ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܕܬܪܝܢ ܛܝ̈ܡܐ

ܛܥܢܐ ܕܝܗܝ̈ܒܬܐ (loading the data)

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

ܓܘܒܝܐ ܕܡܫܬܚܠܦ̈ܢܐ (Variable selection)

ܐܝܡܢ ܟܡܦܠܚܚ ܒܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ؟

ܐܝܡܢ ܕܦܐܪܐ (outcome) ܝܠܗ ܓܢܣܐ – ܫܬܦ ܝܢ ܠܐ، ܐܬܐܣܝ ܝܢ ܠܐ، ܝܗܒ ܩܠܐ ܝܢ ܠܐ – ܘܒܥܝܚ ܕܡܢܒܚ ܠܗ ܡܢ ܡܢܒ̈ܝܢܐ (predictors)، ܡܬܡܫܚ̈ܢܐ ܝܢ ܕܓܢ̈ܣܐ، ܘܕܝܕܥܚ ܡܘܕܝ ܝܠܗ ܝܘܬܪܢܐ ܕܟܠ ܡܢܒܝܢܐ ܥܡ ܐܚܪ̈ܢܐ ܓܘ ܡܘܕܝܠ (Field, 2024, Section 20.2; Pallant, 2020, Chapter 14). ܐܗܐ ܝܠܗ ܦܘܬܝܐ ܕܡܘܕܝܠ (model) ܣܪܛܢܝܐ (linear) ܩܐ ܦܐܪܐ ܕܬܪܝܢ ܛܝ̈ܡܐ: ܒܘܚܪܢܐ ܕܟܝ ܡܪܒܥܐ (chi-square؛ ܦܐܬܐ ܒܘܚܪܢܐ ܕܟܝ ܡܪܒܥܐ ܠܠܐ ܬܠܝܘܬܐ) ܟܒܚܪ ܐܣܘܪܐ ܒܝܢܝ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܕܓܢ̈ܣܐ (categorical variables)؛ ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ (logistic regression) ܟܡܢܒܐ ܦܐܪܐ ܡܢ ܟܡܐ ܡܢܒ̈ܝܢܐ ܐܟܚܕܐ، ܘܐܦ ܡܢ ܡܬܡܫܚ̈ܢܐ. ܩܐ ܦܐܪܐ ܥܡ ܬܠܬܐ ܓܢ̈ܣܐ ܘܠܥܠ – ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܕܓܢ̈ܣܐ ܣܓܝ̈ܐܐ (Multinomial)، ܕܠܝܬ ܓܘ ܐܗܐ ܦܐܬܐ؛ ܩܐ ܦܐܪܐ ܡܬܡܫܚܢܐ – ܪܝܓܪܫܢ ܣܪܛܢܝܐ.

ܡܘܕܝܠ: ܡܢ ܡܣܬܒܪܢܘܬܐ ܠܠܘܓ-ܣܟܘ̈ܝܐ

ܡܘܕܝܠ (model) ܣܪܛܢܝܐ ܟܡܢܒܐ ܛܝܡܐ؛ ܐܟܐ ܛܝܡܐ ܝܠܗ ܡܣܬܒܪܢܘܬܐ (probability)، ܘܐܣܘܪܐ ܣܪܛܢܝܐ ܒܝܢܝܗ̇ ܘܒܝܢܝ ܡܢܒܝܢܐ (predictor) ܗܘܐ ܝܗܒ ܛܝ̈ܡܐ ܠܒܪ ܡܢ 0-1 (ܨܘܪܬܐ 1). ܦܘܫܪܐ: ܠܐ ܟܡܢܒܚ ܡܣܬܒܪܢܘܬܐ ܐܠܐ ܠܘܓ-ܣܟܘ̈ܝܐ (log-odds) ܕܝܠܗ̇ – ln(p/(1 − p)) = b₀ + b₁X₁ + … + bₙXₙ (Field, 2024, Equation 20.13) – ܘܟܫܩܠܚ ܡܣܬܒܪܢܘܬܐ ܒܬܪ ܒܐܘܪܚܐ ܕ-p = 1/(1 + e^{−(b₀ + b₁X₁ + …)}) (ܫܘܝܘܬܐ 20.5). "ܣܟܘ̈ܝܐ" (odds) ܝܢܐ ܦܘܚܡܐ ܒܝܢܝ ܡܣܬܒܪܢܘܬܐ ܕܐܝܢ ܘܡܣܬܒܪܢܘܬܐ ܕܠܐ: ܡܣܬܒܪܢܘܬܐ .75 ܝܠܗ̇ ܣܟܘ̈ܝܐ 3 (3:1). ܦܪܡܝ̈ܛܪܐ (parameters) ܡܫܥܪ̈ܐ ܝܢܐ ܒܡܬܚܙܝܢܘܬܐ ܥܠܝܬܐ (maximum likelihood) – ܒܨܝܐ ܕܡܬܦܢܐ (iterative) ܥܠ ܛܝ̈ܡܐ ܕܝܗܒܝ ܡܣܬܒܪܢܘܬܐ ܪܡܬܐ ܝܬܝܪ ܠܝܗܝ̈ܒܬܐ ܕܚܙ̈ܝܐ ܝܢܐ (Field، ܦܣܩܐ 2.7 ܘ-Tip 20.1) – ܘܡܛܠ ܗܕܐ ܠܝܬ ܐܟܐ "ܡܬܢܝܬܐ ܣܟܝܪܬܐ" (closed-form) ܐܠܐ ܥܒܕܐ ܕܡܬܟܢܫ (converges)، ܘܒܥܕܢ̈ܐ ܐܚܪ̈ܢܐ ܠܐ ܡܬܟܢܫ (ܦܣܩܐ ܕܫܪ̈ܛܐ).

ܦܘܚܡܐ ܕܣܟܘ̈ܝܐ – Exp(B)

ܡܢܝܢܐ ܡܫܘܬܦܐ (coefficient) B ܝܠܗ ܫܘܢܝܐ ܓܘ ܠܘܓ-ܣܟܘ̈ܝܐ (log-odds) ܩܐ ܣܠܩܐ ܕܚܕ ܡܫܘܚܬܐ ܓܘ ܡܢܒܝܢܐ (predictor)، ܐܝܡܢ ܕܐܚܪ̈ܢܐ ܩܝ̈ܡܐ ܝܢܐ – ܘ"ܚܕ ܦܐ ܠܐ ܟܦܗܡ ܡܘܕܝ ܝܠܗ ܫܘܢܝܐ ܓܘ ܠܘܓ-ܣܟܘ̈ܝܐ. ܚܕ ܦܐ ܠܐ" (Field, 2024, Section 20.3.3). ܡܛܠ ܗܕܐ ܟܬܢܚ e^B، ܦܘܚܡܐ ܕܣܟܘ̈ܝܐ (odds ratio): ܦܘܚܡܐ ܒܝܢܝ ܣܟܘ̈ܝܐ ܒܬܪ ܣܠܩܐ ܕܚܕ ܡܫܘܚܬܐ ܓܘ ܡܢܒܝܢܐ ܘܣܟܘ̈ܝܐ ܩܕܡܗ (ܫܘܝܘܬܐ 20.17). OR = 1 – ܠܝܬ ܐܣܘܪܐ؛ OR > 1 – ܣܟܘ̈ܝܐ ܟܣܠܩܝ ܥܡ ܡܢܒܝܢܐ؛ OR < 1 – ܟܢܚܬܝ. ܡܬܠܐ ܕ-Field (ܦܣܩܐ 20.6.3، ܩܘܦܣܐ 20.1): ܐܣܝܘܬܐ (treatment) ܩܘܒܠ ܕܠܐ ܐܣܝܘܬܐ، B = 1.229، OR = e^1.229 = 3.42 – ܣܟܘ̈ܝܐ ܕܚܠܡܐ ܝܢܐ 3.42 ܓܗ̈ܐ ܒܝܫ ܩܐ ܐܢܝ ܕܫܩܠܠܗܘܢ ܐܣܝܘܬܐ؛ ܚܘܫܒܢܐ ܬܪܝܨܐ: ܣܟܘ̈ܝܐ ܕܚܠܡܐ ܕܠܐ ܐܣܝܘܬܐ 24/32 = .75، ܥܡ ܐܣܝܘܬܐ 41/16 = 2.56، ܘܦܘܚܡܐ 3.42. Pallant (2020، ܨܚܚܐ 14): ܩܐ ܡܢܒܝܢܐ ܡܬܡܫܚܢܐ (continuous) OR ܝܠܗ ܩܐ ܟܠ ܡܫܘܚܬܐ (ܫܢܬܐ، ܫܥܬܐ، ܢܘܩܙܐ ܓܘ ܣܒܠܬܐ – ܘܡܛܠ ܗܕܐ ܬܠܝܐ ܝܠܗ ܒܡܫܘܚܬܐ)؛ ܩܐ ܡܢܒܝܢܐ ܕܓܢ̈ܣܐ (categorical) – ܓܢܣܐ ܩܘܒܠ ܓܢܣܐ ܕܫܬܐܣܐ (base)؛ ܘ-OR ܙܥܘܪܐ ܡܢ 1 ܦܫܝܩܐ ܝܠܗ ܠܡܗܦܟܐ (1/OR) – "ܩܐ ܟܠ ܫܥܬܐ ܕܕܡܟܬܐ ܒܨܝܪ، ܣܟܘ̈ܝܐ ܟܪܒܝ 1.56 ܓܗ̈ܐ" – ܘܒܬܪ ܟܗܦܟܚ ܐܦ ܬܚܘܡܐ ܕܬܘܟܠܢܐ. ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܩܐ OR: ܐܢ ܠܐ ܐܝܬ ܓܘܗ 1، ܐܘܪܚܐ ܕܐܣܘܪܐ ܪܫܝܡܐ ܝܠܗ (Field, Section 20.6.3)؛ ܐܢ ܐܝܬ ܓܘܗ 1، ܡܨܐ ܕܓܘ ܟܢܫܐ ܟܠܢܝܐ (population) ܐܘܪܚܐ ܗܘܝܐ ܗܦܝܟܐ.

ܪܫܝܡܘܬܐ ܕܡܘܕܝܠ، R² ܕܠܐ ܫܪܝܪ̈ܐ ܘ-Hosmer-Lemeshow

ܠܘܓ-ܡܬܚܙܝܢܘܬܐ ܘܣܛܝܘܬܐ. ܛܝܒܘܬܐ ܕܦܐܝܘܬܐ (goodness of fit) ܡܫܝܚܐ ܝܠܗ̇ ܒܠܘܓ-ܡܬܚܙܝܢܘܬܐ (log-likelihood؛ Field, 2024, Equation 20.19) – ܕܡܝܐ ܠܓܘܡܪܐ ܕܡܪ̈ܒܥܐ ܕܫܪ̈ܟܐ: ܟܡܐ ܝܕܥܬܐ ܦܝܫܐ ܠܐ ܡܦܫܩܬܐ. ܦܫܝܩܐ ܝܠܗ ܒܝܫ ܠܡܦܠܚܐ ܥܡ ܣܛܝܘܬܐ −2LL (deviance; Equation 20.20)، ܡܛܠ ܕܐܝܬܠܗ̇ ܦܘܠܓܐ ܕܟܝ ܡܪܒܥܐ (chi-square). ܒܘܚܪܢܐ ܕܡܘܕܝܠ (ܫܘܝܘܬܐ 20.21): χ² = (−2LL)_ܣܦܝܩܐ − (−2LL)_ܡܘܕܝܠ، ܥܡ df = ܡܢܝܢܐ ܕܡܢܒ̈ܝܢܐ – ܐܝܢ ܡܢܒ̈ܝܢܐ (predictors) ܐܟܚܕܐ ܟܡܛܝܒܝ ܡܢ ܡܘܕܝܠ ܕܟܡܚܡܐ ܩܐ ܟܠܢܫ ܓܢܣܐ ܕܣܓܝ ܡܬܚܙܐ. ܓܘ Field: 154.084 − 144.158 = 9.926، p = .002. ܓܘ SPSS ܐܗܐ ܝܠܗ Omnibus Tests of Model Coefficients (Pallant, 2020، ܨܚܚܐ 14: "ܒܥܝܚ ܛܝܡܐ ܪܫܝܡܐ"). Wald ܩܐ ܡܢܒܝܢܐ ܝܚܝܕܝܐ (ܦܣܩܐ 20.3.4): z = B/SE، ܕ-SPSS ܟܛܒܥ ܠܗ ܡܪܒܥܐ؛ ܐܠܐ ܐܝܡܢ ܕ-B ܪܒܐ ܝܠܗ، ܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) ܟܡܬܢܦܚܐ ܘ-Wald ܟܙܥܪ (Menard, 2002, as cited in Field) – ܒܘܚܪܢܐ ܕܦܘܚܡܐ ܕܡܬܚܙܝܢܘܬܐ (likelihood ratio test) ܥܡ ܬܘܣܦܬܐ ܕܡܢܒܝܢܐ (ܡܘܕܝܠ ܕܠܐ ܘܡܘܕܝܠ ܥܡ) ܡܗܝܡܢܐ ܝܠܗ ܒܝܫ. R² ܕܠܐ ܫܪܝܪ̈ܐ (pseudo). ܠܝܬ R² ܫܪܝܪܐ؛ Cox & Snell (ܫܘܝܘܬܐ 20.25) ܡܢ ܡܬܘܡ ܠܐ ܟܡܛܐ ܠ-1، ܘ-Nagelkerke (ܫܘܝܘܬܐ 20.26) ܟܬܪܨ ܐܗܐ – "ܡܚܘ̈ܝܢܐ ܕܠܐ ܫܪܝܪ̈ܐ" ܕܠܐ ܝܢܐ ܡܢܬܐ ܕܫܘܚܠܦܐ ܡܦܫܩܐ (explained variance)، ܐܠܐ ܟܡܫܒܩܝ ܠܦܘܚܡܐ ܕܡܘܕ̈ܝܠܐ ܥܠ ܗܘ ܦܐܪܐ (Pallant). ܓܘ Field: .084 ܘ-.113 ܩܐ ܗܘ ܡܘܕܝܠ. Hosmer-Lemeshow. ܒܘܚܪܢܐ ܕܛܝܒܘܬܐ ܕܦܐܝܘܬܐ ܕܟܦܠܓ ܡܫܬܘܬܦ̈ܢܐ (participants) ܠܥܣܪܐ ܓܘ̈ܕܐ ܠܦܘܬ ܡܣܬܒܪܢܘܬܐ ܡܢܒܝܬܐ (predicted probability) ܘܟܦܚܡ ܚܙܝܐ ܥܡ ܡܣܟܝܐ: ܐܟܐ ܒܥܝܚ p ܥܠ ܡܢ .05 – p ܢܚܝܬܐ ܟܐܡܪ ܦܐܝܘܬܐ ܒܝܫܬܐ (Pallant، ܨܚܚܐ 14: SPSS ܟܩܪܐ ܠܗ "ܒܘܚܪܢܐ ܡܗܝܡܢܐ ܡܢ ܟܠܗ" ܩܐ ܦܐܝܘܬܐ). Field ܟܡܥܗܕ ܠܗ ܐܝܟ ܓܘܒܝܐ ܒܠܚܘܕ (ܦܣܩܐ 20.5.11). Gelman ܘ-Hill (2007، ܦܐܬܐ 100) ܟܝܗܒܝ ܢܡܘܣܐ ܕܨܒܥܐ (rule of thumb) ܩܐ ܣܛܝܘܬܐ: ܡܢܒܝܢܐ ܕܝܠܗ ܒܣ ܩܠܐ (noise) ܟܡܢܚܬ ܣܛܝܘܬܐ ܒ-1 ܒܡܨܥܝܬܐ، ܘܡܢܒܝܢܐ ܕܝܗܒ ܝܕܥܬܐ – ܒܝܫ ܡܢ 1؛ k ܡܢܒ̈ܝܢܐ ܕܡܘܣܦ̈ܐ ܝܢܐ ܣܢܝܩܝ ܕܡܢܚܬܝ ܠܗ̇ ܒܝܫ ܡܢ k.

ܒܢܝܢܐ ܕܡܘܕܝܠ: ܡܥܠܬܐ ܡܛܠܨܬܐ، ܕܪ̈ܓܐ ܘܚܣܝܟܘܬܐ

ܦܐܬܐ ܟܡܥܠܐ ܟܠ ܡܢܒ̈ܝܢܐ (predictors) ܓܒܝ̈ܐ ܓܘ ܚܕ ܓܘܫܡܐ (block) – ܡܥܠܬܐ ܡܛܠܨܬܐ (Enter)، ܓܘܒܝܐ ܡܩܕܡܐ (default) ܕ-SPSS ܘܕ-Pallant (2020، ܨܚܚܐ 14). Field (2024، ܦܣܩܐ 20.3.8) ܟܓܒܐ ܒܢܝܢܐ ܒܕܪ̈ܓܐ (hierarchical) ܕܡܕܒܪܐ ܝܠܗ ܡܢ ܬܐܘܪܝܐ: ܟܫܪܚ ܡܢ ܡܢܒܝܢܐ ܪܝܫܝܐ، ܟܡܘܣܦܚ ܓܘ̈ܫܡܐ ܘܟܒܚܪܚ ܓܘ ܟܠ ܕܪܓܐ ܐܢ −2LL ܢܚܬ ܒܪܫܝܡܘܬܐ (Block χ² ܓܘ ܡܦܩܢܐ ܕ-SPSS) – ܘܐܢ ܠܐ، ܟܕܥܪܚ ܠܡܘܕܝܠ ܦܫܝܛܐ ("ܚܣܝܟܘܬܐ" – parsimony: ܠܐ ܟܡܥܠܚ ܡܢܒܝܢܐ ܕܠܐ ܝܘܬܪܢܐ ܕܦܘܫܩܐ). ܓܘ ܡܬܠܐ ܕܝܠܗ ܕ-eel، ܬܘܣܦܬܐ ܕܐܘܪܟܐ ܕܥܩܬܐ ܫܢܝܠܗ χ² ܒ-.002 (p = .964) ܘܥܒܕܐ ܕܚܕ̈ܕܐ (interaction) ܒ-.061 (p = .805) – ܬܪܘܝܗܝ ܡܫܘܕܪ̈ܐ ܝܢܐ. ܓܘ ܣܐܝܛ ܟܥܒܕܚ ܐܗܐ ܒܬܪܝܢ ܪ̈ܗܛܐ: ܡܘܕܝܠ ܥܡ ܡܢܒ̈ܝܢܐ ܒܣܝܣܝ̈ܐ ܘܡܘܕܝܠ ܥܡ ܬܘܣܦܬܐ، ܘܦܘܪܫܢܐ ܒܝܢܝ ܬܪܝܢ χ² ܝܠܗ ܒܘܚܪܢܐ ܕܬܘܣܦܬܐ ܥܡ df = ܡܢܝܢܐ ܕܡܢܒ̈ܝܢܐ ܡܘܣܦ̈ܐ. ܐܘܪ̈ܚܬܐ ܕܦܣܥܐ ܒܬܪ ܦܣܥܐ (Forward/Backward) – Pallant: "ܠܐ ܝܢܐ ܡܩܘܒ̈ܠܬܐ"، ܡܛܠ ܕܡܬܥܒܕܝ ܡܢ ܫܘܚܠܦܐ ܓܕܫܢܝܐ؛ Field: ܠܐ ܩܐ ܒܘܚܪܢܐ ܕܬܐܘܪܝܐ، ܘܐܢ ܒܟܠ ܓܘܢܐ – Backward ܥܡ ܡܫܘܚܬܐ ܕܦܘܚܡܐ ܕܡܬܚܙܝܢܘܬܐ (likelihood ratio). ܥܒܕܐ ܕܚܕ̈ܕܐ ܓܘ ܡܘܕܝܠ ܣܢܝܩܐ ܝܠܗ ܠܬܪܝܢ ܡܥܒܕ̈ܢܘܝܬܐ ܪ̈ܫܝܐ ܕܝܠܗ، ܐܦ ܐܢ ܠܐ ܝܢܐ ܪ̈ܫܝܡܐ (Field).

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܘܚܐ 1. ܩܕܡ ܟܠ ܡܘܕܝܠ ܟܠܗ: χ² ܘ-p (Omnibus). ܠܐ ܪܫܝܡܐ – ܟܦܐܫܚ، ܡܢܒ̈ܝܢܐ (predictors) ܠܐ ܟܡܛܝܒܝ ܚܡܝܢܐ. ܪܫܝܡܐ – ܟܐܙܠܚ ܠ-R² ܕ-Nagelkerke (ܦܘܚܡܐ ܥܡ ܡܘܕ̈ܝܠܐ ܐܚܪ̈ܢܐ) ܘܠ-Hosmer-Lemeshow (p ܥܠ ܡܢ .05 = ܠܝܬ ܣܗܕܘܬܐ ܩܐ ܦܐܝܘܬܐ ܒܝܫܬܐ). ܠܘܚܐ 2. ܩܐ ܟܠ ܡܢܒܝܢܐ: ܐܬܐ ܕ-B ܟܐܡܪ ܐܘܪܚܐ (Pallant: ܐܝܡܢ ܕܟܠ ܡܕܡ ܪܡܝܙܐ ܝܠܗ 0 = ܠܐ، 1 = ܐܝܢ، B ܣܠܝܒܐ = ܡܢܒܝܢܐ ܟܡܙܥܪ ܣܟܘܝܐ ܕ-1)؛ p ܕ-Wald – ܐܝܢ ܝܘܬܪܢܐ ܝܚܝܕܝܐ ܪܫܝܡܐ ܝܠܗ؛ OR ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) – ܪܒܘܬܐ. Pallant ܟܩܪܝܐ ܡܬܠܐ ܕܝܠܗ̇ ܗܟܢܐ: "ܣܟܘ̈ܝܐ ܕܒܪܢܫܐ ܒܕ ܡܘܕܥ ܥܠ ܥܩܬܐ ܕܕܡܟܬܐ ܪ̈ܡܐ ܝܢܐ 7.27 ܓܗ̈ܐ ܒܝܫ ܩܐ ܐܢܝ ܕܐܝܬܠܗܘܢ ܥܩܘܬܐ ܠܡܦܝܫܐ ܕܡܝܟ̈ܐ، ܐܝܡܢ ܕܐܚܪ̈ܢܐ ܩܝ̈ܡܐ ܝܢܐ"؛ ܘܩܐ ܫܥ̈ܐ ܕܕܡܟܬܐ OR = .64 – "ܩܐ ܟܠ ܫܥܬܐ ܕܕܡܟܬܐ ܡܘܣܦܬܐ ܣܟܘ̈ܝܐ ܟܙܥܪܝ ܥܡ ܡܢܝܢܐ .64". ܓܘ ܡܢܒܝܢܐ ܕܓܢ̈ܣܐ (categorical) ܥܡ ܬܠܬܐ ܓܢ̈ܣܐ ܘܠܥܠ، ܣܕܪܐ ܕܡܫܬܚܠܦܢܐ ܟܠܗ (Wald ܥܡ df = ܡܢܝܢܐ ܕܓܢ̈ܣܐ − 1) ܟܐܡܪ ܐܢ ܡܫܬܚܠܦܢܐ ܐܝܬܠܗ ܝܘܬܪܢܐ، ܘܡܫܬܚܠܦ̈ܢܐ ܕܡܬܠܐ (dummies) ܟܐܡܪܝ ܐܝܢܐ ܓܢܣܐ ܦܪܝܫܐ ܝܠܗ ܡܢ ܫܬܐܣܐ. ܠܘܚܐ 3. ܠܘܚܐ ܕܦܘܪܫܐ ܠܓܢ̈ܣܐ (classification table) ܩܘܒܠ ܣܪܛܐ ܕܫܬܐܣܐ (Block 0): ܐܢ 60% ܡܢ ܕܘܡܝܐ (sample) ܓܘ ܚܕ ܓܢܣܐ ܝܢܐ، ܦܘܪܫܐ ܬܪܝܨܐ ܕ-60% ܠܐ ܝܠܗ ܙܟܘܬܐ. Pallant ܟܡܘܣܦܐ ܡܚܘ̈ܝܢܐ ܕܐܣܝܘܬܐ – ܪܓܝܫܘܬܐ (sensitivity)، ܝܚܝܕܝܘܬܐ (specificity)، ܛܝܡܐ ܕܡܢܒܝܢܘܬܐ (positive / negative predictive value) – ܘܦܐܬܐ ܟܚܫܒܐ ܠܗܘܢ ܓܘ ܡܥܝܪܢܘܬܐ ܕܠܘܚܐ. Field (ܦܣܩܐ 20.6.5) ܟܩܪܐ ܐܦ ܨܘܪܬܐ ܕܦܘܪܫܐ ܠܓܢ̈ܣܐ: ܓܘ ܡܘܕܝܠ ܛܒܐ ܡܫܬܘܬܦ̈ܢܐ ܟܡܬܟܢܫܝ ܓܘ ܣܘ̈ܦܐ، ܠܐ ܚܕܪ .5. Gelman ܘ-Hill (2007، ܦܐܬܐ 99-100) ܟܟܬܒܝ ܐܗܐ ܐܝܟ ܡܢܬܐ ܕܛܥܝܘܬܐ: ܡܘܕܝܠ ܣܦܝܩܐ ܟܛܥܐ ܒ-p ܝܢ ܒ-1 − p (ܗܘ ܕܢܚܝܬܐ ܝܠܗ)، ܘ"ܡܢܬܐ ܕܛܥܝܘܬܐ ܕܫܘܝܐ ܝܠܗ̇ ܠܡܢܬܐ ܕܡܘܕܝܠ ܣܦܝܩܐ ܕܚܝܠܬܐ ܝܠܗ̇"؛ ܐܠܐ ܡܢܬܐ ܕܛܥܝܘܬܐ ܠܐ ܟܦܪܫܐ ܒܝܢܝ ܡܢܒܝܢܘܬܐ ܕ-.6 ܘ-.9 – ܡܘܕܝܠ ܕܣܓܝܐܐ ܡܢ ܡܫܬܘܬܦ̈ܢܐ ܕܝܠܗ ܩܪܝܒ̈ܐ ܝܢܐ ܠܡܨܥܝܬܐ ܡܨܐ ܕܗܘܐ ܣܓܝ ܝܗܒ ܝܕܥܬܐ ܓܘ ܣܘ̈ܦܐ ܘܐܦ ܗܫܐ ܡܛܝܒ ܦܘܪܫܐ ܟܠܢܝܐ ܩܠܝܠ. ܠܘܚܐ 4. ܒܘܚܪ̈ܢܐ ܕܡܘܕܝܠ (diagnostics) – ܓܘ ܦܣܩܐ ܕܐܬܐ.

ܫܪ̈ܛܐ ܘܥܩ̈ܬܐ

ܣܪܛܢܝܘܬܐ ܕܠܘܓܝܬ ܘܠܐ ܬܠܝܘܬܐ. ܡܘܕܝܠ (model) ܟܣܒܪ ܐܣܘܪܐ ܣܪܛܢܝܐ (linear) ܒܝܢܝ ܟܠ ܡܢܒܝܢܐ ܡܬܡܫܚܢܐ (continuous predictor) ܘܠܘܓ-ܣܟܘ̈ܝܐ (log-odds؛ Field, 2024, Section 20.4.1) – ܠܐ ܥܡ ܡܣܬܒܪܢܘܬܐ. ܒܘܚܪܢܐ ܕ-Hosmer ܘܐܚܪ̈ܢܐ (2013, as cited in Field, Section 20.7.3): ܟܡܘܣܦܚ ܠܡܘܕܝܠ ܥܒܕܐ ܕܚܕ̈ܕܐ (interaction) ܕܟܠ ܡܢܒܝܢܐ ܡܬܡܫܚܢܐ ܥܡ ܠܘܓ ܕܝܠܗ ܓܢܒܗ؛ ܥܒܕܐ ܕܚܕ̈ܕܐ ܪܫܝܡܐ = ܫܪܛܐ ܥܒܝܪܐ ܝܠܗ. ܦܐܬܐ ܟܥܒܕܐ ܐܗܐ ܒܚܘܕܝܗ̇ ܩܐ ܡܢܒ̈ܝܢܐ ܡܬܡܫܚ̈ܢܐ ܕܛܝ̈ܡܐ ܕܝܠܗܘܢ ܥܠ ܡܢ ܣܦܪ ܝܢܐ (positive؛ ܠܘܚܐ 4). ܘܫܪ̈ܟܐ (residuals) ܠܐ ܬܠܝ̈ܐ ܝܢܐ – ܠܐ ܘܐܠܐ ܕܡܫܚܚ ܠܗܘ ܒܪܢܫܐ ܬܪܝܢ ܓܗ̈ܐ.

ܝܕܥܬܐ ܡܢܬܢܝܬܐ ܡܢ ܡܢܒ̈ܝܢܐ. ܐܢ ܚܕ ܚܘܝܕܐ ܕܓܢ̈ܣܐ ܣܦܝܩܐ ܝܠܗ (ܐܢܫ̈ܐ ܕܟܫܬܝ ܬܘܬܘܢ ܘܟܐܟܠܝ ܒܢܕܘܪ̈ܐ، ܓܘ ܡܬܠܐ ܕ-Field، ܦܣܩܐ 20.4.2)، ܠܡܘܕܝܠ (model) ܠܝܬ ܥܠ ܡܐ ܕܡܫܬܐܣ ܡܣܬܒܪܢܘܬܐ (probability) ܬܡܢ – ܘܐܦ ܩܐ ܡܢܒ̈ܝܢܐ ܡܬܡܫܚ̈ܢܐ: "ܒܪܬ 80، ܣܓܝ ܕܚܝܠܬܐ، ܒܘܕܝܣܛܝܬܐ، ܕܣܡܠܐ" ܢܕܝܪܬܐ ܝܠܗ̇ ܐܦ ܓܘ ܕܘܡܝܐ (sample) ܕܐܠܦܐ. ܐܬܐ: ܛܥܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ (standard errors) ܪ̈ܒܬܐ ܣܓܝ. Field: ܒܨܘ̈ܝܐ ܚܬܝ̈ܬܐ ܟܒܚܪܝ ܠܘ̈ܚܐ ܕܨܠܝܒܘܬܐ (crosstabulation) ܕܟܠ ܡܢܒ̈ܝܢܐ ܕܓܢ̈ܣܐ ܩܕܡ ܡܘܕܝܠ (ܥܡ ܫܪܛܐ ܕܣܓܝܐܘ̈ܬܐ ܡܣܟ̈ܝܬܐ ܡܢ ܦܐܬܐ ܕܟܝ ܡܪܒܥܐ)؛ "ܐܝܢܐ ܕܠܐ ܥܒܕ ܠܐ ܐܗܐ ܘܠܐ ܐܗܐ – ܡܣܟܐ ܠܥܩ̈ܬܐ". ܦܘܪܫܐ ܓܡܝܪܐ (perfect separation؛ ܦܣܩܐ 20.4.3): ܐܝܡܢ ܕܡܢܒܝܢܐ ܝܢ ܚܘܝܕܐ ܕܡܢܒ̈ܝܢܐ ܟܡܢܒܐ ܦܐܪܐ (outcome) ܒܚܬܝܬܘܬܐ – ܩܛ̈ܘܐ ܩܘܒܠ ܓܢ̈ܒܐ ܠܦܘܬ ܡܬܩܠܐ – ܫܘ̈ܥܪܐ (estimates) ܟܥܪܩܝ ܠܠܐ ܬܚܘܡܐ، ܛܥܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ ܟܦܩܥܝ، ܘܬܘܟܢܝܬܐ (software) ܡܨܝܐ "ܕܡܫܠܡܐ ܒܫܠܝܐ ܘܝܗܒܐ ܦܐܪܐ ܛܥܝܐ ܟܠܗ". ܦܐܬܐ ܟܡܫܟܚܐ ܠܐ ܡܬܟܢܫܢܘܬܐ (non-convergence) ܘܡܢ̈ܝܢܐ ܡܫܘܬܦ̈ܐ ܩܝܨܝ̈ܐ ܘܟܡܙܗܪܐ؛ ܦܘܫܪܐ – ܡܘܕܝܠ ܦܫܝܛܐ ܒܝܫ، ܚܘܝܕܐ ܕܓܢ̈ܣܐ، ܝܢ ܝܗܝ̈ܒܬܐ ܒܝܫ. ܪܒܘܬܐ ܕܕܘܡܝܐ (sample size؛ Pallant, 2020, Chapter 14): ܕܘܡܝܐ ܙܥܘܪܐ ܥܡ ܣܓܝ ܡܢܒ̈ܝܢܐ – ܥܩ̈ܬܐ ܕܡܬܟܢܫܢܘܬܐ (convergence)، ܝܬܝܪ ܥܡ ܓܢ̈ܣܐ ܩܠܝܠ̈ܐ؛ ܟܪܗܛܚ ܣܛܐܛܝܣܛܝܩܐ ܡܚܘܝܢܝܬܐ ܩܐ ܟܠ ܡܢܒܝܢܐ ܘܟܡܚܝܕܚ ܝܢ ܟܫܩܠܚ ܓܢ̈ܣܐ ܩܠܝܠ̈ܐ.

Multicollinearity. SPSS ܠܐ ܟܛܒܥ ܒܘܚܪ̈ܢܐ ܕ-collinearity ܓܘ ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ("ܡܐ ܕܟܥܒܕ ܚܙܘܐ ܕܓܠܐ ܕܐܗܐ ܠܐ ܝܠܗ ܚܫܝܚܐ" – Field، ܦܣܩܐ 20.7.4)؛ ܟܪܗܛܚ ܪܝܓܪܫܢ ܣܪܛܢܝܐ (linear regression) ܥܠ ܗܢܝ ܡܫܬܚܠܦ̈ܢܐ ܘܟܩܪܝܚ ܒܣ Tolerance ܘ-VIF: Tolerance ܠܬܚܬ ܡܢ .1 ܝܢ VIF ܥܠ ܡܢ 10 – ܥܩܬܐ (Menard, 2002, as cited in Field; Pallant). ܦܐܬܐ ܟܚܫܒܐ VIF ܬܪܝܨܐܝܬ (ܠܘܚܐ 4). ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ (outliers) ܘܡܫܬܘܬܦ̈ܢܐ ܡܥܒܕܢ̈ܝܐ (Field, Section 20.6.7; Pallant): ܫܪ̈ܟܐ ܡܬܩ̈ܢܐ (standardized residuals؛ ZResid) – ܠܐ ܒܝܫ ܡܢ 5% ܥܠ ܡܢ 2، ܠܐ ܒܝܫ ܡܢ 1% ܥܠ ܡܢ 2.5، ܘܥܠ ܡܢ 3 ܢܘܟܪܝܐ ܝܠܗ؛ Pallant ܟܛܒܥܐ ܡܫܬܘܬܦ̈ܢܐ ܥܠ ܡܢ 2 (Casewise List) ܘܟܡܩܪܒܐ ܕܒܚܪܚ ܠܗܘܢ – ܡܨܐ ܕܗܘܐ ܓܘܕܐ ܕܡܘܕܝܠ ܠܐ ܦܐܐ ܠܗ (ܦܠܚ̈ܐ ܕܡܚܠܦ̈ܢܘܬܐ – shift workers). Field: ܛܝܡܐ ܢܘܟܪܝܐ ܠܐ ܝܠܗ ܣܒܒܐ ܠܫܩܠܬܐ – ܐܠܐ ܠܒܘܚܪܢܐ ܠܡܢܐ؛ ܟܫܩܠܚ ܒܣ ܥܡ ܣܒܒܐ ܟܬܝܒܐ. ܡܚܘ̈ܝܢܐ ܕܡܥܒܕܢܘܬܐ (Cook, DFBeta, leverage) ܠܝܬ ܓܘ ܦܐܬܐ.

ܡܘܕܝ ܠܐ ܟܚܫܒܐ ܐܗܐ ܦܐܬܐ. ܓܘ̈ܫܡܐ ܕܕܪ̈ܓܐ (hierarchical blocks؛ ܟܪܗܛܚ ܬܪܝܢ ܓܗ̈ܐ ܘܟܡܚܣܪܚ χ²)؛ ܐܘܪ̈ܚܬܐ ܕܦܣܥܐ ܒܬܪ ܦܣܥܐ (stepwise)؛ ܥܒ̈ܕܐ ܕܚܕ̈ܕܐ (interactions) ܒܝܢܝ ܡܢܒ̈ܝܢܐ (Field, Section 20.7)؛ bootstrap ܩܐ ܡܢ̈ܝܢܐ ܡܫܘܬܦ̈ܐ (ܦܣܩܐ 20.5.12)؛ ܡܚܘ̈ܝܢܐ ܕܡܥܒܕܢܘܬܐ؛ R ܕ-SPSS ܘ-R²_L ܕ-Hosmer-Lemeshow (ܦܣܩܐ 20.3.7)؛ ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܕܓܢ̈ܣܐ ܣܓܝ̈ܐܐ (multinomial)؛ ܫܘܥܪܐ ܒܐܝܣܝܐ (Bayesian)/ܡܬܚܙܝܢܘܬܐ ܡܬܪܕܝܬܐ (penalized likelihood) ܩܐ ܦܘܪܫܐ (separation؛ Gelman ܘ-Hill، ܓܘ ܦܣܩܐ ܕܐܬܐ).

ܬܠܬܐ ܬܘܣܦ̈ܬܐ ܡܢ Gelman ܘ-Hill: ܦܘܠܓܐ ܥܠ ܐܪܒܥܐ، ܫܪ̈ܟܐ ܟܢܝ̈ܫܐ ܘܦܘܪܫܐ

Gelman ܘ-Hill (2007، ܨܚܚܐ 5) ܟܡܠܦܝ ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ (logistic regression) ܡܢ ܐܘܪܚܐ ܐܚܪܬܐ – ܠܐ ܡܦܩܢܐ ܕ-SPSS ܐܠܐ ܦܗܡܐ ܕܡܘܕܝܠ – ܘܬܠܬܐ ܡܢ ܡܐܢ̈ܐ ܕܝܠܗܘܢ ܥܠܝܠ̈ܐ ܝܢܐ ܓܘ ܦܐܬܐ. ܢܡܘܣܐ ܕ"ܦܘܠܓܐ ܥܠ ܐܪܒܥܐ" (divide-by-four؛ ܦܐܬܐ 82). ܣܪܛܐ ܟܦܝܦܐ ܠܘܓܝܣܛܝܩܝܐ ܬܠܝܠܐ ܝܠܗ ܝܬܝܪ ܓܘ ܡܨܥܬܗ، ܐܝܡܢ ܕ-p = .5، ܘܬܡܢ ܡܨܠܝܢܘܬܐ (slope) ܕܝܠܗ ܚܬܝܬܐܝܬ ܝܠܗ̇ B/4؛ ܡܛܠ ܗܕܐ B/4 ܝܠܗ ܬܚܘܡܐ ܥܠܝܐ (upper bound) ܩܐ ܫܘܢܝܐ ܓܘ ܡܣܬܒܪܢܘܬܐ (probability) ܕܦܐܐ ܠܣܠܩܐ ܕܚܕ ܡܫܘܚܬܐ ܓܘ ܡܢܒܝܢܐ (predictor) – ܩܘܪܒܐ ܛܒܐ ܐܝܡܢ ܕܡܣܬܒܪ̈ܢܘܝܬܐ ܓܘ ܝܗܝ̈ܒܬܐ ܩܪܝܒ̈ܐ ܝܢܐ ܠ-.5، ܘܒܣ ܬܚܘܡܐ ܐܝܡܢ ܕܩܪܝܒ̈ܐ ܝܢܐ ܠ-0 ܝܢ ܠ-1. ܓܘ ܡܬܠܐ ܕܝܠܗܘܢ، B = 0.33 ܩܐ ܡܐܬܝܬܐ (income؛ ܓܘ ܣܒܠܬܐ 1-5) ܟܝܗܒ 0.33/4 = .08: ܓܢܣܐ ܕܡܐܬܝܬܐ ܡܘܣܦܐ ܟܡܪܡܐ ܡܣܬܒܪܢܘܬܐ ܕܝܗܒܬܐ ܕܩܠܐ ܠ-Bush ܒܠܐ ܒܝܫ ܡܢ 8 ܢܘܩ̈ܙܐ ܕܡܢܬܐ ܒܡܐܐ – ܘܢܓܕܬܐ (derivative) ܓܘ ܡܨܥܝܬܐ ܕܝܗܝ̈ܒܬܐ (ܦܐܬܐ 81-82: "ܫܘܥܪܐ ܓܘ ܡܨܥܝܬܐ ܕܝܗܝ̈ܒܬܐ ܘܓܘ ܩܘܪܒܗ̇") ܟܢܦܩܐ .13، ܩܪܝܒܐ. ܠܘܚܐ 2 ܟܛܒܥ B/4 ܩܐ ܟܠ ܡܢܒܝܢܐ، ܘܡܥܝܪܢܘܬܐ ܕܠܘܚܐ – ܡܨܠܝܢܘܬܐ ܓܘ ܡܨܥܝܬܐ ܕܝܗܝ̈ܒܬܐ، B·p̂(1 − p̂). Gelman ܘ-Hill ܟܡܘܕܝ ܕ"ܚܘܫܒܐ ܕܣܟܘ̈ܝܐ ܥܣܩܐ ܝܠܗ ܠܦܗܡܐ، ܘܦܘܚܡ̈ܐ ܕܣܟܘ̈ܝܐ ܛܡܝܪ̈ܐ ܝܢܐ ܒܝܫ"، ܘܡܛܠ ܗܕܐ ܟܓܒܝ ܠܦܘܫܩܐ ܓܘ ܣܒܠܬܐ ܕܡܣܬܒܪܢܘܬܐ ܫܪܫܢܝܬܐ (ܦܐܬܐ 83)؛ ܓܘ ܣܐܝܛ ܟܬܢܚ OR (Field؛ Pallant؛ APA) ܘܟܡܘܣܦܚ B/4 ܐܝܟ ܬܘܪܓܡܐ ܠܡܣܬܒܪܢܘܬܐ. ܢܡܘܣܐ ܐܚܪܢܐ ܕܝܠܗܘܢ (ܦܐܬܐ 83): ܡܢܝܢܐ ܡܫܘܬܦܐ (coefficient) ܕܪܚܝܩܐ ܝܠܗ ܡܢ ܣܦܪ ܒܝܫ ܡܢ ܬܪܬܝܢ ܛܥܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ ܪܫܝܡܐ ܝܠܗ – ܐܗܐ ܝܠܗ ܒܘܚܪܢܐ ܕ-Wald ܕܠܘܚܐ 2 ܒܠܒܘܫܐ ܐܚܪܢܐ.

ܫܪ̈ܟܐ ܟܢܝ̈ܫܐ (binned residuals؛ ܦܐܬܐ 97-98، ܨܘܪ̈ܬܐ 5.13-5.14). ܫܪܟܐ (residual) ܓܘ ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܝܠܗ y − p̂، ܘܡܛܠ ܕ-y ܝܠܗ 0 ܝܢ 1، ܫܪܟܐ ܦܪܝܫܐ (discrete) ܝܠܗ: ܩܐ p̂ = .7 ܝܠܗ −.7 ܝܢ +.3؛ ܨܘܪܬܐ ܕܫܪ̈ܟܐ ܓܘܠܡ̈ܝܐ ܟܡܚܘܝܐ ܬܪܝܢ ܣܪ̈ܛܐ ܘܠܐ ܟܡܠܦܐ ܡܕܡ. ܦܘܫܪܐ: ܟܦܠܓܚ ܡܫܬܘܬܦ̈ܢܐ (participants) ܠܓܘ̈ܕܐ ܕܪܒܘܬܐ ܫܘܝܬܐ ܠܦܘܬ ܡܣܬܒܪܢܘܬܐ ܡܢܒܝܬܐ (predicted probability)، ܘܩܐ ܟܠ ܓܘܕܐ ܟܨܝܪܚ ܡܨܥܝܬܐ ܕܫܪ̈ܟܐ ܩܘܒܠ ܡܨܥܝܬܐ ܕܡܣܬܒܪܢܘܬܐ. ܐܢ ܡܘܕܝܠ ܬܪܝܨܐ ܝܠܗ، ܩܪܝܒ ܠ-95% ܡܢ ܢܘܩ̈ܙܐ ܣܢܝܩܝ ܕܢܦܠܝ ܓܘ ܬܚܘ̈ܡܐ ±2√(p̄(1 − p̄)/n) (n – ܡܢܝܢܐ ܕܡܫܬܘܬܦ̈ܢܐ ܓܘ ܓܘܕܐ)، ܘܠܝܬ ܛܘܦܣܐ (pattern). ܓܘ ܡܬܠܐ ܕܝܠܗܘܢ ܕܒܝܪ̈ܐ ܓܘ Bangladesh (N = 3,020، 40 ܓܘ̈ܕܐ ܕ-75) ܚܕ ܢܘܩܙܐ ܡܢ 40 ܢܦܩ – "ܠܐ ܬܡܗܐ". ܗܝ ܨܘܪܬܐ ܠܦܘܬ ܡܢܒܝܢܐ ܡܬܡܫܚܢܐ (ܨܘܪܬܐ 5.14) ܟܓܠܝܐ ܡܐ ܕܨܘܪܬܐ ܟܠܢܝܬܐ ܟܛܫܝܐ: ܠܦܘܬ ܕܪܓܐ ܕ-arsenic ܐܫܬܟܚ ܓܘܕܐ ܬܚܬܝܐ ܕܓܘܗ ܒܣ 32% ܫܚܠܦܝ ܒܝܪܐ ܩܘܒܠ 49% ܕܡܘܕܝܠ ܡܢܒܐ ܗܘܐ، ܘܛܘܦܣܐ ܕܣܠܩܐ-ܘܢܚܬܐ ܥܠ ܣܪܛܐ – "ܐܬܐ ܩܐ ܥܒܘܕܐ ܕܡܘܕ̈ܝܠܐ ܡܕܪܫܐ" ܕܫܩܠ ܠܘܓܪܝܬܡ (logarithm) ܕܡܢܒܝܢܐ (ܦܐܬܐ 98)، ܝܢ ܕܡܘܣܦ ܡܠܬܐ ܡܪܒܥܬܐ (squared term). ܦܐܬܐ ܟܨܝܪܐ ܨܘܪܬܐ ܕܫܪ̈ܟܐ ܟܢܝ̈ܫܐ ܠܦܘܬ ܡܣܬܒܪܢܘܬܐ ܡܢܒܝܬܐ ܘܠܦܘܬ ܟܠ ܡܢܒܝܢܐ ܡܬܡܫܚܢܐ (ܓܘܒܝܐ ܓܘ ܨܘܪܬܐ)، ܒ-√N ܓܘ̈ܕܐ؛ ܠܘܚܐ 4 ܟܡܢܐ ܓܘ̈ܕܐ ܕܠܒܪ ܡܢ ܬܚܘ̈ܡܐ. ܡܫܠܡܢܘܬܐ ܩܐ ܒܘܚܪܢܐ Hosmer-Lemeshow: ܒܘܚܪܢܐ ܟܝܗܒ ܚܕ p، ܨܘܪܬܐ ܟܡܚܘܝܐ ܐܝܟܐ ܦܐܝܘܬܐ ܟܦܐܫܐ ܒܛܠܬܐ.

ܦܘܪܫܐ (separation) ܘ-non-identification (ܦܐܬܐ 104). ܬܪܝܢ ܣܒ̈ܒܐ ܕܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ "ܠܐ ܝܠܗ identified" – ܕܦܪܡܝ̈ܛܪܐ (parameters) ܠܐ ܡܨܝ ܕܡܫܬܥܪܝ ܡܢ ܝܗܝ̈ܒܬܐ: collinearity، ܐܝܟ ܓܘ ܪܝܓܪܫܢ ܣܪܛܢܝܐ؛ ܘܦܘܪܫܐ، ܕܡܒܘܥܗ ܝܠܗ ܦܪܝܫܘܬܐ (discreteness) ܕܦܐܪܐ (outcome). ܐܢ ܡܢܒܝܢܐ (predictor) ܫܘܝܐ ܝܠܗ ܟܠܗ ܥܡ ܦܐܪܐ – y = 1 ܩܐ ܟܠ ܐܢܫ ܕܥܠ ܡܢ ܬܚܘܡܐ ܚܕ ܘ-y = 0 ܩܐ ܟܠ ܐܢܫ ܕܠܬܚܬ ܡܢܗ – ܫܘܥܪܐ ܛܒܐ ܡܢ ܟܠܗ ܩܐ ܡܢܝܢܐ ܡܫܘܬܦܐ (coefficient) ܝܠܗ ܠܐ ܬܚܘܡܐ (infinity؛ ܨܘܪܬܐ 5.16: ܣܪܛܐ ܠܘܓܝܣܛܝܩܝܐ ܥܡ ܡܨܠܝܢܘܬܐ ܕܠܐ ܬܚܘܡܐ)؛ ܘܐܦ ܚܘܝܕܐ ܣܪܛܢܝܐ ܕܡܢܒ̈ܝܢܐ ܕܫܘܝܐ ܝܠܗ ܥܡ ܦܐܪܐ ܟܡܫܘܪ ܠܐ ܒܨܝܪ ܡܢ ܚܕ ܡܢܝܢܐ ܡܫܘܬܦܐ ܠܠܐ ܬܚܘܡܐ. ܐܗܐ ܝܠܗ ܦܘܪܫܐ ܓܡܝܪܐ (perfect separation) ܕ-Field (ܦܣܩܐ 20.4.3)، ܘܐܬܐ ܕܝܠܗ ܗܝ ܝܠܗ̇ – ܡܢܝܢܐ ܡܫܘܬܦܐ ܪܒܐ ܣܓܝ ܥܡ ܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) ܪܒܬܐ ܣܓܝ. ܦܘܫܪܐ ܕ-Gelman ܘ-Hill ܦܪܝܫܐ ܝܠܗ ܡܢ ܕ-Field: ܒܕܘܟܬܐ ܕܡܦܫܛܐ ܡܘܕܝܠ، ܫܘܥܪܐ ܒܐܝܣܝܐ (Bayesian) ܝܢ ܡܬܚܙܝܢܘܬܐ ܡܬܪܕܝܬܐ (penalized likelihood؛ bayesglm ܓܘ ܨܪܪܐ arm ܓܘ R، ܝܢ brlr) ܕ"ܟܝܗܒ ܩܠܝܠ ܝܕܥܬܐ ܥܠ ܟܠ ܡܢ̈ܝܢܐ ܡܫܘܬܦ̈ܐ، ܐܦ ܥܠ ܐܢܝ ܕܠܐ ܝܢܐ identified ܡܢ ܝܗܝ̈ܒܬܐ ܒܠܚܘܕ"، ܘܟܕܥܪ ܫܘܥܪܐ ܣܟܝܐ (finite). ܦܐܬܐ ܟܒܚܪܐ ܩܐ ܟܠ ܡܢܒܝܢܐ ܐܢ ܫܘܝܐ ܝܠܗ ܟܠܗ ܥܡ ܦܐܪܐ، ܝܢ ܐܢ ܓܘ ܚܕ ܡܢ ܛܝ̈ܡܐ ܕܝܠܗ ܟܠ ܡܫܬܘܬܦ̈ܢܐ ܓܘ ܗܘ ܓܢܣܐ ܝܢܐ (ܩܠܝܬܐ ܣܦܝܩܬܐ)، ܘܟܡܙܗܪܐ (ܠܘܚܐ 4)؛ ܠܐ ܟܫܥܪܐ ܒܐܝܣܐܝܬ – ܦܣܩܐ ܕ-R ܟܡܚܘܝܐ.

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

Analyze › Regression › Binary Logistic… (Pallant, 2020, Chapter 14; Field, 2024, Section 20.5.5): ܦܐܪܐ (outcome) ܠ-Dependent، ܡܢܒ̈ܝܢܐ (predictors) ܠ-Covariates، Method: Enter. ܓܘ button Categorical… – ܡܢܒ̈ܝܢܐ ܕܓܢ̈ܣܐ (categorical)، Contrast: Indicator، Reference Category: First ܘܕܚܩܐ ܥܠ Change (Pallant؛ Field ܟܡܚܘܐ ܐܦ Last – ܠܦܘܬ ܪܡܙܢܘܬܐ ܕܝܘܟܘܢ). ܓܘ button Options…: Classification plots، Hosmer-Lemeshow goodness-of-fit، Casewise listing of residuals، CI for exp(B) ܘ-Iteration history (ܩܐ −2LL ܕܡܘܕܝܠ ܣܦܝܩܐ). ܣܝܢܬܐܟܣ (syntax) ܕ-Pallant، ܥܡ ܬܘܣܦܬܐ ܕ-history:

LOGISTIC REGRESSION VARIABLES outcome
  /METHOD=ENTER sex age fallsleep staysleep hrswknight
  /CONTRAST(sex)=Indicator(1)
  /CONTRAST(fallsleep)=Indicator(1)
  /CONTRAST(staysleep)=Indicator(1)
  /CLASSPLOT
  /CASEWISE OUTLIER(2)
  /PRINT=GOODFIT CI(95) ITER(1)
  /CRITERIA=PIN(.05) POUT(.10) ITERATE(20) CUT(.5).

ܪܡܙܢܘܬܐ ܕܦܐܪܐ: SPSS ܓܘܝܐܝܬ ܟܪܡܙ ܛܝܡܐ ܢܚܝܬܐ 0 ܘܪܡܐ 1 (Dependent Variable Encoding)؛ ܐܢ ܓܢܣܐ ܕܒܥܝܚ ܕܡܢܒܚ ܝܠܗ ܢܚܝܬܐ، ܟܒܢܚ ܡܫܬܚܠܦܢܐ 1/0 – ܣܝܢܬܐܟܣ (syntax) ܕܦܐܬܐ ܟܥܒܕ ܐܗܐ ܒ-COMPUTE ܐܝܡܢ ܕܣܢܝܩܐ ܝܠܗ. ܩܪܝܢܐ ܕܡܦܩܢܐ: Block 0 – ܠܘܚܐ ܕܦܘܪܫܐ ܠܓܢ̈ܣܐ (classification table) ܕܡܘܕܝܠ ܣܦܝܩܐ (ܣܪܛܐ ܕܫܬܐܣܐ) ܘ-Iteration History ܥܡ −2LL ܩܕܡܝܐ؛ Block 1 – Omnibus Tests of Model Coefficients (ܣܕܪܐ Model = χ² ܕܠܘܚܐ 1؛ ܣܕܪܐ Block = ܬܘܣܦܬܐ ܕܓܘܫܡܐ ܐܚܪܝܐ)، Model Summary (−2LL، Cox & Snell، Nagelkerke)، Hosmer and Lemeshow Test، Classification Table = ܠܘܚܐ 3، Variables in the Equation = ܠܘܚܐ 2 (B, S.E., Wald, df, Sig., Exp(B), 95% CI)، Casewise List – ܡܫܬܘܬܦ̈ܢܐ ܥܡ ZResid ܥܠ ܡܢ 2 = ܠܘܚܐ 4. VIF: Analyze › Regression › Linear… ܥܡ ܗܢܝ ܡܫܬܚܠܦ̈ܢܐ ܘ-Statistics › Collinearity diagnostics – ܟܩܪܝܚ ܒܣ ܥܡܘ̈ܕܐ Tolerance ܘ-VIF (Field, Section 20.7.4). ܫܪ̈ܟܐ ܟܢܝ̈ܫܐ: SPSS ܠܐ ܟܨܝܪ ܠܗܘܢ؛ /SAVE=PRED RESID ܟܢܛܪ ܡܣܬܒܪܢܘܬܐ ܡܢܒܝܬܐ ܘܫܪܟܐ، RANK /NTILES ܟܟܢܫ ܘ-MEANS ܟܚܫܒ ܡܨܥܝ̈ܬܐ ܩܐ ܟܠ ܓܘܕܐ – ܬܚܘ̈ܡܐ ܘܨܘܪܬܐ ܓܘ ܦܐܬܐ. Button "ܡܚܬܬܐ ܕܣܝܢܬܐܟܣ SPSS" ܓܘ ܡܦܩܢܐ ܟܒܢܐ ܟܠ ܕܪ̈ܓܐ – ܛܥܢܐ، ܟܬܒܐ ܕܪ̈ܡܙܐ (codebook)، ܪܡܙܢܘܬܐ ܕܦܐܪܐ ܐܢ ܣܢܝܩܐ ܝܠܗ، LOGISTIC REGRESSION ܥܡ /SAVE، REGRESSION ܩܐ VIF، ܟܢܫܐ ܕܫܪ̈ܟܐ، ܘܒܘܚܪܢܐ ܕܣܪܛܢܝܘܬܐ ܕܠܘܓܝܬ.

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

glm(…, family = binomial) ܓܘ R ܒܣܝܣܝܐ؛ ܡܢܒܝܢܐ ܕܓܢ̈ܣܐ (categorical predictor) ܐܝܟ factor ܟܫܩܠ ܪܡܙܢܘܬܐ (dummy coding) ܥܡ ܕܪܓܐ ܩܕܡܝܐ ܐܝܟ ܫܬܐܣܐ (base) – ܐܝܟ Indicator(first). exp(coef) ܘ-exp(confint.default) ܟܝܗܒܝ OR ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܥܠ ܣܒܠܬܐ ܕܠܘܓ (ܐܝܟ SPSS؛ confint ܕܠܐ .default ܟܝܗܒ ܬܚܘܡܐ ܕ-profile likelihood، ܦܪܝܫܐ ܩܠܝܠ)؛ hoslem.test ܡܢ ܨܪܪܐ ResourceSelection – ܒܘܚܪܢܐ Hosmer-Lemeshow؛ binnedplot ܘ-bayesglm ܡܢ ܨܪܪܐ arm ܕ-Gelman ܘ-Hill – ܨܘܪܬܐ ܕܫܪ̈ܟܐ ܟܢܝ̈ܫܐ ܘܫܘܥܪܐ ܒܐܝܣܝܐ ܩܐ ܦܘܪܫܐ (separation). ܣܩܪܝܦܬ (script) ܪܗܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ (sample data file؛ ܒ-Rscript، ܥܡ png() ܚܕܪ ܨܘܪܬܐ). ܢܡܘܣܐ ܕܣܐܝܛ (site rule) ܩܐ ܣܘܪܝܬ ܒ-R: ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8، ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ، ܘܫܡ̈ܗܐ ܥܒܪ̈ܝܐ ܣܢܝܩܝ ܠܐܬܪܐ (locale) UTF-8 (ܓܘ Windows: R 4.2 ܘܠܥܠ، ܝܢ Sys.setlocale('LC_ALL', 'Hebrew')).

# ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܕܬܪܝܢ ܛܝ̈ܡܐ – ܦܪܘܦܣܘܪ ܣܛܐܛ. ܐܗܐ ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8؛ ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ
library(readxl)             # ܩܪܝܢܐ ܕܐܩܣܠ
library(ResourceSelection)  # hoslem.test
library(arm)                # binnedplot, bayesglm (Gelman & Hill)

# ܛܥܢܐ: ܛܘܦܣܐ ܬܩܝܢܐ – ܣܕܪܐ = ܡܫܬܘܬܦܢܐ، ܥܡܘܕܐ = ܡܫܬܚܠܦܢܐ؛ ܓܠܝܘܢܐ "נתונים"
d <- read_excel("C:/Rdata/DATA_logistic_example_heb.xlsx", sheet = "נתונים")
d$"סוג_יישוב" <- factor(d$"סוג_יישוב")        # ܡܢܒܝܢܐ ܕܓܢ̈ܣܐ – dummy coding، ܓܢܣܐ ܩܕܡܝܐ (1 = ܡܕܝܢܬܐ) ܫܬܐܣܐ

# ܡܘܕܝܠ: ܫܘܬܦܘܬܐ (0/1) ܡܢ ܣܢܝ̈ܐ ܕܥܡܪܐ، ܪܓܫܐ ܕܫܝܟܘܬܐ، ܥܘܡܪܐ، ܓܢܣܐ ܘܙܢܐ ܕܡܬܐ؛ ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (listwise) ܐܝܟ ܓܘ SPSS
m <- glm(השתתפות ~ ותק_בקהילה + תחושת_שייכות + גיל + מגדר + סוג_יישוב, data = d, family = binomial)
summary(m)$coefficients          # B، ܛܥܝܘܬܐ ܬܩܝܢܬܐ، z (Wald ܓܘ SPSS = z²)، p
exp(coef(m))                     # ܦܘܚܡ̈ܐ ܕܣܟܘ̈ܝܐ Exp(B): ܣܢܝ̈ܐ ܕܥܡܪܐ 1.11، ܫܝܟܘܬܐ 2.81، ܩܝܒܘܨ ܩܘܒܠ ܡܕܝܢܬܐ 2.22
exp(confint.default(m))          # ܬܚܘܡܐ ܕܬܘܟܠܢܐ 95% ܩܐ OR (ܥܠ ܣܒܠܬܐ ܕܠܘܓ، ܐܝܟ SPSS)
nobs(m)                          # N = 294

# ܡܘܕܝܠ ܩܘܒܠ ܡܘܕܝܠ ܣܦܝܩܐ: χ² ܕܦܘܚܡܐ ܕܡܬܚܙܝܢܘܬܐ، ܘ-R² ܕܠܐ ܫܪܝܪ̈ܐ
mf <- model.frame(m); m0 <- glm(השתתפות ~ 1, data = mf, family = binomial)   # ܡܘܕܝܠ ܣܦܝܩܐ ܥܠ ܗܢܝ 294 ܡܫܬܘܬܦ̈ܢܐ
chi2 <- m0$deviance - m$deviance; df <- m0$df.residual - m$df.residual
c(chi2 = chi2, df = df, p = pchisq(chi2, df, lower.tail = FALSE))       # 59.13, 6, p < .001
n <- nobs(m); cs <- 1 - exp(chi2 / -n); nag <- cs / (1 - exp(-m0$deviance / n))
c(cox_snell = cs, nagelkerke = nag)                                    # .182, .243

# ܠܘܚܐ ܕܦܘܪܫܐ ܠܓܢ̈ܣܐ ܓܘ ܬܚܘܡܐ .5
table(observed = m$y, predicted = as.integer(fitted(m) >= 0.5))     # 99 47 / 50 98 – 67.0% ܬܪܝܨܐ

# ܒܘܚܪܢܐ Hosmer-Lemeshow (10 ܓܘ̈ܕܐ) – hoslem.test ܟܟܢܫ ܠܦܘܬ ܕܪ̈ܓܐ ܡܢ ܡܐܐ ܕ-p (quantile) ܘܡܛܠ ܗܕܐ ܡܨܐ ܕܗܘܐ ܦܪܝܫܐ ܩܠܝܠ ܡܢ ܦܐܬܐ ܘܡܢ SPSS ܐܝܡܢ ܕܐܝܬ ܛܝ̈ܡܐ ܡܬܢ̈ܝܐ
hoslem.test(m$y, fitted(m), g = 10)                                    # 15.53, df 8, p = .050 (ܦܐܬܐ: 15.05, p = .058)

# ܒܘܚܪܢܐ ܕ-multicollinearity: VIF ܡܢ ܪܝܓܪܫܢ ܣܪܛܢܝܐ ܥܠ ܗܢܝ ܡܢܒ̈ܝܢܐ (Field, 2024، ܦܣܩܐ 20.7.4)
lm_vif <- lm(השתתפות ~ ותק_בקהילה + תחושת_שייכות + גיל + מגדר + סוג_יישוב, data = d)
1 / (1 - summary(lm(ותק_בקהילה ~ תחושת_שייכות + גיל + מגדר + סוג_יישוב, data = model.frame(lm_vif)))$r.squared)   # VIF ܕܣܢܝ̈ܐ ܕܥܡܪܐ = 1.01

# ܫܪ̈ܟܐ ܟܢܝ̈ܫܐ (Gelman & Hill, 2007، ܦܐܬܐ 97-98) – binnedplot ܡܢ ܨܪܪܐ arm؛ nclass = ܡܢܝܢܐ ܕܓܘ̈ܕܐ (ܦܐܬܐ: √N = 17)
binnedplot(fitted(m), residuals(m, type = "response"), nclass = 17, xlab = "Estimated Pr(participation)")
# ܛܝ̈ܡܐ ܓܢܒܝܗܝ: ܡܨܥܝܬܐ ܕ-p̂، ܡܨܥܝܬܐ ܕܫܪܟܐ ܘ-2·sd/√n ܓܘ ܟܠ ܓܘܕܐ (arm ܟܚܫܒ ܬܚܘܡܐ ܡܢ ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܫܪ̈ܟܐ ܓܘ ܓܘܕܐ، ܠܐ ܡܢ p̄(1 − p̄) ܐܝܟ ܓܘ ܟܬܒܐ – ܦܐܬܐ ܐܝܟ ܟܬܒܐ)
br <- arm:::binned.resids(fitted(m), residuals(m, type = "response"), nclass = 17)$binned
round(br[, c("xbar", "ybar", "n", "2se")], 4)                          # ܓܘܕܐ 1: p̂ .135، ܫܪܟܐ −.135، n 17 (ܦܐܬܐ: ܐܝܟ ܚܕ)

# ܢܡܘܣܐ ܕ"ܦܘܠܓܐ ܥܠ ܐܪܒܥܐ" (Gelman & Hill, 2007، ܦܐܬܐ 82): B/4 – ܬܚܘܡܐ ܥܠܝܐ ܩܐ ܫܘܢܝܐ ܓܘ ܡܣܬܒܪܢܘܬܐ ܩܐ ܡܫܘܚܬܐ ܕܡܢܒܝܢܐ
round(coef(m)[-1] / 4, 3)                                              # ܣܢܝ̈ܐ ܕܥܡܪܐ .026، ܫܝܟܘܬܐ .258، ܩܝܒܘܨ ܩܘܒܠ ܡܕܝܢܬܐ .199

# ܦܘܪܫܐ ܓܡܝܪܐ (Gelman & Hill, 2007، ܦܐܬܐ 104): glm ܟܡܙܗܪ "fitted probabilities numerically 0 or 1 occurred"؛ bayesglm ܟܝܗܒ ܫܘܥܪܐ ܣܟܝܐ
x <- c(-3, -2.5, -1, 0, 0.5, 1, 1.5, 2.5, 3, 3.5, 4, 5, 6); y <- as.integer(x > 2)
coef(summary(glm(y ~ x, family = binomial)))        # B = 44.3, SE = 55,296 – ܠܐ ܟܦܫܩܚ
coef(summary(bayesglm(y ~ x, family = binomial)))   # B = 1.86, SE = .88

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

Field (2024، ܦܣܩܐ 20.8): ܐܝܟ ܟܠ ܡܘܕܝܠ ܣܪܛܢܝܐ – ܠܘܚܐ (table) ܥܡ B، ܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) ܘ-p، ܦܘܚܡܐ ܕܣܟܘ̈ܝܐ (odds ratio) ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval)، ܡܢܝܢܐ ܩܝܡܐ (constant / intercept؛ ܕܩܪܘܝܐ ܡܨܐ ܕܡܬܢܐ ܫܘܝܘܬܐ)، ܘܣܛܐܛܝܣܛܝܩܐ ܟܠܢܝܬܐ ܕܡܘܕܝܠ (R², χ²) ܓܘ ܡܥܝܪܢܘܬܐ ܕܠܘܚܐ؛ ܐܦ ܡܢܒ̈ܝܢܐ (predictors) ܕܠܐ ܪܫܝܡ̈ܐ ܝܢܐ، "ܡܛܠ ܕܐܗܐ ܡܨܐ ܕܗܘܐ ܒܥܠ ܛܝܡܐ ܐܝܟ ܝܕܥܬܐ ܕܐܝܢܝ ܡܢܒ̈ܝܢܐ ܪ̈ܫܝܡܐ ܝܢܐ". ܠܦܘܬ APA (2020، ܦܣܩܐ 6.36) R² ܘ-p ܕܠܐ ܣܦܪ ܩܕܡܝܐ؛ OR ܡܨܐ ܕܥܒܪ ܥܠ 1 ܘܡܛܠ ܗܕܐ ܟܬܝܒܐ ܝܠܗ ܥܡ ܣܦܪ. Pallant (2020، ܨܚܚܐ 14) ܟܡܚܘܝܐ ܦܣܩܐ: "ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܬܪܝܨܐ ܥܒܝܕܐ ܝܠܗ ܩܐ ܒܘܚܪܢܐ ܕܡܥܒܕܢܘܬܐ ܕ… ܥܠ ܣܟܘ̈ܝܐ ܕ… ܡܘܕܝܠ ܓܡܝܪܐ ܪܫܝܡܐ ܝܠܗ، χ²(5, N = 241) = 76.02, p < .001، ܝܥܢܝ ܟܦܪܫ ܒܝܢܝ… ܡܘܕܝܠ ܦܪܫ ܬܪܝܨܐܝܬ 75.1% ܡܢ ܡܫܬܘܬܦ̈ܢܐ. ܐܝܟ ܕܡܚܘܝܐ ܝܠܗ ܓܘ ܠܘܚܐ 1، ܒܣ ܬܠܬܐ ܡܢ ܡܫܬܚܠܦ̈ܢܐ ܝܗܒܝ ܝܘܬܪܢܐ ܝܚܝܕܝܐ ܪܫܝܡܐ… ܡܢܒܝܢܐ ܚܝܠܢܐ ܡܢ ܟܠܗ ܗܘܐ…، ܥܡ ܦܘܚܡܐ ܕܣܟܘ̈ܝܐ 7.27" – ܘܒܬܪܗ̇ ܠܘܚܐ B / SE / Wald / df / p / OR / 95% CI. ܡܐܡܪ̈ܐ ܕܬܘܢܝܐ (report sentences) ܓܘ ܦܐܬܐ ܒܢܝ̈ܐ ܝܢܐ ܥܠ ܦܣܩܐ ܕ-Pallant، ܘܠܘܚܐ 2 ܝܠܗ ܠܘܚܐ ܕܝܠܗ̇.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܦܘܫܩܐ ܕ-B ܐܝܟ ܓܘ ܪܝܓܪܫܢ ܣܪܛܢܝܐ. B ܝܠܗ ܫܘܢܝܐ ܓܘ ܠܘܓ-ܣܟܘ̈ܝܐ (log-odds)؛ ܟܬܢܚ OR. ܘܐܦ OR ܠܐ ܝܠܗ "ܫܘܢܝܐ ܓܘ ܡܣܬܒܪܢܘܬܐ": 3 ܓܗ̈ܐ ܓܘ ܣܟܘ̈ܝܐ ܠܐ ܝܠܗ 3 ܓܗ̈ܐ ܓܘ ܡܣܬܒܪܢܘܬܐ (probability) – ܢܡܘܣܐ ܕ"ܦܘܠܓܐ ܥܠ ܐܪܒܥܐ" ܕ-Gelman ܘ-Hill ܟܝܗܒ ܬܚܘܡܐ ܩܐ ܫܘܢܝܐ ܓܘ ܡܣܬܒܪܢܘܬܐ.

ܫܓܝܫܘܬܐ ܓܘ ܐܘܪܚܐ ܕܪܡܙܢܘܬܐ. OR ܕ-.64 ܘ-1.56 ܝܢܐ ܗܝ ܡܫܟܚܢܘܬܐ؛ SPSS ܟܡܢܒܐ ܛܝܡܐ ܪܡܐ، ܘܦܐܬܐ – ܓܢܣܐ ܕܓܒܝܬܘܢ. ܟܐܡܪܚ ܒܡ̈ܠܐ ܕܡܢܘ ܝܢܐ ܣܟܘ̈ܝܐ ܘܩܐ ܡܘܕܝ، ܘܟܗܦܟܚ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܐܟܚܕܐ ܥܡ ܗܦܝܟܐ.

ܡܥܠܬܐ ܕܡܫܬܚܠܦܢܐ ܕܓܢ̈ܣܐ ܥܡ ܬܠܬܐ ܓܢ̈ܣܐ ܐܝܟ ܡܢܝܢܐ. "ܡܕܝܢܬܐ = 1، ܡܘܫܒ = 2، ܩܝܒܘܨ = 3" ܐܝܟ ܡܢܒܝܢܐ ܡܬܡܫܚܢܐ (continuous predictor) ܟܐܡܪ ܕܩܝܒܘܨ ܝܠܗ "ܬܠܬܐ ܓܗ̈ܐ ܡܕܝܢܬܐ". ܟܪܫܡܚ "ܕܓܢ̈ܣܐ" ܘܟܫܩܠܚ ܡܫܬܚܠܦ̈ܢܐ ܕܡܬܠܐ (dummies).

ܩܪܝܢܐ ܕ-R² ܕܠܐ ܫܪܝܪܐ ܐܝܟ ܫܘܚܠܦܐ ܡܦܫܩܐ. Cox & Snell ܘ-Nagelkerke ܟܦܚܡܝ ܡܘܕ̈ܝܠܐ؛ ܠܐ ܟܐܡܪܝ "ܡܘܕܝܠ ܟܡܦܫܩ 24%".

ܬܡܗܐ ܡܢ ܡܢܬܐ ܒܡܐܐ ܕܦܘܪܫܐ ܕܠܐ ܣܪܛܐ ܕܫܬܐܣܐ. 70% ܬܪܝܨܐ ܐܝܡܢ ܕܣܪܛܐ ܕܫܬܐܣܐ ܝܠܗ 68% – ܡܕܡ ܠܐ. ܘܒܐܘܪܚܐ ܗܦܝܟܬܐ: ܡܘܕܝܠ ܪܫܝܡܐ ܡܨܐ ܕܦܪܫ ܒܝܫܐܝܬ، ܘܠܐ ܝܠܗ ܦܣܝܠܐ ܡܛܠ ܗܕܐ.

ܫܒܩܬܐ ܕܛܥܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ ܪ̈ܒܬܐ ܣܓܝ ܕܠܐ ܚܙܝܐ. SE ܕ-40 ܥܡ OR ܕܡܠܝܘܢ ܠܐ ܝܠܗ ܡܫܟܚܢܘܬܐ – ܝܠܗ ܦܘܪܫܐ ܓܡܝܪܐ (perfect separation) ܝܢ ܩܠܝܬܐ ܣܦܝܩܬܐ (empty cell؛ Field, Section 20.4).

ܫܒܩܬܐ ܠ-SPSS ܕܓܒܐ ܡܢܒ̈ܝܢܐ. Stepwise – ܠܐ ܩܐ ܒܘܚܪܢܐ ܕܗܘܦܘܬܣ̈ܝܣ (hypotheses؛ Pallant؛ Field). ܟܒܢܚ ܒܕܪ̈ܓܐ، ܠܦܘܬ ܬܐܘܪܝܐ.

ܐܡܪܬܐ "ܥܠܬܐ ܝܠܗ". ܦܘܚܡܐ ܕܣܟܘ̈ܝܐ ܓܘ ܒܘܨܝܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ (correlational) ܝܠܗ "ܐܣܝܪܐ ܥܡ"؛ ܥܠܬܢܘܬܐ (causality) ܣܢܝܩܐ ܝܠܗ̇ ܠܬܘܩܢܐ ܕܒܘܨܝܐ (research design؛ ܦܐܬܐ ܡܫܬܚܠܦ̈ܢܐ ܘܬܘܩ̈ܢܐ ܕܒܘܨܝܐ).

ܡܒܘ̈ܥܐ

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

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

Gelman, A., & Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge University Press.

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

Hosmer ܘܐܚܪ̈ܢܐ (2013)، Menard (2002)، Cox ܘ-Snell (1989)، Nagelkerke (1991)، Agresti (2013) ܘ-Lo ܘܐܚܪ̈ܢܐ (2004) – ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Field (2024)؛ Tabachnick ܘ-Fidell (2013)، Hosmer ܘ-Lemeshow (2000)، Peat (2001) ܘ-Wright (1995) – ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Pallant (2020)؛ Landwehr ܘܐܚܪ̈ܢܐ (1984)، Albert ܘ-Anderson (1984)، Firth (1993) ܘ-Heinze ܘ-Schemper (2003) – ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Gelman ܘ-Hill (2007، ܦܐܬܐ 105). ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ (site rule)، ܓܘ ܪܫܝܡܬܐ ܕܡܒܘ̈ܥܐ (reference list) ܟܡܬܚܙܝ ܒܣ ܡܒܘ̈ܥܐ ܕܩܪܝ̈ܐ ܝܢܐ ܓܘ ܫܪܫܐ ܕܝܗܝ.