ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܡܒܨܝܢܐ

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ܟܡܕܒܩܚ ܥܡܘ̈ܕܐ ܬܪܝܨܐܝܬ ܡܢ ܓܠܝܘܢܐ (ܥܡ ܣܕܪܐ ܕܪ̈ܫܐ) – ܝܢ ܡܐܛܪܝܟܣ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ – ܟܪܫܡܚ ܓܘ ܐܩܣܠ، ܟܢܣܚܚ، ܘܟܡܕܒܩܚ ܗܪܟܐ:

ܦܣܘ̈ܩܐ ܘܓܘܒܝ̈ܐ

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ܐܝܡܢ ܡܦܠܚܝܚ (When to use)؟

ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ (factor analysis) ܟܦܢܐ ܥܠ ܫܘܐܠܐ ܚܕ: ܐܝܢܝ ܦܣܘ̈ܩܐ (items) "ܟܐܙܠܝ ܐܟܚܕܐ"، ܘܡܘܕܝ ܩܐܐܡ ܒܬܪܝܗܝ. Field ܟܡܢܐ ܬܠܬܐ ܡܦܠܚܢ̈ܘܬܐ – ܠܡܦܗܡ ܒܢܝܢܐ ܕܓܘܕܐ ܕܡܫܬܚܠܦ̈ܢܐ (variables)، ܠܡܒܢܐ ܦܢܩܝܬܐ ܕܫܘܐ̈ܠܐ (questionnaire)، ܘܠܡܙܥܘܪܐ ܡܫܬܚܠܦ̈ܢܐ ܣܓܝ̈ܐܐ ܠܡܫܘ̈ܚܬܐ ܩܠܝܠ̈ܐ "ܥܡ ܢܛܪܬܐ ܕܒܢܘܬ ܡܢ ܝܕܥܬܐ ܕܡܨܝܐ" (2024، ܦܣܩܐ 18.2). ܥܠܬܐ (factor) ܝܠܗ "ܡܫܬܚܠܦܢܐ ܕܠܐ ܚܙܝܐ، ܕܟܡܥܒܕ ܥܠ ܒܢܘܬ ܡܢ ܡܚܘܝܢܐ ܚܕ ܘܟܡܦܫܩ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܐܢܝ" (Brown, 2015, p. 10).

ܡܒܨܝܢܐ – ܝܗܝ̈ܒܬܐ ܟܦܣܩܝ ܒܢܝܢܐ: ܠܐ ܟܬܚܡܚ ܡܢ ܩܕܡ ܟܡܐ ܥܠ̈ܠܬܐ ܐܝܬ ܘܐܝܢܐ ܦܣܘܩܐ ܕܐܝܢܐ ܥܠܬܐ ܝܠܗ (Brown, 2015, pp. 11, 19). ܡܫܪܪܢܐ (CFA) – ܒܨܘܝܬܐ ܟܬܚܡܐ ܒܢܝܢܐ ܡܢ ܩܕܡ ܘܟܒܚܪܐ ܠܗ. ܓܘ ܒܢܝܢܐ ܕܦܢܩܝܬܐ ܕܫܘܐ̈ܠܐ ܟܡܦܠܚܚ ܩܕܡ ܒܡܒܨܝܢܐ، ܘܒܬܪܟܢ، ܓܘ ܕܘܡܝܐ ܐܚܪܢܐ، ܒܡܫܪܪܢܐ (ܬܡܢ، ܦܐܬܐ 12) – ܦܐܬܐ "ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܡܫܪܪܢܐ".

ܥܠ̈ܠܬܐ ܝܢ ܡܢܘ̈ܬܐ؟

ܬܪܬܝܢ ܫܪ̈ܒܬܐ ܕܟܡܬܚܙܝ ܕܡܝ̈ܐ ܓܘ ܡܦܩܢܐ (output). ܦܘܫܩܐ ܕܡܢܘ̈ܬܐ ܪ̈ܫܝܬܐ (PCA) ܟܡܦܫܩ ܟܠ ܫܘܚܠܦܐ (variance) ܕܦܣܘ̈ܩܐ، ܘ"ܠܐ ܟܫܥܪ ܡܫܬܚܠܦ̈ܢܐ ܕܠܐ ܡܫܝ̈ܚܐ ܝܢܐ، ܒܣ ܟܡܫܢܐ ܠܡܫܝ̈ܚܐ" (Field, 2024, Section 18.3). ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܟܡܦܫܩ ܒܣ ܫܘܚܠܦܐ ܡܫܘܬܦܐ – ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܦܣܘ̈ܩܐ – ܘܟܣܒܪ ܕܟܠ ܦܣܘܩܐ ܐܝܬ ܓܘܗ ܐܦ ܫܘܚܠܦܐ ܝܚܝܕܝܐ ܘܛܥܝܘܬܐ ܕܡܫܘܚܬܐ (ibid., Section 18.3.2; Brown, 2015, p. 11).

ܡܒܘ̈ܥܐ ܦܠܝܓ̈ܐ ܝܢܐ، ܘܗܪܟܐ ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ. Brown ܩܫܝܐ ܝܠܗ: ܐܢ ܢܝܫܐ ܦܐܫ ܠܡܘܕܝܠ ܕܥܠ̈ܠܬܐ ܡܫܘܬ̈ܦܬܐ – ܠܡܬܠܐ ܠܡܒܢܐ ܦܢܩܝܬܐ ܕܫܘܐ̈ܠܐ ܕܟܡܫܚܐ ܡܘܕܥ̈ܢܘܬܐ – PCA "ܠܐ ܝܠܗ ܫܠܝܡܐ ܒܚܫܒܐ ܘܒܡܬܡܛܝܩܝ" (2015، ܦܐܬܐ 20)، ܘܫܘܥܪ̈ܐ ܕܥܠ̈ܠܬܐ ܟܡܬܢܝ ܛܒ ܒܢܘܬ ܓܘ CFA (ܬܡܢ). Pallant ܟܡܚܘܝܐ PCA ܒܡܬܠܐ، ܘܟܡܝܬܝܐ Tabachnick ܘ-Fidell: ܥܠ̈ܠܬܐ ܐܡܬܝ ܕܟܒܥܐ ܦܘܫܪܐ ܬܐܘܪܝܐ "ܕܟܝܐ ܡܢ ܫܘܚܠܦܐ ܝܚܝܕܝܐ ܘܡܢ ܛܥܝܘܬܐ"، ܡܢܘ̈ܬܐ ܐܡܬܝ ܕܟܒܥܐ "ܟܢܘܫܝܐ ܐܡܦܝܪܝܐ" ܕܝܗܝ̈ܒܬܐ (2020، ܨܚܚܐ 15). Field ܟܡܚܘܐ principal axis factoring، ܘܟܐܡܪ ܕܒܥܕܢܐ ܪܓܝܠܐ ܦܐܪ̈ܐ ܕܡܝ̈ܐ ܝܢܐ، ܐܠܐ ܥܡ ܒܨܝܪ ܡܢ 20 ܦܣܘ̈ܩܐ ܘܫܘܬܦܘܬܐ ܢܚܝܬܐ (ܬܚܘܬ .4) ܡܨܝܐ ܕܗܘܝܐ ܦܪ̈ܝܫܐ (2024، ܦܣܩܐ 18.4.3). ܓܘ ܦܐܬܐ ܓܘܒܝܐ ܡܩܕܡܐ ܝܠܗ ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ (PAF)، ܘ-PCA ܐܝܬܘܗܝ.

ܐܢ ܝܗܝ̈ܒܬܐ ܦܐܫܝ؟

ܪܒܘܬܐ ܕܕܘܡܝܐ. "ܕܘܡܝܐ ܕ-300 ܘܠܥܠ ܡܚܬܡܠܐ ܒܕ ܝܗܒ ܦܘܫܪܐ ܩܝܡܐ" (Field, 2024, Section 18.5.3). Comrey ܘ-Lee ܟܩܪܝ ܠ-100 "ܒܝܫܐ"، ܠ-300 "ܛܒܐ" ܘܠ-1,000 "ܡܝܬܪܐ" (ܐܝܟ ܕܡܝܬܝܐ ܝܠܗ ܬܡܢ)؛ ܐܠܐ ܪܒܘܬܐ ܕܣܢܝܩܐ ܬܠܝܐ ܝܠܗ ܐܦ ܒܛܥ̈ܢܐ ܘܒܫܘܬܦܘܬܐ: ܥܠܬܐ ܥܡ ܐܪܒܥܐ ܛܥ̈ܢܐ ܒܢܘܬ ܡܢ .6 ܩܝܡܬܐ ܝܠܗ ܒܟܠ ܪܒܘܬܐ ܕܕܘܡܝܐ (Guadagnoli & Velicer, 1988)، ܘܐܡܬܝ ܕܟܠ ܫܘܬܦܘܬܐ ܒܢܘܬ ܡܢ .6، ܐܦ ܒܨܝܪ ܡܢ 100 ܡܨܐ ܕܣܦܩ (MacCallum et al., 1999؛ ܬܪܘܝܗܝ ܐܝܟ ܕܡܝܬܝ̈ܐ ܝܢܐ ܬܡܢ). Pallant ܟܡܣܦܩܐ ܒ-150 ܘܠܥܠ ܘܒܦܘܚܡܐ ܕܚܡܫܐ ܡܫܬܘܬܦ̈ܢܐ ܠܟܡܝܘܬܐ ܩܐ ܟܠ ܦܣܘܩܐ (2020، ܨܚܚܐ 15).

ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ. ܟܡܣܟܚ ܠܣܓܝ̈ܐܐ ܒܢܘܬ ܡܢ .3 – ܐܢ ܠܐ ܠܝܬ ܡܘܕܝ ܠܡܟܢܫ (Pallant, 2020, Chapter 15; Field, 2024, Section 18.5.4) – ܘܕܠܐ ܐܣܘܪ̈ܐ ܒܢܘܬ ܡܢ .9، ܕܐܢܝ ܩܪܝܒ ܝܢܐ ܠܬܢܝܢܘܬܐ. determinant ܕܡܐܛܪܝܟܣ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܣܢܝܩ ܝܠܗ ܕܗܘܐ ܒܢܘܬ ܡܢ 0.00001؛ ܬܚܘܬ ܐܗܐ – multicollinearity ܩܫܝܬܐ (Field, 2024, Box 18.3).

KMO (Kaiser–Meyer–Olkin) – ܟܡܐ ܡܢ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܦܣܘ̈ܩܐ ܟܐܬܝ ܡܢ ܡܕܡ ܡܫܘܬܦܐ ܘܠܐ ܡܢ ܙܘܓ̈ܐ ܝܚܝܕ̈ܝܐ: ܦܘܚܡܐ ܒܝܢܝ ܓܘܡܪܐ ܕܡܪ̈ܒܥܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܠܓܘܡܪܐ ܕܡܪ̈ܒܥܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܘܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܡܢܬܢ̈ܝܐ. ܒܢܘܬ ܡܢ .9 "ܡܝܬܪܐ"، .8 "ܛܒܐ ܣܓܝ"، .7 "ܡܨܥܝܐ"، .6 "ܟܪܝܗܐ"، .5 "ܒܝܫܐ"، ܘܬܚܘܬ .5 – ܠܐ ܡܩܒܠܐ (Kaiser & Rice, 1974، ܐܝܟ ܕܡܝܬܝ̈ܐ ܝܢܐ ܓܘ Field, 2024، ܦܣܩܐ 18.5.2). Pallant ܟܒܥܝܐ .6 ܠܟܡܝܘܬܐ (2020، ܨܚܚܐ 15). ܩܐ ܟܠ ܦܣܘܩܐ ܐܝܬ ܐܦ KMO ܕܝܠܗ (MSA) – "ܒܢܘܬ ܡܢ 0.5 ܠܟܡܝܘܬܐ"؛ ܦܣܘܩܐ ܕܬܚܘܬܗ ܟܚܫܒܚ ܠܡܦܠܛ ܠܗ ܘܠܡܪܗܛ ܡܢ ܪܝܫ (Field, 2024, Section 18.7.1). ܒܘܚܪܢܐ ܕ-Bartlett ܟܒܚܪ ܐܢ ܡܐܛܪܝܟܣ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܝܠܗ identity matrix – ܝܥܢܝ ܐܢ ܠܝܬ ܚܕ ܐܣܘܪܐ. Pallant ܟܒܥܝܐ ܕܗܘܐ ܪܫܝܡܐ (2020، ܨܚܚܐ 15)؛ Field ܟܡܥܗܕ ܕܓܘ ܕܘܡܝܐ ܪܒܐ ܐܗܘ "ܩܪܝܒ ܠܟܠ ܐܝܡܢ" ܪܫܝܡܐ ܝܠܗ، ܘܡܛܠ ܗܕܐ "ܕܠܐ ܦܐܝܕܐ" – ܐܠܐ ܐܢ ܠܐ ܝܠܗ ܪܫܝܡܐ (2024، ܦܣܩܐ 18.5.4).

ܦܠܛܬܐ

Principal axis factoring (PAF) – ܟܫܚܠܦܚ 1 ܓܘ ܣܪܛܐ ܡܨܠܝܢܐ ܕܡܐܛܪܝܟܣ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܫܘܥܪܐ ܕܫܘܬܦܘܬܐ (communality)، ܟܫܪܚ ܡܢ ܐܣܘܪܐ ܣܓܝܐܐ ܡܪܒܥܐ ܕܟܠ ܦܣܘܩܐ ܥܡ ܟܠ ܐܚܪ̈ܢܐ (SMC)، ܘܟܡܬܢܚ ܗܠ ܕܫܘܬܦܘܬܐ ܩܝܡܐ (Field, 2024, Sections 18.4.2, 18.4.4). ܡܬܚܙܝܢܘܬܐ ܥܠܝܬܐ (ML) – ܟܝܗܒܐ ܐܦ ܒܘܚܪܢܐ ܕܦܐܝܘܬܐ ܘܡܚܘ̈ܝܢܐ ܕܦܐܝܘܬܐ، ܐܠܐ ܟܒܥܝܐ ܦܘܠܓܐ ܢܘܪܡܠܝܐ (normal distribution) ܕܡܫܬܚܠܦ̈ܢܐ ܣܓܝ̈ܐܐ، ܘܡܝܠܐ ܝܠܗ ܒܢܘܬ ܠܦܘܫܪ̈ܐ ܠܐ ܬܪ̈ܝܨܐ؛ PAF "ܚܐܪܐ ܝܠܗ ܡܢ ܫܪ̈ܛܐ ܕܦܘܠܓܐ". ܡܛܠ ܗܕܐ Brown ܟܡܪܚܩ PAF ܐܡܬܝ ܕܦܘܠܓܐ ܪܚܝܩܐ ܝܠܗ ܡܢ ܢܘܪܡܠܝܐ ܝܢ ܐܡܬܝ ܕ-ML ܠܐ ܦܠܚ، ܘ-ML ܐܡܬܝ ܕܫܪ̈ܛܐ ܡܫܡܠ̈ܝܐ ܝܢܐ (2015، ܦܐ̈ܬܐ 19-20). ܡܢܘ̈ܬܐ ܪ̈ܫܝܬܐ – ܛܝ̈ܡܐ ܕܝܠܢ̈ܝܐ (eigenvalues) ܘ-eigenvectors ܕܡܐܛܪܝܟܣ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܕܗ.

ܟܡܐ ܥܠ̈ܠܬܐ؟

"ܦܣܩܬܐ ܕܚܫܝܚܬܐ ܡܢ ܟܠܗ" ܓܘ ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܡܒܨܝܢܐ (exploratory factor analysis (EFA)) (Brown, 2015, p. 20). ܛܝܡܐ ܕܝܠܢܝܐ (eigenvalue) ܕܥܠܬܐ ܝܠܗ ܟܡܐ ܡܢ ܫܘܚܠܦܐ ܐܗܝ ܟܡܦܫܩܐ؛ ܓܘܡܪܐ ܕܛܝ̈ܡܐ ܕܝܠܢ̈ܝܐ ܝܠܗ ܡܢܝܢܐ ܕܦܣܘ̈ܩܐ (ܬܡܢ، ܦܐ̈ܬܐ 22-23).

• Kaiser – ܛܝܡܐ ܕܝܠܢܝܐ ܒܢܘܬ ܡܢ 1. ܓܘܒܝܐ ܡܩܕܡܐ (default) ܕ-SPSS، ܘܒܝܫܐ ܡܢ ܟܠܗ: ܐܗܘ "ܟܫܥܪ ܒܝܬܝܪܘܬܐ" ܡܢܝܢܐ ܕܥܠ̈ܠܬܐ (Field, 2024, Section 18.4.5)، ܘܬܚܘܡܐ ܨܒܝܢܝܐ ܝܠܗ – ܡܛܠ ܛܥܝܘܬܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ، ܛܝܡܐ ܕܝܠܢܝܐ ܕ-.99 ܝܢ 1.01 (Brown, 2015, p. 23).
• ܨܘܪܬܐ scree (scree; Cattell, 1966, as cited in Field, 2024, Section 18.4.5) – ܟܢܛܪܚ ܥܠ̈ܠܬܐ ܕܩܕܡ "elbow"، ܢܚܬܬܐ ܚܪܝܦܬܐ ܐܚܪܝܬܐ. ܬܠܝܐ ܝܠܗ ܒܚܫܒܐ ܕܒܨܘܝܐ (Brown, 2015, p. 24)، ܘܫܪܝܪܐ ܝܠܗ "ܐܡܬܝ ܕܐܝܬ ܒܢܘܬ ܡܢ 200 ܡܫܬܘܬܦ̈ܢܐ" (Stevens, 2002, as cited in Field).
• ܦܘܫܩܐ ܒܓܢܒ ܚܕ̈ܕܐ (Horn, 1965, as cited in Field & Pallant) – ܟܦܚܡܚ ܟܠ ܛܝܡܐ ܕܝܠܢܝܐ ܥܡ ܛܝܡܐ ܕܝܠܢܝܐ ܓܘ ܗܘ ܕܘܟܐ ܓܘ ܛܘܦ̈ܣܐ ܓܕܫܢ̈ܝܐ ܕܝܗܝ̈ܒܬܐ ܒܗܝ ܪܒܘܬܐ، ܕܠܐ ܚܕ ܒܢܝܢܐ، ܘܟܢܛܪܚ ܥܠܬܐ ܗܠ ܕܛܝܡܐ ܫܪܝܪܐ ܪܒܐ ܝܠܗ ܡܢ ܓܕܫܢܝܐ. ܐܗܐ ܝܠܗ ܓܘܒܝܐ ܡܩܕܡܐ ܡܪܚܩܐ: Field – "ܠܐ ܝܠܗ ܚܫܒܐ ܒܝܫܐ ܠܡܓܒܐ ܦܘܫܩܐ ܒܓܢܒ ܚܕ̈ܕܐ ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ" (2024، ܦܣܩܐ 18.4.5)؛ Pallant – ܚܬܝܬܐ ܡܢ ܒܝܢܝ ܬܠܬܐ (2020، ܨܚܚܐ 15). ܓܘ ܦܐܬܐ – 100 ܛܘܦ̈ܣܐ ܕܝܗܝ̈ܒܬܐ ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ، ܐܝܟ ܓܒܝ Pallant، ܥܡ ܙܪܥܐ (random seed)، ܗܟܢܐ ܕܣܩܪܝܦܬ ܕܟܡܚܬܚ ܟܡܬܢܐ ܠܗܘܢ ܚܬܝܬܐܝܬ. ܓܘܒܝܐ ܡܩܕܡܐ ܝܠܗ ܙܪܥܐ 2026؛ "ܙܪܥܐ ܚܕܬܐ" ܟܝܗܒ ܙܪܥܐ ܐܚܪܢܐ، ܘܥܡܘܕܐ "ܓܕܫܢܝܐ" ܟܫܢܐ ܒܟܡܐ ܡܢ ܐܠܦ̈ܐ – ܐܡܬܝ ܕܛܝܡܐ ܕܝܠܢܝܐ ܫܪܝܪܐ ܩܪܝܒܐ ܝܠܗ ܣܓܝ ܠܡܫܘܚܬܐ، ܛܒܐ ܝܠܗ ܠܒܚܪܐ ܟܡܐ ܙܪ̈ܥܐ ܝܢ ܠܡܪܒܐ ܡܢܝܢܐ ܕܛܘܦ̈ܣܐ ܕܝܗܝ̈ܒܬܐ.

ܡܨܥܝܬܐ ܝܢ ܕܪܓܐ ܡܢ ܡܐܐ 95؟ ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ: Horn، Pallant ܘ-Brown ܟܦܚܡܝ ܥܡ ܡܨܥܝܬܐ (mean) ܕܛܝ̈ܡܐ ܓܕܫܢ̈ܝܐ (Pallant, 2020, Chapter 15; Brown, 2015, pp. 24-25)؛ Glorfeld (1995, as cited in Brown, 2015, p. 33, Note 7) ܟܡܪܚܩ ܕܪܓܐ ܡܢ ܡܐܐ 95 (percentile)، ܩܐ ܬܘܪܨܐ ܕܡܝܠܢܘܬܐ ܩܠܝܠܬܐ ܠܡܦܠܛ ܒܢܘܬ ܡܢ ܕܣܢܝܩ، ܘ-Field ܟܡܦܠܚ ܒܗ ܓܘ ܡܬܠܐ (2024، ܦܣܩܐ 18.8). ܓܘܒܝܐ ܡܩܕܡܐ ܓܘ ܦܐܬܐ – ܡܨܥܝܬܐ. ܘܬܪܝܢ ܡܐܢ̈ܐ ܐܚܪ̈ܢܐ: ܫܘܬܦܘܬܐ (communality) ܒܬܪ ܦܠܛܬܐ – ܫܘܬܦܘܬܐ ܢܚܝܬܐ ܟܡܚܘܝܐ ܕܦܠܛܝ̈ܐ ܝܢܐ ܥܠ̈ܠܬܐ ܩܠܝܠ̈ܐ ܡܢ ܕܣܢܝܩ (Field, 2024, Section 18.4.5)؛ ܘܫܪ̈ܟܐ (residuals) – ܦܘܪܫܢܐ ܒܝܢܝ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܘܒܝܢܝ ܡܐ ܕܥܠ̈ܠܬܐ ܟܡܬܢܝ: ܐܢ ܒܢܘܬ ܡܢ 50% ܡܢܝܗܝ ܪ̈ܒܐ ܝܢܐ ܡܢ 0.05، "ܐܝܬ ܥܠܬܐ ܠܦܘܪܟܐ" (ܦܣܩܐ 18.7.2). ܓܘ ML ܐܝܬ ܐܦ ܒܘܚܪܢܐ χ²، ܐܠܐ ܠܐ ܟܓܒܚ ܠܦܘܬܗ ܒܠܚܘܕ (Brown, 2015, p. 26).

ܚܘܕܪܐ

ܥܡ ܒܢܘܬ ܡܢ ܥܠܬܐ (factor) ܚܕܐ ܐܝܬ ܦܘܫܪ̈ܐ ܕܠܐ ܣܟܐ ܕܦܐܫܝ ܠܝܗܝ̈ܒܬܐ ܒܗܝ ܡܫܘܚܬܐ، ܘܚܘܕܪܐ (rotation) ܟܓܒܐ ܡܢܝܗܝ ܦܫܝܩܐ ܡܢ ܟܠܗ ܠܦܘܫܩܐ – "ܒܢܝܢܐ ܦܫܝܩܐ": ܩܐ ܟܠ ܦܣܘܩܐ (item) ܛܥܢܐ ܪܡܐ ܚܕ، ܘܩܐ ܟܠ ܥܠܬܐ ܟܡܐ ܦܣܘ̈ܩܐ ܥܡ ܛܥ̈ܢܐ ܪ̈ܡܐ (Thurstone, 1947, as cited in Brown, 2015, p. 27). ܚܘܕܪܐ ܠܐ ܟܫܢܐ ܦܐܝܘܬܐ (ܬܡܢ). orthogonal (varimax) – ܥܠ̈ܠܬܐ ܟܦܝܫܝ ܕܠܐ ܐܣܘܪܐ ܕܚܕ̈ܕܐ. ܡܨܠܝܢܐ (oblimin ܬܪܝܨܐ، promax) – ܫܪܝܐ ܝܠܗ ܩܐܠܗܘܢ ܕܗܘܝ ܐܣܝܪ̈ܐ.

ܬܠܬܐ ܡܒܘ̈ܥܐ ܟܡܪܚܩܝ ܚܘܕܪܐ ܡܨܠܝܢܐ (oblique rotation): "ܓܘ ܣܓܝܐܐ ܡܢ ܓܕܫ̈ܐ ܚܘܕܪܐ ܡܨܠܝܢܐ ܛܒܐ ܝܠܗ ܒܢܘܬ، ܡܛܠ ܕܐܗܘ ܟܡܚܘܐ ܒܐܘܪܚܐ ܫܪܝܪܬܐ ܒܢܘܬ" ܐܣܘܪ̈ܐ ܒܝܢܝ ܥܠ̈ܠܬܐ، ܘܐܢ ܥܠ̈ܠܬܐ ܫܪܝܪܐܝܬ ܕܠܐ ܐܣܘܪܐ ܝܢܐ، ܐܗܘ ܒܕ ܝܗܒ ܩܪܝܒ ܠܗܘ ܦܘܫܪܐ (Brown, 2015, p. 28)؛ Pallant "ܟܠ ܐܝܡܢ" ܟܫܪܝܐ ܒܡܨܠܝܢܐ، ܘܐܢ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܥܠ̈ܠܬܐ ܒܢܘܬ ܡܢ .3 – ܟܡܘܕܥܐ ܠܗ (2020، ܨܚܚܐ 15)؛ Field: ܐܝܬ "ܥܠ̈ܠܬܐ ܚܝ̈ܠܢܝܬܐ" ܠܡܚܫܒ ܕܚܘ̈ܕܪܐ orthogonal ܠܐ ܦܐܫܝ ܠܝܗܝ̈ܒܬܐ ܥܠ ܒܢܝ̈ ܐܢܫܐ، ܘܓܘ ܡܨܠܝܢܐ – oblimin ܬܪܝܨܐ ܥܡ δ = 0، "ܡܬܦܗܡܢܐ ܩܐ ܣܓܝܐܐ ܡܢ ܦܘܫܩ̈ܐ" (2024، ܦܣܩܐ 18.4.6). ܓܘܒܝܐ ܡܩܕܡܐ ܓܘ ܦܐܬܐ – oblimin ܬܪܝܨܐ ܥܡ Kaiser normalization، ܐܝܟ SPSS.

ܓܘ ܚܘܕܪܐ ܡܨܠܝܢܐ ܐܝܬ ܬܪܝܢ ܡܐܛܪܝܟܣ̈: pattern matrix – ܐܣܘܪܐ ܝܚܝܕܝܐ ܕܦܣܘܩܐ ܥܡ ܟܠ ܥܠܬܐ، ܐܝܟ ܡܢܝܢܐ ܡܫܘܬܦܐ ܕܪܝܓܪܫܢ ܡܢܬܢܝܐ؛ ܘstructure matrix – ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܦܣܘܩܐ ܘܥܠܬܐ، ܫܘܝܐ ܠ-pattern ܡܘܚܠܦܐ ܒܡܐܛܪܝܟܣ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܥܠ̈ܠܬܐ. "ܣܓܝܐܐ ܡܢ ܒܨܘ̈ܝܐ ܟܦܫܩܝ pattern matrix" (Field, 2024, Section 18.7.4; Brown, 2015, pp. 28-29)، ܘ-structure ܛܒܐ ܝܠܗ ܠܒܚܪܐ ܘܠܡܘܕܥ (Field؛ Pallant). ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܒܢܘܬ ܡܢ .80-.85 ܒܝܢܝ ܬܪܬܝܢ ܥܠ̈ܠܬܐ ܟܡܚܘܐ ܕܐܢܝ ܫܪܝܪܐܝܬ ܠܐ ܝܢܐ ܦܪ̈ܝܫܐ (Brown, 2015, p. 28).

ܦܘܫܩܐ ܕܛܥ̈ܢܐ

ܛܥܢܐ (loading) ܝܠܗ، ܒܩܘܪܒܐ، ܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation) ܒܝܢܝ ܦܣܘܩܐ ܘܥܠܬܐ (Field, 2024, Section 18.3.1). Stevens ܟܡܪܚܩ ܠܡܦܫܩ ܛܥ̈ܢܐ ܒܢܘܬ ܡܢ .4، "ܘܐܝܬ ܕܓܒܝ .3؛ ܠܝܬ ܚܪܫܘܬܐ ܓܘ ܐܢܝ ܡܢܝ̈ܢܐ" (ܐܝܟ ܕܡܝܬܝܐ ܝܠܗ ܓܘ Field, 2024، ܦܣܩܐ 18.4.7؛ ܐܦ Brown, 2015، ܦܐܬܐ 27). ܓܘ ܡܦܩܢܐ ܟܛܫܚ ܛܥ̈ܢܐ ܬܚܘܬ .3 ܘܟܛܟܣܚ ܠܦܘܬ ܪܒܘܬܐ (Field, 2024, Section 18.6.4; Pallant, 2020, Chapter 15). ܦܣܘܩܐ ܕܛܥܝܢܐ ܝܠܗ ܥܠ ܬܪܬܝܢ ܥܠ̈ܠܬܐ ܟܡܚܫܒܚ ܠܗ ܥܡ ܥܠܬܐ ܕܛܥܢܐ ܪܡܐ؛ ܐܢ ܛܥ̈ܢܐ ܕܡܝ̈ܐ ܝܢܐ – ܡܚܬܡܠܐ ܦܣܘܩܐ "ܠܐ ܝܠܗ ܛܒܐ ܠܦܘܪܫܢܐ" ܒܝܢܝ ܬܪܝܢ ܡܘܕܥ̈ܢܘܬܐ (Field, 2024, Section 18.7.3). ܦܣܘܩܐ ܕܟܬܝܒܐ ܝܠܗ ܗܦܝܟܐܝܬ ܛܥܝܢܐ ܝܠܗ ܒܠܐ (ܦܣܩܐ 18.9.4). ܫܡܐ ܕܥܠܬܐ ܟܝܗܒܚ ܠܦܘܬ ܡܐ ܕܡܫܘܬܦܐ ܝܠܗ ܠܦܣܘ̈ܩܐ ܕܛܥܝ̈ܢܐ ܝܢܐ ܥܠܗ – ܘܬܘܟܢܝܬܐ ܠܐ ܟܥܒܕܐ ܐܗܐ ܩܐܠܘܟܘܢ (Pallant, 2020, Chapter 15).

ܫܪܝܪܘܬܐ ܘܡܢܝ̈ܢܐ ܕܥܠܬܐ

ܒܬܪ ܦܘܫܩܐ ܟܚܫܒܚ ܐܠܦܐ ܕ-Cronbach ܩܐ ܟܠ ܥܠܬܐ ܒܦܪܝܫܘܬܐ، ܒܬܪ ܗܘܦܟܐ ܕܦܣܘ̈ܩܐ ܕܟܬܝܒ̈ܐ ܝܢܐ ܗܦܝܟܐܝܬ (Field, 2024, Sections 18.9.3-18.9.4) – ܦܐܬܐ ܟܥܒܕ ܐܗܐ ܡܢ ܓܢܒܗ، ܠܦܘܬ ܥܠܬܐ ܕܟܠ ܦܣܘܩܐ ܛܥܝܢܐ ܝܠܗ ܥܠܗ ܚܝܠܢܐܝܬ ܡܢ ܟܠܗ ܘܠܦܘܬ ܪܘܫܡܐ ܕܛܥܢܐ. ܛܝܡܐ ܕ-.7-.8 "ܡܩܒܠܐ ܝܠܗ ܒܦܬܝܘܬܐ"، ܐܠܐ ܬܚܘܡ̈ܐ ܟܠܢܝ̈ܐ "ܠܐ ܝܢܐ ܡܬܦܗܡܢ̈ܐ"، ܘܐܠܦܐ ܠܐ ܝܠܗ ܡܚܘܝܢܐ ܕܣܒܠܬܐ ܕܚܕ ܡܫܘܚܬܐ ܝܠܗ (ܬܡܢ). ܩܐ ܚܘܫܒܐ ܓܡܝܪܐ، ܥܡ "ܐܠܦܐ ܐܢ ܦܣܘܩܐ ܫܩܝܠܐ" – ܦܐܬܐ "ܐܠܦܐ ܕ-Cronbach ܘܡܢܝܢܐ ܕܣܒܠܬܐ".

ܡܢܝ̈ܢܐ ܕܥܠܬܐ (factor scores) ܚܫܝ̈ܒܐ ܝܢܐ ܒܐܘܪܚܐ ܕܪܝܓܪܫܢ (Thurstone; Field, 2024, Section 18.3.3; Brown, 2015, p. 32)، ܘܡܨܝܐ ܠܡܚܬܐ ܠܗܘܢ ܐܝܟ ܥܡܘ̈ܕܐ ܚܕ̈ܬܐ ܓܘ ܦܐܝܠ. ܐܠܐ "ܒܥܕܢܐ ܪܓܝܠܐ ܠܐ ܟܡܦܠܚܚ ܒܡܢܝ̈ܢܐ ܕܥܠܬܐ ܒܝܕܗܘܢ"، ܐܠܐ ܒܓܘܡܪܐ ܝܢ ܒܡܨܥܝܬܐ ܕܦܣܘ̈ܩܐ ܕܛܥܝ̈ܢܐ ܝܢܐ ܥܠ ܥܠܬܐ (Field, 2024, Section 18.7.5). ܩܐ ܡܢܝ̈ܢܐ ܕܥܠܬܐ ܐܝܬ ܐܦ "indeterminacy": ܓܘ̈ܕܐ ܕܡܢܝ̈ܢܐ ܕܠܐ ܣܟܐ ܦܐܫܝ ܠܗܢ ܛܥ̈ܢܐ؛ ܦܐܬܐ ܟܡܘܕܥ ܡܢܝܢܐ ܡܫܘܬܦܐ ܕ-determinacy – ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܡܢܝܢܐ ܘܥܠܬܐ – ܘ-Gorsuch ܟܒܥܐ .80 ܠܟܡܝܘܬܐ (as cited in Brown, 2015, p. 32).

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܘܚܐ 1 – ܦܐܝܘܬܐ ܕܝܗܝ̈ܒܬܐ؛ ܠܘܚܐ 2 (ܟܦܝܠܐ) – KMO ܩܐ ܟܠ ܦܣܘܩܐ؛ ܠܘܚܐ 3 ܘܨܘܪܬܐ 1 – ܛܝ̈ܡܐ ܕܝܠܢ̈ܝܐ، ܦܘܫܩܐ ܒܓܢܒ ܚܕ̈ܕܐ ܘܨܘܪܬܐ scree؛ ܠܘܚܐ 4 – ܛܥ̈ܢܐ (ܓܘ ܚܘܕܪܐ ܡܨܠܝܢܐ – pattern matrix) ܥܡ ܫܘܬܦܘܬܐ، ܘܒܬܪܗ structure matrix (ܟܦܝܠܬܐ) ܘܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܥܠ̈ܠܬܐ؛ ܠܘܚܐ ܐܚܪܝܐ – ܐܠܦܐ ܩܐ ܟܠ ܥܠܬܐ.

ܓܘ ܡܬܠܐ (306 ܬܠܡܝ̈ܕܐ ܥܡ ܝܗܝ̈ܒܬܐ ܓܡܝܪ̈ܬܐ، 12 ܦܣܘ̈ܩܐ): KMO = .78 – "ܡܨܥܝܐ"، ܘܟܠ ܦܣܘ̈ܩܐ ܒܢܘܬ ܡܢ .5؛ χ²(66) = 824.33, p < .001؛ determinant .064. ܬܠܬܐ ܛܝ̈ܡܐ ܕܝܠܢ̈ܝܐ – 3.27، 1.76، 1.69 – ܪ̈ܡܐ ܝܢܐ ܡܢ ܡܨܥܝܬܐ ܓܕܫܢܝܬܐ (1.34، 1.25، 1.18)، ܘܐܪܒܥܝܐ، 0.80، ܢܚܝܬܐ ܝܠܗ ܡܢ 1.12: ܦܘܫܩܐ ܒܓܢܒ ܚܕ̈ܕܐ ܘ-Kaiser ܫܠܡܝ ܥܠ ܬܠܬܐ ܥܠ̈ܠܬܐ. ܒܬܪ PAF ܘ-oblimin: load، engagement ܘ-support، ܟܠ ܚܕ ܥܡ ܐܪܒܥܐ ܦܣܘ̈ܩܐ، ܘܦܣܘܩܐ ܗܦܝܟܐ ܓܘ ܟܠ ܚܕ ܛܥܝܢܐ ܝܠܗ ܒܠܐ؛ "ܐܢܐ ܟܝܠܦܢ ܥܡ ܚܒܪ̈ܐ ܕܩܘܪܣ" ܛܥܝܢܐ ܝܠܗ ܐܦ ܥܠ engagement (.35) ܘܐܦ ܥܠ support (.41) – ܛܥܢܐ ܥܠ ܥܠ̈ܠܬܐ ܣܓܝ̈ܐܐ (cross-loading). ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܥܠ̈ܠܬܐ .24-.30 ܒܛܝܡܐ ܫܪܝܪܐ، ܘܐܠܦܐ .69، .73 ܘ-.74.

ܫܪ̈ܛܐ ܘܙܘܗܪ̈ܐ (Assumptions and warnings)

ܕܪܓܐ ܕܡܫܘܚܬܐ. ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܓܘ ܦܐܬܐ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܕ-Pearson ܝܢܐ؛ ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܥܠ ܦܣܘ̈ܩܐ ܕ-Likert ܟܣܒܪ ܕܐܢܝ ܩܪܝܒ̈ܐ ܝܢܐ ܒܣܦܝܩܘܬܐ ܠܣܒܠܬܐ ܕܪܘ̈ܚܩܐ ܫܘ̈ܝܐ (ܥܝܕܐ ܕܣܐܝܛ – ܦܐܬܐ "ܡܫܬܚܠܦ̈ܢܐ ܘܕܪ̈ܓܐ ܕܡܫܘܚܬܐ"). ܩܐ ܦܣܘ̈ܩܐ ܕܬܪܝܢ ܛܝ̈ܡܐ Field ܟܡܩܪܒ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ tetrachoric (2024، ܦܣܩܐ 18.5.5) – ܠܐ ܓܘ ܦܐܬܐ. ܦܘܠܓܐ. ܢܘܪܡܠܝܘܬܐ ܚܫܝܚܬܐ ܝܠܗ ܒܣ ܩܐ ܒܘܚܪ̈ܢܐ ܘܩܐ ܟܠܢܝܘܬܐ (ܬܡܢ)؛ ML ܟܒܥܐ ܠܗ (Brown, 2015, p. 19). ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ. ܦܐܬܐ ܟܦܠܛ ܡܫܬܘܬܦ̈ܢܐ ܥܡ ܛܝܡܐ ܚܣܝܪܐ ܓܘ ܚܕ ܡܢ ܦܣܘ̈ܩܐ؛ Field ܟܡܙܗܪ ܡܢ ܫܩܠܬܐ "ܙܘܓܢܝܬܐ"، ܕܓܘܗ "ܫܘܥܪ̈ܐ ܡܨܝܐ ܕܡܫܬܓܫܝ" (2024، ܦܣܩܐ 18.6.4).

ܓܕܫ̈ܐ ܕ-Heywood. ܫܘܬܦܘܬܐ ܕ-1 ܘܠܥܠ – ܒܥܕܢܐ ܪܓܝܠܐ ܐܡܬܝ ܕܦܠܛܝ̈ܐ ܝܢܐ ܥܠ̈ܠܬܐ ܒܢܘܬ ܡܢ ܕܣܢܝܩ ܝܢ ܐܡܬܝ ܕܝܗܝ̈ܒܬܐ ܥܡ ܥܘܩ̈ܐ ܝܢܐ (Brown, 2015, p. 19; Chapter 5, Note 7, p. 185)؛ ܦܐܬܐ ܟܡܙܗܪ. ܡܥܒܕ̈ܢܘܝܬܐ ܕܢܘܣܚܐ. ܦܣܘ̈ܩܐ ܕܟܬܝܒ̈ܐ ܝܢܐ ܗܦܝܟܐܝܬ ܡܨܝܐ ܕܒܢܝ "ܥܠܬܐ" ܕܠܐ ܝܠܗ ܡܘܕܥܢܘܬܐ ܐܠܐ ܐܘܪܚܐ – ܣܒܠܬܐ ܕܚܕ ܡܫܘܚܬܐ ܥܡ ܢܘܣ̈ܚܐ ܚܠܝܛ̈ܐ "ܡܝܠܐ ܝܠܗ" ܠܡܦܠܛ ܒܬܪܬܝܢ ܥܠ̈ܠܬܐ (Brown, 2015, pp. 3, 202). "ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ ܕܒܨܘܝܐ". ܦܘܫܩܐ ܡܒܨܝܢܐ ܡܠܝܐ ܝܠܗ ܦܣܩ̈ܬܐ – ܡܢܝܢܐ ܕܥܠ̈ܠܬܐ، ܦܠܛܬܐ، ܚܘܕܪܐ، ܐܝܢܝ ܦܣܘ̈ܩܐ ܠܡܦܠܛ – ܘܡܛܠ ܗܕܐ ܐܗܘ ܣܢܝܩ ܝܠܗ "ܒܣ ܠܡܕܒܪ ܗܘܦܘܬܣ̈ܝܣ ܕܐܬܝ̈ܐ" (Field, 2024, Section 18.7.6).

ܡܘܕܝ ܠܐ ܟܚܫܒܐ ܐܗܐ ܦܐܬܐ. ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ polychoric ܘ-tetrachoric، ܒܘܚܪܢܐ MAP، ܚܘ̈ܕܪܐ quartimax، equamax ܘ-geomin، ܡܢܝ̈ܢܐ ܕ-Bartlett ܘ-Anderson-Rubin، ܦܘܫܩܐ ܥܠ ܡܐܛܪܝܟܣ ܕܫܘܚܠܦ̈ܐ ܡܫܘܬܦ̈ܐ (covariance matrix)، ܘ-ESEM.

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

Analyze › Dimension Reduction › Factor: ܟܡܥܠܚ ܦܣܘ̈ܩܐ؛ ܓܘ Descriptives – KMO and Bartlett's test، Determinant، Anti-image ܘ-Reproduced؛ ܓܘ Extraction – ܐܘܪܚܐ ܘܡܢܝܢܐ ܕܥܠ̈ܠܬܐ؛ ܓܘ Rotation – ܚܘܕܪܐ؛ ܓܘ Options – Sorted by size ܘ-Suppress small coefficients ܥܡ .3 (Field, 2024, Section 18.6; Pallant, 2020, Chapter 15). ܦܘܫܩܐ ܒܓܢܒ ܚܕ̈ܕܐ ܠܝܬ ܓܘ ܪܫܝܡܬܐ (Menu)؛ Field ܟܡܪܗܛ ܠܗ ܒܝܕ R ܓܘ SPSS (SPSS Tip 18.1)، ܘ-Pallant – ܓܘ ܬܘܟܢܝܬܐ ܦܪܝܫܬܐ (2020، ܨܚܚܐ 15). SPSS ܟܡܘܩܦ ܦܠܛܬܐ ܒܬܪ 25 iterations ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ (Field, 2024, Section 18.6.2)؛ ܣܝܢܬܐܟܣ ܕܦܐܬܐ ܟܒܥܐ 1,000 ܘ-convergence ܚܬܝܬܬܐ، ܐܝܟ ܓܘ ܦܐܬܐ. ܣܝܢܬܐܟܣ ܐܦ ܐܝܬ ܓܘܗ RELIABILITY ܩܐ ܟܠ ܥܠܬܐ. ܓܘ PSPP، ܬܘܟܢܝܬܐ ܚܐܪܬܐ، ܪܗܛܠܢ PAF ܘ-PCA ܥܡ varimax ܘ-promax؛ ML ܘ-oblimin ܠܝܬ ܓܘܗ. ܫܒ̈ܝܠܐ ܝܢܐ ܝܕܥܬܐ ܟܠܢܝܬܐ ܥܠ ܬܘܟܢܝܬܐ.

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

ܚܒܝܫܘܬܐ psych (Revelle): KMO، cortest.bartlett، fa (PAF, ML) ܘ-principal (PCA)، ܘ-alpha؛ ܚܘܕܪܐ – ܡܢ GPArotation. ܚܙܝܡܘܢ: fa ܥܡ rotate = "oblimin" ܟܡܚܕܪ ܕܠܐ Kaiser normalization، ܘܡܛܠ ܗܕܐ ܟܝܗܒ ܛܥ̈ܢܐ ܦܪ̈ܝܫܐ ܩܠܝܠ ܡܢ SPSS؛ ܩܐ ܡܫܩܠܐ ܐܝܟ SPSS ܘܐܝܟ ܦܐܬܐ – GPArotation::oblimin(L, normalize = TRUE)، ܐܝܟ ܓܘ ܣܩܪܝܦܬ ܕܠܬܚܬ. ܦܘܫܩܐ ܒܓܢܒ ܚܕ̈ܕܐ ܓܘ ܣܩܪܝܦܬ ܟܒܢܐ ܛܘܦ̈ܣܐ ܓܕܫܢ̈ܝܐ ܒ-rnorm، ܒܗܘ ܙܪܥܐ ܘܒܗܘ ܡܘܠܕܢܐ ܐܝܟ ܦܐܬܐ. ܣܩܪܝܦܬ ܕܠܬܚܬ ܪܗܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ ܐܢܓܠܝܙܝܐ (R 4.3.3, psych 2.4.1)، ܘܛܝ̈ܡܐ ܓܘ ܡܥܝܪ̈ܢܘܬܐ ܫܘ̈ܝܐ ܝܢܐ ܠܦܐܬܐ. ܢܡܘܣܐ ܕܣܐܝܛ ܩܐ ܣܘܪܝܬ ܓܘ R: ܦܐܝܠ UTF-8، ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ، ܘܫܡ̈ܗܐ ܕܡܫܬܚܠܦ̈ܢܐ ܒܐܢܓܠܝܙܝܐ.

# ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܡܒܨܝܢܐ – ܦܪܘܦܣܘܪ ܣܛܐܛ. ܐܗܐ ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8؛ ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ
suppressMessages({ library(readxl); library(psych); library(GPArotation) })   # install.packages(c("readxl", "psych", "GPArotation"))

# ܛܥܢܐ: ܓܠܝܘܢܐ "Data" ܓܘ ܦܐܝܠ ܕܡܬܠܐ ܐܢܓܠܝܙܝܐ؛ 12 ܦܣܘ̈ܩܐ، ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ
d <- as.data.frame(read_excel("C:/Rdata/DATA_efa_example_eng.xlsx", sheet = "Data"))
x <- na.omit(d[, 3:14]); R <- cor(x); n <- nrow(x); n
# ܦܐܪܐ: 306

# ܦܐܝܘܬܐ ܕܝܗܝ̈ܒܬܐ
KMO(R)$MSA; cortest.bartlett(R, n = n)$chisq; det(R)
# ܦܐܪܐ: KMO = .780, χ²(66) = 824.33, determinant .064

# ܦܘܫܩܐ ܒܓܢܒ ܚܕ̈ܕܐ: 100 ܛܘܦ̈ܣܐ ܓܕܫܢ̈ܝܐ ܕܝܗܝ̈ܒܬܐ ܒܗܝ ܪܒܘܬܐ؛ ܙܪܥܐ 2026 – ܐܝܟ ܓܘ ܦܐܬܐ
ev <- eigen(R)$values
set.seed(2026); rnd <- t(sapply(1:100, function(r) eigen(cor(matrix(rnorm(n * 12), n, 12)), only.values = TRUE)$values))
round(rbind(data = ev, random = colMeans(rnd))[, 1:5], 3)
# ܦܐܪܐ: 3.269, 1.759, 1.688 ܒܢܘܬ ܡܢ 1.337, 1.250, 1.177؛ ܐܪܒܥܝܐ 0.801 ܬܚܘܬ 1.116 – ܬܠܬܐ ܥܠ̈ܠܬܐ

# PAF ܥܡ ܬܠܬܐ ܥܠ̈ܠܬܐ، ܘܒܬܪܟܢ oblimin ܬܪܝܨܐ ܥܡ Kaiser normalization (ܐܝܟ SPSS)
L <- unclass(fa(R, nfactors = 3, fm = "pa", rotate = "none", n.obs = n, max.iter = 1000, min.err = 1e-9)$loadings)
r <- GPArotation::oblimin(L, normalize = TRUE)
print(round(unclass(r$loadings), 2)); round(r$Phi, 2)
# ܦܐܪܐ: load – .53 ܗܠ .67 (load4 −.59)، engagement – .46 ܗܠ .84، support – .41 ܗܠ .79؛ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܥܠ̈ܠܬܐ .24 ܗܠ .30 ܒܛܝܡܐ ܫܪܝܪܐ
# ܛܟܣܐ ܘܪܘܫܡܐ ܕܥܠ̈ܠܬܐ ܡܨܝܐ ܕܗܘܝܐ ܦܪ̈ܝܫܐ ܡܢ ܦܐܬܐ – ܦܐܬܐ ܟܛܟܣ ܠܦܘܬ ܓܘܡܪܐ ܕܡܪ̈ܒܥܐ ܕܛܥ̈ܢܐ ܘܟܗܦܟ ܪܘܫܡܐ ܗܟܢܐ ܕܓܘܡܪܐ ܕܥܡܘܕܐ ܚܝܘܒܝܐ ܗܘܐ

# ܐܠܦܐ ܩܐ ܟܠ ܥܠܬܐ – ܦܣܘܩܐ ܐܪܒܥܝܐ ܓܘ ܟܠ ܓܘܕܐ ܗܦܝܟܐ ܝܠܗ (ܓܘ support – ܬܠܝܬܝܐ)
psych::alpha(x[, 1:4], keys = c(1, 1, 1, -1))$total$raw_alpha
psych::alpha(x[, 5:8], keys = c(1, 1, 1, -1))$total$raw_alpha
psych::alpha(x[, 9:12], keys = c(1, 1, -1, 1))$total$raw_alpha
# ܦܐܪܐ: .69, .73, .74

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

ܡܘܕܝ ܠܡܘܕܥ: ܐܘܪܚܐ ܕܦܠܛܬܐ، ܐܝܟܢܐ ܦܣܝܩܐ ܝܠܗ ܡܢܝܢܐ ܕܥܠ̈ܠܬܐ (factors) ("ܥܡ ܦܘܫܩܐ ܒܓܢܒ ܚܕ̈ܕܐ")، ܚܘܕܪܐ (rotation)، ܫܘܚܠܦܐ ܡܦܫܩܐ (explained variance) ܘܛܝ̈ܡܐ ܕܝܠܢ̈ܝܐ (eigenvalues)، ܘܠܘܚܐ (table) ܥܡ ܟܠ ܛܥ̈ܢܐ، ܠܐ ܒܣ ܪ̈ܡܐ (Pallant, 2020, Chapter 15)؛ ܦܐܝܘܬܐ ܕܝܗܝ̈ܒܬܐ (KMO)؛ ܘܠܘܚܐ ܕܛܥ̈ܢܐ ܕܓܘܗ ܛܥ̈ܢܐ ܒܢܘܬ ܡܢ .40 ܡܬܚܫܟ̈ܢܐ ܝܢܐ، ܥܡ ܛܝ̈ܡܐ ܕܝܠܢ̈ܝܐ، ܡܢܬܐ ܒܡܐܐ ܕܫܘܚܠܦܐ ܘܐܠܦܐ ܓܘ ܣܕܪ̈ܐ ܐܚܪ̈ܝܐ (Field, 2024, Section 18.8, Table 18.1). Field ܟܡܪܚܩ ܐܦ ܠܡܫܘܬܦ ܡܐܛܪܝܟܣ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ، ܕܐܚܪ̈ܢܐ ܡܨܝܝ ܠܡܬܢܐ (ܬܡܢ). ܢܡܘ̈ܣܐ ܕܨܘܪܬܐ (APA, 2020, Section 6.36): ܛܥ̈ܢܐ، ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܘ-KMO – ܕܠܐ ܨܦܪܐ ܩܕܡ ܢܘܩܙܐ؛ χ² – ܥܡ. ܦܣܩܐ ܕܡܫܟܚ̈ܢܘܬܐ (results paragraph) ܓܘ ܡܦܩܢܐ ܒܢܝܐ ܝܠܗ ܗܟܢܐ، ܒܣܘܪܝܬ ܘܒܐܢܓܠܝܙܝܐ.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܠܡܓܒܐ ܡܢܝܢܐ ܕܥܠ̈ܠܬܐ ܠܦܘܬ Kaiser. "ܟܫܥܪ ܒܝܬܝܪܘܬܐ"، ܝܚܝܕܐܝܬ ܥܡ ܦܣܘ̈ܩܐ ܣܓܝ̈ܐܐ (Field, 2024, Section 18.4.5).

ܚܘܕܪܐ orthogonal "ܡܛܠ ܕܐܗܐ ܝܠܗ ܓܘܒܝܐ ܡܩܕܡܐ". ܓܘ ܝܗܝ̈ܒܬܐ ܥܠ ܒܢܝ̈ ܐܢܫܐ ܥܠ̈ܠܬܐ ܩܪܝܒ ܠܟܠ ܐܝܡܢ ܐܣܝܪ̈ܐ ܝܢܐ (Field, 2024, Section 18.4.6; Brown, 2015, p. 28).

ܠܡܦܫܩ structure matrix ܒܕܘܟܬܐ ܕ-pattern، ܝܢ ܠܡܘܕܥ ܚܕܐ ܡܢܝܗܝ ܒܣ ܕܠܐ ܡܐܡܪܐ ܐܝܢܐ (Field, 2024, Section 18.7.4; Pallant, 2020, Chapter 15).

ܠܚܫܒܐ ܐܠܦܐ ܥܠ ܟܠ ܦܣܘ̈ܩܐ ܐܟܚܕܐ، ܝܢ ܕܠܐ ܗܘܦܟܐ ܕܦܣܘ̈ܩܐ ܗܦܝ̈ܟܐ – ܐܠܦܐ ܟܦܠܛ ܢܚܝܬܐ، ܘܐܦ ܒܠܐ (Field, 2024, Section 18.9.4).

ܠܡܩܪܐ ܠ-PCA "ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ" ܕܠܐ ܡܚܘܝܐ. Field ܒܝܕܗ ܟܡܘܕܐ ܕܐܗܘ ܟܚܐܪ ܠܗܘܢ ܐܝܟ ܕܚܕ ܗܘܘ (2024، ܦܣܩܐ 18.2، ܡܥܝܪܢܘܬܐ 2) – ܐܠܐ ܓܘ ܬܘܢܝܐ ܟܟܬܒܚ ܡܘܕܝ ܪܗܛܐ ܝܠܗ.

ܠܫܪܪܐ ܒܢܝܢܐ ܥܠ ܗܘ ܕܘܡܝܐ ܕܓܘܗ ܡܫܟܚܠܗܘܢ ܠܗ. ܡܒܨܝܢܐ ܘܡܫܪܪܢܐ – ܓܘ ܕܘ̈ܡܝܐ ܦܪ̈ܝܫܐ (Brown, 2015, p. 12).

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.

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

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

Cattell (1966)، Comrey ܘ-Lee (1992)، Guadagnoli ܘ-Velicer (1988)، Kaiser ܘ-Rice (1974)، MacCallum et al. (1999) ܘ-Stevens (2002) – ܐܝܟ ܕܡܝܬܝ̈ܐ ܝܢܐ ܓܘ Field (2024)؛ Horn (1965) – ܓܘ Pallant (2020) ܘ-Field؛ Tabachnick ܘ-Fidell (2013) – ܓܘ Pallant؛ Glorfeld (1995)، Gorsuch (1983)، Hu ܘ-Bentler (1999) ܘ-Thurstone (1947) – ܓܘ Brown (2015). ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ (site rule)، ܓܘ ܪܫܝܡܬܐ ܕܡܒܘ̈ܥܐ (reference list) ܟܡܬܚܙܝ ܒܣ ܡܒܘ̈ܥܐ ܕܩܪܝ̈ܐ ܝܢܐ ܓܘ ܢܘܣܚܐ ܩܕܡܝܐ. Field ܘ-Pallant ܡܝܬܝ̈ܐ ܝܢܐ ܠܦܘܬ ܦܣܩܐ ܘܨܚܚܐ (ܟܬܒ̈ܐ ܐܠܩܛܪܘܢܝ̈ܐ ܠܐ ܟܢܛܪܝ ܡܢܝ̈ܢܐ ܕܦܐ̈ܬܐ ܛܒܝ̈ܥܐ)، Brown – ܠܦܘܬ ܦܐܬܐ ܛܒܝܥܬܐ. ܩܪܝ̈ܐ ܝܢܐ ܨܚܚܐ 18 ܕ-Field، ܨܚܚܐ 15 ܕ-Pallant، ܘܨܚܚܐ 2 ܘܦܐ̈ܬܐ ܡܢ ܨܚ̈ܚܐ 1، 3 ܘ-5 ܕ-Brown. ܚܘܫܒܐ ܓܘ ܦܐܬܐ ܫܪܝܪܐ ܝܠܗ ܩܘܒܠ R 4.3.3 (psych, GPArotation, factanal, varimax, promax – ܥܡ ܦܘܫܩܐ ܒܓܢܒ ܚܕ̈ܕܐ، ܕܘܡܝܐ ܒܬܪ ܕܘܡܝܐ)، ܩܘܒܠ PSPP، ܘܩܘܒܠ ܠܘܚܐ 2.2 ܕ-Brown (2015) – ܛܝ̈ܡܐ ܕܝܠܢ̈ܝܐ، ܫܘܬܦܘܬܐ ܩܕܡܝܬܐ، ܛܥ̈ܢܐ ܕ-ML ܘ-χ².

ܛܥܝ̈ܘܬܐ ܕܡܫܟܚܠܢ ܓܘ ܡܒܘ̈ܥܐ. Pallant (2020، ܨܚܚܐ 15): ܫܘܬܦܘܬܐ ܕܛܒܝܥܬܐ ܝܠܗ ܩܐ ܦܘܫܪܐ ܕܬܪܝܢ ܡܢܘ̈ܬܐ ܫܩܝܠܬܐ ܝܠܗ ܡܢ ܦܘܫܪܐ ܕܐܪܒܥܐ (ܓܘ ܬܪܝܢ ܡܢܘ̈ܬܐ ܐܢܝ ܠܐ ܡܨܝܐ ܕܗܘܝܐ – ܠܡܬܠܐ .714 ܩܐ ܦܣܘܩܐ ܕܛܝܡܐ ܥܠܝܐ ܕܝܠܗ ܒܩܘܪܒܐ .27 ܝܠܗ؛ ܓܘ ܟܬܝܒܬܐ ܒܝܕܗ .258)؛ ܘܓܘ ܠܘܚܐ 15.2 "898" ܒܕܘܟܬܐ ܕ-.898. Field (2024، ܦܣܩܐ 18.8): "ܒܢܘܬ ܡܢ 40% ܡܢ ܫܘܚܠܦܐ" ܫܩܝܠܐ ܝܠܗ ܡܢ ܛܝ̈ܡܐ ܕܝܠܢ̈ܝܐ ܩܕܡܝ̈ܐ، ܐܡܬܝ ܕܦܘܫܪܐ ܒܝܕܗ ܟܡܦܫܩ 36.28%؛ ܘܡܨܥܝܬܐ ܕܫܘܬܦܘܬܐ ܓܘ ܦܣܩܐ 18.7.2 ܚܫܝܒܬܐ ܝܠܗ ܡܢ ܥܡܘܕܐ ܩܕܡܝܐ. Brown (2015): ܓܘ ܦܐܬܐ 15 O1 ܩܪܝܐ ܝܠܗ "tearfulness" (ܓܘ ܠܘܚܐ – hopelessness)؛ ܓܘ ܦܐܬܐ 27 ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܥܠ̈ܠܬܐ "ܒܝܢܝ ܨܦܪܐ ܘܚܕ" – ܐܢܝ ܡܨܝܐ ܕܗܘܝܐ ܒܠ̈ܐ.