡܫܘܥܪܐ ܒ-ML ܥܡ fixed.x = TRUE (ܓܘܒܝܐ ܡܩܕܡܐ – ܚܬܝܬܐܝܬ ܬܘܩܢܐ ܕܦܐܬܐ)، summary(fit.measures = TRUE, standardized = TRUE) ܟܝܗܒ ܠܘ̈ܚܐ 1-4 (ܥܡܘܕܐ Std.all = β)، ܘ-se = "bootstrap" ܥܡ parameterEstimates(boot.ci.type = "perc") – ܬܚܘ̈ܡܐ ܕ-bootstrap؛ ܥܡ iseed ܫܘܝܐ ܠܙܪܥܐ ܕܦܐܬܐ – ܗܢܝ ܕܘ̈ܡܝܐ ܘܗܢܝ ܬܚܘ̈ܡܐ ܐܝܟ ܓܘ ܦܐܬܐ. ܣܩܪܝܦܬ ܪܗܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ ܘܝܗܒܠܗ ܛܝ̈ܡܐ ܕܠܘ̈ܚܐ (ܓܘ ܡܥܝܪ̈ܢܘܬܐ). ܢܡܘܣܐ ܕܣܐܝܛ ܩܐ ܣܘܪܝܬ ܓܘ R: ܦܐܝܠ UTF-8، ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ، ܫܡ̈ܗܐ ܟܪ̈ܝܐ ܒܐܢܓܠܝܙܝܐ ܩܐ ܡܬܢܝܬܐ، ܘܣܒܝܒܘܬܐ UTF-8 ܩܐ ܫܡ̈ܗܐ ܥܒܪ̈ܝܐ (ܓܘ Windows: R 4.2 ܘܠܥܠ، ܝܢ Sys.setlocale('LC_ALL', 'Hebrew')).

# ܦܘܫܩܐ ܕܫܒ̈ܝܠܐ – ܦܪܘܦܣܘܪ ܣܛܐܛ. ܐܗܐ ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8؛ ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ
library(readxl)   # ܩܪܝܢܐ ܕܐܩܣܠ
library(lavaan)   # ܡܘܕܝ̈ܠܐ ܕܫܘܝ̈ܘܬܐ ܒܢܝܢܝ̈ܬܐ: sem, parameterEstimates, fitMeasures

# ܛܥܢܐ: ܛܘܦܣܐ ܬܩܝܢܐ – ܣܕܪܐ = ܡܫܬܘܬܦܢܐ، ܥܡܘܕܐ = ܡܫܬܚܠܦܢܐ؛ ܓܠܝܘܢܐ "נתונים"
d <- read_excel("C:/Rdata/DATA_path_example_heb.xlsx", sheet = "נתונים")
d <- d[, c("קבוצה", "גיל", "עמדות_ציון", "שימוש_יומי")]
names(d) <- c("grp", "age", "att", "use")                 # ܫܡ̈ܗܐ ܟܪ̈ܝܐ ܒܐܢܓܠܝܙܝܐ ܩܐ ܡܬܢܝܬܐ ܕܡܘܕܝܠ
d <- d[complete.cases(d), ]                               # ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (113 ܡܢ 120)

# ܡܘܕܝܠ: ܓܘܕܐ ܘܥܘܡܪܐ -> ܚܘܫ̈ܒܐ (a1, a2)؛ ܚܘܫ̈ܒܐ ܘܥܘܡܪܐ -> ܡܦܠܚܢܘܬܐ (b, c)؛ ܡܥܒܕ̈ܢܘܝܬܐ ܠܐ ܬܪ̈ܝܨܬܐ ܘܟܠܢ̈ܝܬܐ ܒ-:=
model <- "
  att ~ a1*grp + a2*age
  use ~ b*att + c*age
  ind_grp := a1*b
  ind_age := a2*b
  tot_age := c + a2*b
"
fit <- sem(model, data = d)                               # ML, fixed.x = TRUE – ܐܝܟ ܓܘ ܦܐܬܐ
summary(fit, fit.measures = TRUE, standardized = TRUE, rsquare = TRUE)   # χ²(1) = 1.948, p = .163; CFI .989, TLI .944, RMSEA .092 [.000, .286], SRMR .029; a1 −0.420 (p = .002), a2 0.012 (.022), b 1.446 (< .001), c −0.026 (.002); Std.all −.279, .202, .703, −.211; R² .121, .477; ind_grp −0.607 (SE 0.201, p = .003), ind_age 0.017 (.025), tot_age −0.008 (.459)

# ܠܘܚܐ 1 – ܡܚܘ̈ܝܢܐ ܕܦܐܝܘܬܐ ܒܠܚܘܕ
fitMeasures(fit, c("chisq", "df", "pvalue", "cfi", "tli", "rmsea", "rmsea.ci.lower", "rmsea.ci.upper", "srmr", "aic", "bic"))   # 1.948, 1, .163, .989, .944, .092, .000, .286, .029, 600.155, 616.519

# ܠܘܚܐ 4 – ܬܚܘ̈ܡܐ ܕ-bootstrap ܕܕܪ̈ܓܐ ܡܢ ܡܐܐ (percentile) ܩܐ ܡܥܒܕ̈ܢܘܝܬܐ ܡܚܕ̈ܕܬܐ (1000 ܕܘ̈ܡܝܐ)؛ iseed = ܙܪܥܐ ܕܦܐܬܐ – ܗܢܝ ܕܘ̈ܡܝܐ، ܗܢܝ ܬܚܘ̈ܡܐ
fitb <- sem(model, data = d, se = "bootstrap", bootstrap = 1000, iseed = 2026)
pe <- parameterEstimates(fitb, boot.ci.type = "perc")
pe[pe$op == ":=", c("label", "est", "se", "ci.lower", "ci.upper")]   # ind_grp −0.607 [−1.082, −0.208]; ind_age 0.017 [0.000, 0.034] (ܬܚܘܡܐ ܬܚܬܝܐ −0.0004 – ܬܚܘܡܐ ܐܝܬ ܓܘܗ ܣܦܪ)؛ tot_age −0.008 [−0.031, 0.014] – ܐܝܟ ܓܘ ܦܐܬܐ

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

ܟܡܘܕܥܚ ܐܘܪܚܐ ܕܫܘܥܪܐ ܘܬܘܪܓܡܐ ܕܡܚܫܒܢܐ (software)، N، ܦܐܝܘܬܐ (χ² ܥܡ df ܘ-p، CFI، TLI، RMSEA ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval)، SRMR)، ܘܒܬܪ ܗܕܐ ܫܒ̈ܝܠܐ (B ܥܡ ܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) ܝܢ ܬܚܘܡܐ ܕܬܘܟܠܢܐ، β، p) ܘܡܥܒܕ̈ܢܘܝܬܐ ܠܐ ܬܪ̈ܝܨܬܐ (indirect effects) ܥܡ ܬܚܘܡܐ ܕ-bootstrap ܘܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size) – ܘܒܕܘܟܬܐ ܕܪܫܝܡܬܐ ܐܪܝܟܬܐ، ܨܘܪܬܐ ܥܡ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ (APA, 2020، ܦܣܩܐ 6.43: "ܡܘܕܥܘܢ ܝܕܥܬܐ ܣܦܩܬܐ ܕܩܪܘܝܐ ܡܨܐ ܕܡܫܪܪ ܦܘܫܩ̈ܐ"؛ ܦܣܩܐ 6.44: ܠܡܚܕܕܐ ܩܛܝ̈ܢܘܬܐ CFI، RMSEA، SEM ܓܘ ܡܬܚܙܝܢܘܬܐ ܩܕܡܝܬܐ ܕܝܗܝ، ܠܐ ܐܝܟ ܪ̈ܘܫܡܐ ܣܛܐܛܝܣܛܝܩ̈ܝܐ ܬܩܝ̈ܢܐ). ܡܬܠܐ ܕ-Field (2024، ܦܣܩܐ 11.4.6): "ܐܫܬܟܚܬ ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܪܫܝܡܬܐ ܕܚܙܝܐ ܕܦܘܪܢܘܓܪܦܝܐ ܥܠ ܒܓܕܘܬܐ ܒܝܕ ܐܣܝܪܘܬܐ ܠܙܘܘܓܐ، b = 0.13, 95% BCa CI [0.02, 0.27]. ܡܥܒܕܢܘܬܐ ܙܥܘܪܬܐ ܒܣܓܝ ܝܘܬ̇ܗ̇، ܡܚܘܝܢܐ ܕܡܨܥܝܘܬܐ 0.04" – ܘܥܡܗ̇ ܨܘܪܬܐ ܕܡܘܕܝܠ ܥܡ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܥܠ ܓܐܪ̈ܐ ܘܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (ܨܘܪܬܐ 11.12). ܩܐ ܡܘܕܝ̈ܠܐ ܚܠܘ̈ܦܝܐ – ܠܘܚܐ ܕܦܘܚܡܐ ܐܝܟ ܠܘܚܐ 7.19 ܕ-APA (χ²، df، p، RMSEA ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ، AIC، BIC ܘ-ΔAIC/ΔBIC)، ܘܩܐ ܡܘܕܝܠ ܕܡܫܘܚܬܐ (measurement model) – ܐܝܟ ܠܘܚܐ 7.21 (NFI، CFI، RMSEA ܩܐ ܟܠ ܡܘܕܝܠ).

ܢܡܘ̈ܣܐ ܕܨܘܪܬܐ (APA, 2020, Section 6.36): B، χ²، z ܘܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܩܐ B ܥܡ ܣܦܪ ܩܕܡ ܢܘܩܙܐ؛ β، R²، CFI، TLI، RMSEA، SRMR ܘ-p ܕܠܐ (ܠܐ ܡܨܝ ܕܣܠܩܝ ܒܢܘܬ ܡܢ 1)؛ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܒܛܘܦܣܐ 95% CI [LL, UL]، ܘܩܐ ܬܚܘܡܐ ܕ-bootstrap ܟܡܚܘܝܚ ܙܢܐ (ܕܕܪ̈ܓܐ ܡܢ ܡܐܐ / BCa) ܘܡܢܝܢܐ ܕܕܘ̈ܡܝܐ. ܦܣܩܐ ܕܡܫܟܚ̈ܢܘܬܐ (results paragraph) ܕܓܘ ܡܦܩܢܐ ܒܢܝܐ ܝܠܗ ܗܟܐ، ܒܣܘܪܝܬ ܘܒܐܢܓܠܝܙܝܐ.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܠܡܒܢܝܐ ܡܘܕܝܠ ܡܢ ܝܗܝ̈ܒܬܐ. ܠܡܘܣܦܐ ܓܐܪ̈ܐ ܗܠ ܕܦܐܝܘܬܐ ܛܒܬܐ ܗܘܝܐ، ܘܒܬܪ ܗܕܐ ܠܡܘܕܥܐ ܐܝܟ ܕܗܘܦܘܬܣܝܣ (hypothesis) ܒܚܝܪܬܐ ܗܘܝܐ (Field, 2024، ܦܣܩܐ 11.4.1 – ܫܪ̈ܛܐ ܗܘܦܘܬܣ̈ܝܣ ܡܢ ܩܕܡ ܝܢܐ).

ܠܡܩܪܐ p < .05 ܕ-χ² ܐܝܟ "ܛܒܐ". ܗܦܝܟܐܝܬ: ܒܘܚܪܢܐ ܟܒܚܪ ܡܘܕܝܠ ܐܝܟ ܗܘܦܘܬܣܝܣ ܕܣܦܝܩܘܬܐ (null hypothesis) – ܪܫܝܡܘܬܐ (significance) ܝܠܗ̇ ܣܠܝܬܐ. ܘܓܘ ܡܘܕܝܠ ܡܠܝܐ (saturated) ܠܝܬ ܒܘܚܪܢܐ ܟܠ ܥܩܪܐ.

ܠܡܒܥܝܐ ܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation) ܦܫܝܛܐ ܒܝܢܝ X ܘ-Y ܐܝܟ ܫܪܛܐ ܩܐ ܡܨܥܝܘܬܐ (mediation). ܓܘ ܡܨܥܝܘܬܐ ܠܐ ܫܠܡܬܐ ܡܥܒܕܢܘܬܐ ܟܠܢܝܬܐ ܙܥܘܪܬܐ ܝܠܗ̇ ܝܢ ܣܦܪ – Field (ܦܣܩܐ 11.4.2) ܟܡܣܠܐ ܫܪܛܐ ܕ-Baron ܘ-Kenny ܥܠ ܦܬܐ ܕܫܘܥܪܐ ܕܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕܝܠܗ̇.

ܠܡܦܠܛܐ "ܡܨܥܝܘܬܐ ܓܡܝܪܬܐ" ܡܢ ܫܘܢܝܐ ܓܘ ܪܫܝܡܘܬܐ (significance). "p ܕܥܒܪ ܡܢ .049 ܠ-.051" ܠܐ ܝܠܗ ܡܫܟܚܢܘܬܐ (Field, Section 11.4.2)؛ ܟܡܘܕܥܚ ab، ܬܚܘܡܐ ܕ-bootstrap ܘܡܚܘܝܢܐ ܕܡܨܥܝܘܬܐ.

ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܫܘܝܐ ܠܬܪܝܢ ܓܢ̈ܒܐ ܩܐ ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ. ܦܘܠܓܐ (distribution) ܕ-ab ܥܩܝܡܐ ܝܠܗ؛ Field (ܦܣܩܐ 11.4.6) – "ܡܘܕܥܘܢ ܬܚܘ̈ܡܐ ܕ-bootstrap".

ܠܡܦܫܩܐ ܓܐܪܐ ܐܝܟ ܥܠܬܐ. ܦܘܫܩܐ ܕܫܒ̈ܝܠܐ (path analysis) ܟܣܒܪ ܦܢܝܬܐ ܕܓܐܪ̈ܐ، ܠܐ ܟܡܚܘܐ ܠܗ̇؛ ܡܘܕܝܠ ܥܡ ܓܐܪ̈ܐ ܗܦܝ̈ܟܐ ܡܨܐ ܕܦܐܐ ܒܗܝ ܡܫܘܚܬܐ (Pallant, 2020، ܨܚܚܐ 10 – ܦܘܚܡܐ ܕܡܘܕܝ̈ܠܐ ܚܠܘ̈ܦܝܐ).

ܡܘܕܝܠ ܪܒܐ ܥܠ ܕܘܡܝܐ ܙܥܘܪܐ. ܒܨܝܪ ܡܢ ܥܣܪܐ ܡܫܬܘܬܦ̈ܢܐ (participants) ܩܐ ܟܠ ܦܪܡܝܛܪ – ܫܘܥܪ̈ܐ ܠܐ ܩܝ̈ܡܐ ܘܒܘܚܪ̈ܢܐ ܢܘܪܡܠܝ̈ܐ ܠܐ ܫܪܝܪ̈ܐ؛ ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ bootstrap ܣܢܝܩ ܝܠܗ ܝܬܝܪ (Field, Section 11.4.7).

ܠܡܦܚܡܐ β ܒܝܢܝ ܡܘܕܝ̈ܠܐ ܦܪ̈ܝܫܐ. ܡܢܝܢܐ ܡܬܩܢܐ (standardized) ܬܠܝܐ ܝܠܗ ܒܣܛܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ ܕܕܘܡܝܐ؛ ܩܐ ܡܝܛܐ-ܐܢܐܠܝܣܝܣ (meta-analysis) ܡܘܕܥܘܢ ܐܦ B ܘܡܚܘܝܢܐ ܕܡܨܥܝܘܬܐ (Field, Section 11.4.3).

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.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.

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.

Baron ܘ-Kenny (1986)، Sobel (1982)، MacKinnon (2008)، Preacher ܘ-Hayes (2008)، Preacher ܘ-Kelley (2011)، Hayes (2022)، Lambert ܘܐܚܪ̈ܢܐ (2012) ܘ-Bronstein ܘܐܚܪ̈ܢܐ (2019) – ܐܝܟ ܕܡܝܬܝ̈ܐ ܝܢܐ ܓܘ Field (2024)؛ Tabachnick ܘ-Fidell (2013) – ܐܝܟ ܕܡܝܬܝ̈ܐ ܝܢܐ ܓܘ Pallant (2020). ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ (site rule)، ܓܘ ܪܫܝܡܬܐ ܕܡܒܘ̈ܥܐ (reference list) ܟܡܬܚܙܝ ܒܣ ܡܒܘ̈ܥܐ ܕܩܪܝ̈ܐ ܝܢܐ ܓܘ ܫܪܫܐ ܕܝܗܝ. Bentler (1990) ܘ-Browne ܘ-Cudeck (1993) – ܐܝܟ ܕܡܝܬܝ̈ܐ ܝܢܐ ܓܘ Brown (2015). Field (2024) ܘ-Pallant (2020) ܒܢܘܣܚܐ ܕܝܓܝܛܠܝܐ ܕܪܕܝܐ (reflowable) – ܡܬܝܬܐ ܠܦܘܬ ܦܣܩܐ ܘܨܚܚܐ؛ Cohen (1988) ܘ-APA (2020) – ܠܦܘܬ ܦܐܬܐ ܘܦܣܩܐ ܕܡܦܩܬܐ ܛܒܝܥܬܐ. ܚܘܫܒܢܐ ܓܘ ܦܐܬܐ ܡܫܪܪܐ ܝܠܗ ܩܘܒܠ ܚܒܝܫܘܬܐ lavaan 0.6-17 ܓܘ R.