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Latent profile analysis

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Afrah Bushnaq

The document discusses latent profile analysis (LPA), which is a person-centered approach in psychological research. LPA aims to identify unobserved subgroups or profiles of individuals based on their responses to certain variables. The document outlines the key features of LPA, including its assumptions, methodology, applications in different fields, and comparison to other variable-centered and cluster analysis techniques. It also provides examples of LPA research studies.

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‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻦ‬ latent profile analysis ‫إ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ا‬ ‫د‬ : ‫أ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ا‬ ‫ح‬ , ‫ﺸ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ق‬ Afrahbushnaq@gmail.com ‫ﻗ‬ ‫ﻴ‬ ‫ﺎ‬ ‫س‬ ‫و‬ ‫ﺗ‬ ‫ﻘ‬ ‫ﻮ‬ J ‫ﻢ‬ ‫ﻋ‬ ‫ﺎ‬ ‫م‬ 1442 ‫ه‬
‫ﺟ‬ ‫ﺪ‬ ‫ﻭ‬ ‫ﻝ‬ ‫ﺍ‬ ‫ﶈ‬ ‫ﺘ‬ ‫ﻮ‬ ‫ﻳ‬ ‫ﺎ‬ ‫ﺕ‬ : 6 . 5 . 1 . 3 . ‫ﻣ‬ ‫ﻮ‬ ‫ﻗ‬ ‫ﻌ‬ ‫ﻪ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﺴ‬ ‫ﺒ‬ ‫ﺔ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻵ‬ ‫ﺧ‬ ‫ﺮ‬ ‫ﻯ‬ . 4 . 2 . ‫ﺗ‬ ‫ﻌ‬ ‫ﺮ‬ ‫ﻳ‬ ‫ﻔ‬ ‫ﻪ‬ . ‫ﺳ‬ ‫ﺒ‬ ‫ﺐ‬ ‫ﺗ‬ ‫ﺴ‬ ‫ﻤ‬ ‫ﻴ‬ ‫ﺘ‬ ‫ﻪ‬ ‫ﺑ‬ ‫ﻬ‬ ‫ﺬ‬ ‫ﺍ‬ ‫ﺍ‬ ‫ﻹ‬ ‫ﺳ‬ ‫ﻢ‬ . ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺮ‬ ‫ﻕ‬ ‫ﺑ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﻪ‬ ‫ﻭ‬ ‫ﺑ‬ ‫ﲔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻠ‬ ‫ﻲ‬ . ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺮ‬ ‫ﻕ‬ ‫ﺑ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﻪ‬ ‫ﻭ‬ ‫ﺑ‬ ‫ﲔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻨ‬ ‫ﻘ‬ ‫ﻮ‬ ‫ﺩ‬ ‫ﻱ‬ . ‫ﺑ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﻳ‬ ‫ﺔ‬ ‫ﻧ‬ ‫ﺸ‬ ‫ﺄ‬ ‫ﺗ‬ ‫ﻪ‬ ‫ﻭ‬ ‫ﺗ‬ ‫ﻄ‬ ‫ﻮ‬ ‫ﺭ‬ ‫ﻩ‬ .
‫ﺟ‬ ‫ﺪ‬ ‫ﻭ‬ ‫ﻝ‬ ‫ﺍ‬ ‫ﶈ‬ ‫ﺘ‬ ‫ﻮ‬ ‫ﻳ‬ ‫ﺎ‬ ‫ﺕ‬ : 12 . 11 . 7 . 9 . ‫ﻣ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﺩ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻪ‬ . 10 . 8 . ‫ﺍ‬ ‫ﻓ‬ ‫ﱰ‬ ‫ﺍ‬ ‫ﺿ‬ ‫ﺎ‬ ‫ﺗ‬ ‫ﻪ‬ ‫ﻭ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﻭ‬ ‫ﻃ‬ ‫ﻪ‬ . ‫ﻫ‬ ‫ﺪ‬ ‫ﻓ‬ ‫ﻪ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﺳ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﻲ‬ . ‫ﺍ‬ ‫ﻷ‬ ‫ﺳ‬ ‫ﺌ‬ ‫ﻠ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﺤ‬ ‫ﺜ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻲ‬ ‫ﳚ‬ ‫ﻴ‬ ‫ﺐ‬ ‫ﻋ‬ ‫ﻨ‬ ‫ﻬ‬ ‫ﺎ‬ . ‫ﺧ‬ ‫ﻄ‬ ‫ﻮ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﻣ‬ ‫ﺎ‬ ‫ﻗ‬ ‫ﺒ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ . ‫ﺧ‬ ‫ﻄ‬ ‫ﻮ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ .
‫ﺟ‬ ‫ﺪ‬ ‫ﻭ‬ ‫ﻝ‬ ‫ﺍ‬ ‫ﶈ‬ ‫ﺘ‬ ‫ﻮ‬ ‫ﻳ‬ ‫ﺎ‬ ‫ﺕ‬ : 13 . ‫ﻣ‬ ‫ﺜ‬ ‫ﺎ‬ ‫ﻝ‬ ‫ﲝ‬ ‫ﺜ‬ ‫ﻲ‬ . 14 . ‫ﳎ‬ ‫ﺎ‬ ‫ﻻ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﻣ‬ ‫ﻪ‬ ‫ﻭ‬ ‫ﺗ‬ ‫ﻄ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﺗ‬ ‫ﻪ‬ . 15 . ‫ﻣ‬ ‫ﺎ‬ ‫ﳉ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﺪ‬ ‫ﰲ‬ ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ . 16 . ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﺍ‬ ‫ﻣ‬ ‫ﺞ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺴ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺪ‬ ‫ﻣ‬ ‫ﺔ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ . 17 . ‫ﻣ‬ ‫ﺜ‬ ‫ﺎ‬ ‫ﻝ‬ ‫ﺗ‬ ‫ﻄ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﻘ‬ ‫ﻲ‬ Mplus . 18 . ‫ﺍ‬ ‫ﳌ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺟ‬ ‫ﻊ‬ .
1 . ‫ﻣ‬ ‫ﻮ‬ ‫ﻗ‬ ‫ﻌ‬ ‫ﻪ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﺴ‬ ‫ﺒ‬ ‫ﺔ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻵ‬ ‫ﺧ‬ ‫ﺮ‬ ‫ﻯ‬
‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻘ‬ ‫ﺴ‬ ‫ﻴ‬ ‫ﻢ‬ ‫ﺣ‬ ‫ﺴ‬ ‫ﺐ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﻫ‬ ‫ﺞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﺤ‬ ‫ﺚ‬ ‫ﰲ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻔ‬ ‫ﺲ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻨ‬ ‫ﻬ‬ ‫ﺞ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺮ‬ ‫ﻛ‬ ‫ﺰ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ (Variables Centered Approach's): ‫ﺍ‬ ‫ﳌ‬ ‫ﻨ‬ ‫ﻬ‬ ‫ﺞ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺮ‬ ‫ﻛ‬ ‫ﺰ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺩ‬ (person Centered Approach's): ‫ﻳ‬ ‫ﺼ‬ ‫ﻒ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﺣ‬ ‫ﺴ‬ ‫ﺐ‬ ‫ﺩ‬ ‫ﺭ‬ ‫ﺟ‬ ‫ﺎ‬ ‫ﺗ‬ ‫ﻬ‬ ‫ﻢ‬ ، ‫ﻭ‬ ‫ﻻ‬ ‫ﻳ‬ ‫ﻬ‬ ‫ﺘ‬ ‫ﻢ‬ ‫ﺑ‬ ‫ﺪ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺳ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺴ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﳋ‬ ‫ﺼ‬ ‫ﺎ‬ ‫ﺋ‬ ‫ﺺ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺸ‬ ‫ﺨ‬ ‫ﺼ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﺧ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺩ‬ . ‫ﻳ‬ ‫ﻬ‬ ‫ﺘ‬ ‫ﻢ‬ ‫ﺑ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺬ‬ ‫ﻳ‬ ‫ﻦ‬ ‫ﻳ‬ ‫ﺸ‬ ‫ﱰ‬ ‫ﻛ‬ ‫ﻮ‬ ‫ﻥ‬ ‫ﰲ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺴ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺃ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﳋ‬ ‫ﺼ‬ ‫ﺎ‬ ‫ﺋ‬ ‫ﺺ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺸ‬ ‫ﺨ‬ ‫ﺼ‬ ‫ﻴ‬ ‫ﺔ‬ . ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻦ‬ ) LPA ( ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ) LCA ( . ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻨ‬ ‫ﻘ‬ ‫ﻮ‬ ‫ﺩ‬ ‫ﻱ‬ ) CA ( . ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻠ‬ ‫ﻲ‬ ) FA ( ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﳓ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﺭ‬ ) RA ( . ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻦ‬ ) ANOVA ( .
‫ﺍ‬ ‫ﳌ‬ ‫ﻨ‬ ‫ﻬ‬ ‫ﺞ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺮ‬ ‫ﻛ‬ ‫ﺰ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ (Variables Centered Approach's): ‫ﺍ‬ ‫ﳌ‬ ‫ﻨ‬ ‫ﻬ‬ ‫ﺞ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺮ‬ ‫ﻛ‬ ‫ﺰ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺩ‬ (person Centered Approach's):
2 . ‫ﺗ‬ ‫ﻌ‬ ‫ﺮ‬ ‫ﻳ‬ ‫ﻔ‬ ‫ﻪ‬
‫ﺗ‬ ‫ﻌ‬ ‫ﺮ‬ ‫ﻳ‬ ‫ﻒ‬ ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻦ‬ ) LPA ( : § ‫ﻫ‬ ‫ﻮ‬ ‫ﻃ‬ ‫ﺮ‬ ‫ﻳ‬ ‫ﻘ‬ ‫ﺔ‬ ‫ﺗ‬ ‫ﺴ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺪ‬ ‫ﻡ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﺬ‬ ‫ﺟ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ . § ‫ﻳ‬ ‫ﻘ‬ ‫ﻮ‬ ‫ﻡ‬ ‫ﺑ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﺪ‬ ‫ﺍ‬ ƒ ‫ﻤ‬ ‫ﻮ‬ ‫ﻋ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺮ‬ ‫ﻋ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ) ‫ﺍ‬ ‫ﻟ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﻣ‬ ‫ﺸ‬ ‫ﺎ‬ ‫ﻫ‬ ‫ﺪ‬ ‫ﺓ‬ ( ، ‫ﺑ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﻡ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ ‫ﳎ‬ ‫ﻤ‬ ‫ﻮ‬ ‫ﻋ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻔ‬ ‫ﺮ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﺕ‬ . § ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﰲ‬ ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺴ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻤ‬ ‫ﻜ‬ ‫ﻦ‬ ‫ﺃ‬ ‫ﻥ‬ ‫ﺗ‬ ‫ﻜ‬ ‫ﻮ‬ ‫ﻥ‬ ‫ﺍ‬ ‫ﲰ‬ ‫ﻴ‬ ‫ﺔ‬ ) Nominal ( ، ‫ﺗ‬ ‫ﺮ‬ ‫ﺗ‬ ‫ﻴ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺔ‬ ) Ordinal ( ، ‫ﺃ‬ ‫ﻭ‬ ‫ﻣ‬ ‫ﺘ‬ ‫ﺼ‬ ‫ﻠ‬ ‫ﺔ‬ ) Continuous ( .
3 . ‫ﺳ‬ ‫ﺒ‬ ‫ﺐ‬ ‫ﺗ‬ ‫ﺴ‬ ‫ﻤ‬ ‫ﻴ‬ ‫ﺘ‬ ‫ﻪ‬ ‫ﺑ‬ ‫ﻬ‬ ‫ﺬ‬ ‫ﺍ‬ ‫ﺍ‬ ‫ﻹ‬ ‫ﺳ‬ ‫ﻢ‬
‫ﻣ‬ ‫ﺸ‬ ‫ﺘ‬ ‫ﻖ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﺳ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﲟ‬ ‫ﻴ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﻥ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻔ‬ ‫ﺴ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﻭ‬ ‫ﻗ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺱ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺮ‬ ‫ﻭ‬ ‫ﻕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺮ‬ ‫ﺩ‬ ‫ﻳ‬ ‫ﺔ‬ . ‫ﻳ‬ ‫ﺘ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻌ‬ ‫ﺒ‬ ‫ﲑ‬ ‫ﻋ‬ ‫ﻦ‬ ‫ﺩ‬ ‫ﺭ‬ ‫ﺟ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﺑ‬ ‫ﺮ‬ ‫ﺳ‬ ‫ﻢ‬ ‫ﺑ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﻲ‬ ‫ﻳ‬ ‫ﺴ‬ ‫ﻤ‬ ‫ﻰ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ . ‫ﺳ‬ ‫ﺒ‬ ‫ﺐ‬ ‫ﺗ‬ ‫ﺴ‬ ‫ﻤ‬ ‫ﻴ‬ ‫ﺘ‬ ‫ﻪ‬ ‫ﺑ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻦ‬ :
4 . ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺮ‬ ‫ﻕ‬ ‫ﺑ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﻪ‬ ‫ﻭ‬ ‫ﺑ‬ ‫ﲔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻠ‬ ‫ﻲ‬
‫ﻣ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺃ‬ ‫ﻭ‬ ‫ﻣ‬ ‫ﻔ‬ ‫ﺮ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﻋ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺨ‬ ‫ﻔ‬ ‫ﻀ‬ ‫ﺔ‬
F1 F2 F3 ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﻋ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻠ‬ ‫ﻲ‬ ‫ﺍ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﻜ‬ ‫ﺸ‬ ‫ﺎ‬ ‫ﰲ‬ (EFA):
F1 F2 F3 ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﻋ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻠ‬ ‫ﻲ‬ ‫ﺍ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﻜ‬ ‫ﺸ‬ ‫ﺎ‬ ‫ﰲ‬ (EFA):
‫ﺑ‬ ‫ﺮ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻦ‬ (LPA):
‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻦ‬ (LPA): ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻠ‬ ‫ﻲ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﻜ‬ ‫ﺸ‬ ‫ﺎ‬ ‫ﰲ‬ (EFA): F1 F2 F3 Item 1 0.53 Item 2 0.43 Item 3 0.61 Item 4 0.48 Item 5 0.51 Item 6 0.55 ‫ﻣ‬ ‫ﺼ‬ ‫ﻔ‬ ‫ﻮ‬ ‫ﻓ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﻂ‬ Pattern matrix ‫ﳕ‬ ‫ﺎ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻦ‬ LPA model Profile 1 Profile 2 + 8.15 3.2 - 7.2 3.6 / 9.1 5.5 * 9.3 4.1 % 7.3 3.3 ^ 6.7 3.9
‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻦ‬ (LPA): ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻠ‬ ‫ﻲ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﻜ‬ ‫ﺸ‬ ‫ﺎ‬ ‫ﰲ‬ (EFA): F1 F2 F3 Item 1 0.53 Item 2 0.43 Item 3 0.61 Item 4 0.48 Item 5 0.51 Item 6 0.55 ‫ﻣ‬ ‫ﺼ‬ ‫ﻔ‬ ‫ﻮ‬ ‫ﻓ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﻂ‬ Pattern matrix ‫ﳕ‬ ‫ﺎ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻦ‬ LPA model Profile 1 Profile 2 + 8.15 3.2 - 7.2 3.6 / 9.1 5.5 * 9.3 4.1 % 7.3 3.3 ^ 6.7 3.9 F1 = + F2 = * F3 = ^ ‫ﺫ‬ ‫ﻭ‬ ‫ﻱ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻘ‬ ‫ﺪ‬ ‫ﺭ‬ ‫ﺓ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﺫ‬ ‫ﻭ‬ ‫ﻱ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻘ‬ ‫ﺪ‬ ‫ﺭ‬ ‫ﺓ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻨ‬ ‫ﺨ‬ ‫ﻔ‬ ‫ﻀ‬ ‫ﺔ‬
5 . ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺮ‬ ‫ﻕ‬ ‫ﺑ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﻪ‬ ‫ﻭ‬ ‫ﺑ‬ ‫ﲔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻨ‬ ‫ﻘ‬ ‫ﻮ‬ ‫ﺩ‬ ‫ﻱ‬
‫ﺍ‬ ‫ﻟ‬ ‫ﻄ‬ ‫ﺮ‬ ‫ﻕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺮ‬ ‫ﻛ‬ ‫ﺰ‬ ‫ﺓ‬ ‫ﺣ‬ ‫ﻮ‬ ‫ﻝ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻦ‬ LPA & LCA ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻨ‬ ‫ﻘ‬ ‫ﻮ‬ ‫ﺩ‬ ‫ﻱ‬ CA - ‫ﳕ‬ ‫ﻮ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﻗ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺱ‬ Measurement model . - ‫ﲢ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﳕ‬ ‫ﺎ‬ ‫ﻁ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﺸ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﻬ‬ ‫ﺔ‬ ‫ﺑ‬ ‫ﻮ‬ ‫ﺍ‬ ‫ﺳ‬ ‫ﻄ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺣ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺔ‬ . - ‫ﻻ‬ ‫ﻳ‬ ‫ﻌ‬ ‫ﺘ‬ ‫ﱪ‬ ‫ﳕ‬ ‫ﻮ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﻗ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺱ‬ Measurement model . - ‫ﲢ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﳕ‬ ‫ﺎ‬ ‫ﻁ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﺸ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﻬ‬ ‫ﺔ‬ ‫ﺑ‬ ‫ﻮ‬ ‫ﺍ‬ ‫ﺳ‬ ‫ﻄ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺴ‬ ‫ﺎ‬ ‫ﻓ‬ ‫ﺔ‬ .
6 . ‫ﺑ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﻳ‬ ‫ﺔ‬ ‫ﻧ‬ ‫ﺸ‬ ‫ﺄ‬ ‫ﺗ‬ ‫ﻪ‬ ‫ﻭ‬ ‫ﺗ‬ ‫ﻄ‬ ‫ﻮ‬ ‫ﺭ‬ ‫ﻩ‬
1950 1974 1979 1997 - 1995 Lazarsfeld Goodman Haberman Clogg Hagenaars Vermunt - ‫ﻗ‬ ‫ﺪ‬ ّ ‫ﻡ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﻷ‬ ‫ﻭ‬ ‫ﻝ‬ ‫ﻣ‬ ‫ﺮ‬ ‫ﺓ‬ . - ‫ﻟ‬ ‫ﻠ‬ ‫ﻤ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺛ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺋ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﺔ‬ . - ‫ﺃ‬ ‫ﻭ‬ ‫ﺟ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻼ‬ ‫ﻗ‬ ‫ﺔ‬ ‫ﺑ‬ ‫ﲔ‬ ‫ﳕ‬ ‫ﺎ‬ ‫ﺫ‬ ‫ﺝ‬ LC ‫ﻭ‬ log- linear ‫ﳉ‬ ‫ﺪ‬ ‫ﻭ‬ ‫ﻝ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻮ‬ ‫ﺍ‬ ‫ﻓ‬ ‫ﻖ‬ ‫ﺑ‬ ‫ﻮ‬ ‫ﺟ‬ ‫ﻮ‬ ‫ﺩ‬ ‫ﺧ‬ ‫ﻼ‬ ‫ﻳ‬ ‫ﺎ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﻏ‬ ‫ﺔ‬ . - ‫ﺗ‬ ‫ﻄ‬ ‫ﻮ‬ ‫ﻳ‬ ‫ﺮ‬ ‫ﻭ‬ ‫ﺗ‬ ‫ﻮ‬ ‫ﺳ‬ ‫ﻴ‬ ‫ﻊ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺸ‬ ‫ﻤ‬ ‫ﻞ‬ : ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺸ‬ ‫ﱰ‬ ‫ﻛ‬ ‫ﺔ‬ ، ‫ﺍ‬ ‫ﻻ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﻘ‬ ‫ﻼ‬ ‫ﻝ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻮ‬ ‫ﺿ‬ ‫ﻌ‬ ‫ﻲ‬ ، ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱰ‬ ‫ﺗ‬ ‫ﻴ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﺼ‬ ‫ﻠ‬ ‫ﺔ‬ ، ‫ﻗ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﻣ‬ ‫ﺘ‬ ‫ﻜ‬ ‫ﺮ‬ ‫ﺭ‬ ‫ﺓ‬ ، ‫ﻣ‬ ‫ﻨ‬ ‫ﺒ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺕ‬ ، ‫ﻣ‬ ‫ﺘ‬ ‫ﻌ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺴ‬ ‫ﺘ‬ ‫ﻮ‬ ‫ﻳ‬ ‫ﺎ‬ ‫ﺕ‬ . - ‫ﻗ‬ ‫ﺪ‬ ّ ‫ﻡ‬ ‫ﺧ‬ ‫ﻮ‬ ‫ﺍ‬ ‫ﺭ‬ ‫ﺯ‬ ‫ﻣ‬ ‫ﻴ‬ ‫ﺔ‬ ML ‫ﻟ‬ ‫ﺘ‬ ‫ﻘ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﺮ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﻣ‬ ‫ﱰ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﻮ‬ ‫ﺫ‬ ‫ﺝ‬ . - ‫ﻣ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﻛ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﺘ‬ ‫ﻌ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﺓ‬ ، ‫ﻭ‬ ‫ﻣ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﻣ‬ ‫ﺘ‬ ‫ﻌ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﺓ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﺔ‬ .
‫ﺍ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﺼ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﻣ‬ ‫ﻬ‬ ‫ﻤ‬ ‫ﻪ‬ : LCA LPA LTA ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ) Latent class analysis ( : ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻦ‬ ) Latent profile analysis ( : ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﻧ‬ ‫ﺘ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﻝ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻦ‬ ) Latent Transition analysis ( : Њ ‫ﳕ‬ ‫ﻮ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺛ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﺖ‬ Static . Њ ‫ﻣ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﻛ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺔ‬ ‫ﲟ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺗ‬ ‫ﺼ‬ ‫ﻨ‬ ‫ﻴ‬ ‫ﻔ‬ ‫ﻴ‬ ‫ﺔ‬ . Њ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻔ‬ ‫ﺴ‬ ‫ﲑ‬ ‫ﻳ‬ ‫ﻜ‬ ‫ﻮ‬ ‫ﻥ‬ ‫ﺑ‬ ‫ﻘ‬ ‫ﻴ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺣ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺔ‬ . Њ ‫ﳕ‬ ‫ﻮ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺛ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﺖ‬ Static . - ‫ﻣ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﻛ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺔ‬ ‫ﲟ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﻣ‬ ‫ﺘ‬ ‫ﺼ‬ ‫ﻠ‬ ‫ﺔ‬ . - ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻔ‬ ‫ﺴ‬ ‫ﲑ‬ ‫ﻳ‬ ‫ﻜ‬ ‫ﻮ‬ ‫ﻥ‬ ‫ﺑ‬ ‫ﻘ‬ ‫ﻴ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻮ‬ ‫ﺳ‬ ‫ﻄ‬ ‫ﺎ‬ ‫ﺕ‬ . Њ ‫ﳕ‬ ‫ﻮ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﻣ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﺮ‬ ‫ﻙ‬ Dynamic . - ‫ﻣ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﻛ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺔ‬ ‫ﲟ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺗ‬ ‫ﺼ‬ ‫ﻨ‬ ‫ﻴ‬ ‫ﻔ‬ ‫ﻴ‬ ‫ﺔ‬ . - ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻔ‬ ‫ﺴ‬ ‫ﲑ‬ ‫ﻳ‬ ‫ﻜ‬ ‫ﻮ‬ ‫ﻥ‬ ‫ﺑ‬ ‫ﻘ‬ ‫ﻴ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺣ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺔ‬ .
‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ) LCA ( : ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻦ‬ ) LPA ( :
7 . ‫ﻣ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﺩ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻪ‬
‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ) LCA ( : ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻦ‬ ) LPA ( : ṔЊ ṕ
‫ﻣ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺟ‬ ‫ﻮ‬ ‫ﺩ‬ ‫ﺓ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻘ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺱ‬ : .1 ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﺲ‬ . rho .2 ‫ﺩ‬ ‫ﺭ‬ ‫ﺟ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺼ‬ ‫ﻞ‬ ‫ﺑ‬ ‫ﲔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ . gamma
8 . ‫ﺍ‬ ‫ﻓ‬ ‫ﱰ‬ ‫ﺍ‬ ‫ﺿ‬ ‫ﺎ‬ ‫ﺗ‬ ‫ﻪ‬ ‫ﻭ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﻭ‬ ‫ﻃ‬ ‫ﻪ‬
.1 ‫ﺃ‬ ‫ﻥ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﻣ‬ ‫ﺄ‬ ‫ﺧ‬ ‫ﻮ‬ ‫ﺫ‬ ‫ﺓ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﳎ‬ ‫ﻤ‬ ‫ﻮ‬ ‫ﻋ‬ ‫ﺔ‬ ‫ﻏ‬ ‫ﲑ‬ ‫ﻣ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﺴ‬ ‫ﺔ‬ ، ‫ﺗ‬ ‫ﻨ‬ ‫ﺘ‬ ‫ﺞ‬ ‫ﻣ‬ ‫ﺰ‬ ‫ﻳ‬ ‫ﺞ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺫ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺗ‬ ‫ﻮ‬ ‫ﺯ‬ ‫ﻳ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺧ‬ ‫ﺎ‬ ‫ﺻ‬ ‫ﺔ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﻫ‬ ‫ﺎ‬ ) K ( . .2 ‫ﻣ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻼ‬ ‫ﺣ‬ ‫ﻈ‬ ‫ﺔ‬ ) y ( ‫ﺗ‬ ‫ﻜ‬ ‫ﻮ‬ ‫ﻥ‬ ‫ﻣ‬ ‫ﻮ‬ ‫ﺯ‬ ‫ﻋ‬ ‫ﺔ‬ ‫ﺗ‬ ‫ﻮ‬ ‫ﺯ‬ ‫ﻳ‬ ‫ﻊ‬ ‫ﻃ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﻌ‬ ‫ﻲ‬ . .3 ‫ﻣ‬ ‫ﺘ‬ ‫ﻮ‬ ‫ﺳ‬ ‫ﻂ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﻬ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳋ‬ ‫ﺎ‬ ‫ﺻ‬ ‫ﺔ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ) µk ( ‫ﻫ‬ ‫ﻲ‬ ‫ﻋ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﺓ‬ ‫ﻋ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﺘ‬ ‫ﻮ‬ ‫ﺳ‬ ‫ﻂ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻼ‬ ‫ﺣ‬ ‫ﻈ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﳋ‬ ‫ﺎ‬ ‫ﺻ‬ ‫ﺔ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ) k ( . .4 ‫ﺍ‬ ‫ﻻ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﻘ‬ ‫ﻼ‬ ‫ﻝ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻮ‬ ‫ﺿ‬ ‫ﻌ‬ ‫ﻲ‬ ‫ﻭ‬ ‫ﻫ‬ ‫ﻮ‬ ‫ﺃ‬ ‫ﻥ‬ ‫ﻛ‬ ‫ﻞ‬ ) y ( ‫ﻏ‬ ‫ﲑ‬ ‫ﻣ‬ ‫ﺮ‬ ‫ﺗ‬ ‫ﺒ‬ ‫ﻄ‬ ‫ﺔ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﺧ‬ ‫ﻞ‬ ‫ﻛ‬ ‫ﻞ‬ ‫ﺑ‬ ‫ﺮ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ) k ( ، ‫ﻭ‬ ‫ﲨ‬ ‫ﻴ‬ ‫ﻊ‬ ‫ﻋ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺻ‬ ‫ﺮ‬ ‫ﻣ‬ ‫ﺼ‬ ‫ﻔ‬ ‫ﻮ‬ ‫ﻓ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻦ‬ ‫ﻏ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻘ‬ ‫ﻄ‬ ‫ﺮ‬ ‫ﻳ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﳋ‬ ‫ﺎ‬ ‫ﺻ‬ ‫ﺔ‬ ‫ﺏ‬ ) k ( ‫ﻫ‬ ‫ﻲ‬ ‫ﺻ‬ ‫ﻔ‬ ‫ﺮ‬ . .5 ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﺲ‬ ‫ﻭ‬ ‫ﻫ‬ ‫ﻮ‬ ‫ﺃ‬ ‫ﻥ‬ ‫ﻋ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺻ‬ ‫ﺮ‬ ‫ﻣ‬ ‫ﺼ‬ ‫ﻔ‬ ‫ﻮ‬ ‫ﻓ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻦ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺸ‬ ‫ﱰ‬ ‫ﻙ‬ ‫ﺍ‬ ‫ﳋ‬ ‫ﺎ‬ ‫ﺻ‬ ‫ﺔ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺗ‬ ‫ﻘ‬ ‫ﻴ‬ ‫ﺪ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﳌ‬ ‫ﺴ‬ ‫ﺎ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﺓ‬ ‫ﻋ‬ ‫ﱪ‬ ) k ( . .6 ‫ﺃ‬ ‫ﻥ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﲣ‬ ‫ﺘ‬ ‫ﻠ‬ ‫ﻒ‬ ‫ﻓ‬ ‫ﻘ‬ ‫ﻂ‬ ‫ﰲ‬ ‫ﻣ‬ ‫ﻮ‬ ‫ﻗ‬ ‫ﻊ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ) y ( ) µk ( ، ‫ﻭ‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺲ‬ ‫ﺷ‬ ‫ﻜ‬ ‫ﻞ‬ ‫ﻋ‬ ‫ﻼ‬ ‫ﻗ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ) y ( . ‫ﺍ‬ ‫ﻓ‬ ‫ﱰ‬ ‫ﺍ‬ ‫ﺿ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻦ‬ ) LPA ( :
9 . ‫ﻫ‬ ‫ﺪ‬ ‫ﻓ‬ ‫ﻪ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﺳ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﻲ‬
1. 3. 5. 2. 4. Timeline ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺼ‬ ‫ﻨ‬ ‫ﻴ‬ ‫ﻒ‬ ‫ﺍ‬ ‫ﻹ‬ ‫ﺛ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻨ‬ ‫ﺒ‬ ‫ﺆ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻔ‬ ‫ﺴ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻘ‬ ‫ﻖ‬
10 . ‫ﺍ‬ ‫ﻷ‬ ‫ﺳ‬ ‫ﺌ‬ ‫ﻠ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﺤ‬ ‫ﺜ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻲ‬ ‫ﳚ‬ ‫ﻴ‬ ‫ﺐ‬ ‫ﻋ‬ ‫ﻨ‬ ‫ﻬ‬ ‫ﺎ‬
- ‫ﻫ‬ ‫ﻞ‬ ‫ﻫ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﻙ‬ ‫ﻓ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺃ‬ ‫ﻭ‬ ‫ﺑ‬ ‫ﺮ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﻛ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﻪ‬ ‫ﺍ‬ ‫ﻋ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺩ‬ ‫ﺍ‬ ً ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻔ‬ ‫ﺮ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﺕ‬ ‫؟‬ - ‫ﻛ‬ ‫ﻢ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺃ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻮ‬ ‫ﺟ‬ ‫ﻮ‬ ‫ﺩ‬ ‫ﺓ‬ ‫ﰲ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﺎ‬ ‫ﺕ‬ ‫؟‬ - ‫ﻣ‬ ‫ﺎ‬ ‫ﻫ‬ ‫ﻮ‬ ‫ﺣ‬ ‫ﺠ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺃ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ) Prevalence ( ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ‫؟‬ Њ ‫ﻛ‬ ‫ﻴ‬ ‫ﻒ‬ ‫ﲣ‬ ‫ﺘ‬ ‫ﻠ‬ ‫ﻒ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﺘ‬ ‫ﺎ‬ ‫ﺋ‬ ‫ﺞ‬ ‫ﻋ‬ ‫ﱪ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺨ‬ ‫ﺘ‬ ‫ﻠ‬ ‫ﻔ‬ ‫ﺔ‬ ‫؟‬ Њ ‫ﺇ‬ ‫ﺫ‬ ‫ﺍ‬ ‫ﺍ‬ ‫ﻓ‬ ‫ﱰ‬ ‫ﺿ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺃ‬ ‫ﻥ‬ ‫ﺃ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﳝ‬ ‫ﻜ‬ ‫ﻦ‬ ‫ﺗ‬ ‫ﺼ‬ ‫ﻨ‬ ‫ﻴ‬ ‫ﻔ‬ ‫ﻬ‬ ‫ﻢ‬ ‫ﺇ‬ ‫ﱃ‬ ‫ﻓ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺃ‬ ‫ﻭ‬ ‫ﺑ‬ ‫ﺮ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﻛ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ، ‫ﻛ‬ ‫ﻴ‬ ‫ﻒ‬ ‫ﳝ‬ ‫ﻜ‬ ‫ﻨ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺇ‬ ‫ﺛ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﻫ‬ ‫ﺬ‬ ‫ﻩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺮ‬ ‫ﺿ‬ ‫ﻴ‬ ‫ﺔ‬ ‫؟‬ Њ ‫ﻫ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺃ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﻗ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﻠ‬ ‫ﺔ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﺘ‬ ‫ﻜ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺭ‬ ‫ﻋ‬ ‫ﱪ‬ ‫ﻋ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﳐ‬ ‫ﺘ‬ ‫ﻠ‬ ‫ﻔ‬ ‫ﺔ‬ ‫ﳑ‬ ‫ﻴ‬ ‫ﺰ‬ ‫ﺓ‬ ، ‫ﺃ‬ ‫ﻭ‬ ‫ﻋ‬ ‫ﱪ‬ ‫ﻧ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﻁ‬ ‫ﺯ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﺘ‬ ‫ﻌ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﺓ‬ ‫؟‬ - ‫ﺑ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻈ‬ ‫ﺮ‬ ‫ﺇ‬ ‫ﱃ‬ ‫ﳕ‬ ‫ﻂ‬ ‫ﺍ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﺔ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﺩ‬ ‫ﻣ‬ ‫ﻌ‬ ‫ﲔ‬ ، ‫ﻣ‬ ‫ﺎ‬ ‫ﻫ‬ ‫ﻲ‬ ‫ﺍ‬ ‫ﺣ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻧ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺅ‬ ‫ﻩ‬ ‫ﺇ‬ ‫ﱃ‬ ‫ﺑ‬ ‫ﺮ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺃ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺌ‬ ‫ﺔ‬ ‫ﻛ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺔ‬ ‫؟‬ - ‫ﻫ‬ ‫ﻞ‬ ‫ﳝ‬ ‫ﻜ‬ ‫ﻦ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻨ‬ ‫ﺒ‬ ‫ﺆ‬ ‫ﺑ‬ ‫ﻌ‬ ‫ﻀ‬ ‫ﻮ‬ ‫ﻳ‬ ‫ﺔ‬ ‫ﺑ‬ ‫ﺮ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﻣ‬ ‫ﻌ‬ ‫ﲔ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﺧ‬ ‫ﻼ‬ ‫ﻝ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺸ‬ ‫ﱰ‬ ‫ﻛ‬ ‫ﺔ‬ ‫؟‬
11 . ‫ﺧ‬ ‫ﻄ‬ ‫ﻮ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﻣ‬ ‫ﺎ‬ ‫ﻗ‬ ‫ﺒ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬
.1 ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻌ‬ ‫ﺮ‬ ‫ﻳ‬ ‫ﻒ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﳌ‬ ‫ﺸ‬ ‫ﻜ‬ ‫ﻠ‬ ‫ﺔ‬ ‫ﻭ‬ ‫ﻫ‬ ‫ﺪ‬ ‫ﻑ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﺤ‬ ‫ﺚ‬ . .2 ‫ﲢ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺒ‬ ‫ﺔ‬ ‫ﺑ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ء‬ ً ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ 1 . .3 ‫ﺣ‬ ‫ﺠ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺐ‬ : ‫ﺃ‬ ‫ﻛ‬ ‫ﱪ‬ ‫ﻣ‬ ‫ﻦ‬ 500 . ‫ﺧ‬ ‫ﻄ‬ ‫ﻮ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﻣ‬ ‫ﺎ‬ ‫ﻗ‬ ‫ﺒ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ : ‫ﻗ‬ ‫ﺒ‬ ‫ﻞ‬ ‫ﲨ‬ ‫ﻊ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﺎ‬ ‫ﺕ‬ : ‫ﺑ‬ ‫ﻌ‬ ‫ﺪ‬ ‫ﲨ‬ ‫ﻊ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﺎ‬ ‫ﺕ‬ : .1 ‫ﺍ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻘ‬ ‫ﺪ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺐ‬ : ML ‫ﻟ‬ ‫ﻠ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﺼ‬ ‫ﻠ‬ ‫ﺔ‬ ، MLR ‫ﻟ‬ ‫ﻠ‬ ‫ﺘ‬ ‫ﻮ‬ ‫ﺯ‬ ‫ﻳ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﻃ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﺔ‬ . .2 ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻞ‬ ‫ﻣ‬ ‫ﻊ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻔ‬ ‫ﻘ‬ ‫ﻮ‬ ‫ﺩ‬ ‫ﺓ‬ ) MAR ( : FIML or MI ‫ﻭ‬ ‫ﲡ‬ ‫ﻨ‬ ‫ﺐ‬ ‫ﺍ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﻡ‬ List & pairwise deletion .3 Global vs. Local solution
‫ﲢ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺒ‬ ‫ﺔ‬ : ‫ﺧ‬ ‫ﻄ‬ ‫ﻮ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﻣ‬ ‫ﺎ‬ ‫ﻗ‬ ‫ﺒ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ :
12 . ‫ﺧ‬ ‫ﻄ‬ ‫ﻮ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬
‫ﺧ‬ ‫ﻄ‬ ‫ﻮ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺇ‬ ‫ﺟ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ء‬ ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻦ‬ LPA :
‫ﻳ‬ ‫ﻌ‬ ‫ﻨ‬ ‫ﻲ‬ ‫ﺃ‬ ‫ﻥ‬ ‫ﻳ‬ ‫ﻜ‬ ‫ﻮ‬ ‫ﻥ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﻮ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﻣ‬ ‫ﻌ‬ ‫ﺮ‬ ‫ﻑ‬ ‫ﺑ‬ ‫ﺸ‬ ‫ﻜ‬ ‫ﻞ‬ ‫ﺟ‬ ‫ﻴ‬ ‫ﺪ‬ ) well - identify ( .
‫ﻳ‬ ‫ﻌ‬ ‫ﻨ‬ ‫ﻲ‬ ‫ﺃ‬ ‫ﻥ‬ ‫ﻧ‬ ‫ﻘ‬ ‫ﻮ‬ ‫ﻡ‬ ‫ﺑ‬ ‫ﺘ‬ ‫ﻘ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻤ‬ ‫ﻜ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻘ‬ ‫ﺪ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺐ‬ : ML ‫ﻟ‬ ‫ﻠ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﺼ‬ ‫ﻠ‬ ‫ﺔ‬ ، MLR ‫ﻟ‬ ‫ﻠ‬ ‫ﺘ‬ ‫ﻮ‬ ‫ﺯ‬ ‫ﻳ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﻃ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﺔ‬ .
2 Њ ‫ﺗ‬ ‫ﻘ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻤ‬ ‫ﻜ‬ ‫ﻨ‬ ‫ﺔ‬ .
‫ﻳ‬ ‫ﻌ‬ ‫ﻨ‬ ‫ﻲ‬ ‫ﺍ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﻮ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺐ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﻻ‬ ‫ﻋ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺩ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ : 1 Њ ‫ﺍ‬ ‫ﳌ‬ ‫ﻌ‬ ‫ﻘ‬ ‫ﻮ‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻈ‬ ‫ﺮ‬ ‫ﻳ‬ ‫ﺔ‬ . 2 Њ ‫ﺍ‬ ‫ﳌ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﻧ‬ ‫ﺔ‬ ‫ﺑ‬ ‫ﲔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﻡ‬ ‫ﻣ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻼ‬ ‫ﺋ‬ ‫ﻤ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﺴ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺔ‬ : AIC, BIC……. 3 Њ ‫ﺍ‬ ‫ﻟ‬ ‫ﺪ‬ ‫ﻗ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻲ‬ ‫ﰎ‬ ‫ﻓ‬ ‫ﻴ‬ ‫ﻬ‬ ‫ﺎ‬ ‫ﺗ‬ ‫ﻘ‬ ‫ﺴ‬ ‫ﻴ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﰲ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ : ‫ﲟ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﺩ‬ ‫ﻗ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻘ‬ ‫ﺴ‬ ‫ﻴ‬ ‫ﻢ‬ Entropy 4 Њ ‫ﻣ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﻧ‬ ‫ﺔ‬ ‫ﻧ‬ ‫ﺴ‬ ‫ﺒ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺣ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺨ‬ ‫ﺘ‬ ‫ﻠ‬ ‫ﻔ‬ ‫ﺔ‬ ‫ﻟ‬ ‫ﻼ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻲ‬ ‫ﲢ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﻣ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﻧ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺑ‬ ‫ﲔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﻮ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﻮ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺫ‬ ‫ﻭ‬ ‫ﻱ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺌ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﺩ‬ ‫ﻧ‬ ‫ﻰ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﻪ‬ .
‫ﺍ‬ ‫ﻟ‬ ‫ﺴ‬ ‫ﻠ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺕ‬ Disadvantages ‫ﺍ‬ ‫ﻹ‬ ‫ﳚ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺕ‬ Advantages ‫ﻣ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺭ‬ Choice criteria ‫ﺧ‬ ‫ﺼ‬ ‫ﺎ‬ ‫ﺋ‬ ‫ﺼ‬ ‫ﻪ‬ Characterization ‫ﻣ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﺩ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻪ‬ Formula ‫ﺍ‬ ‫ﳌ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ indicator ‫ﺯ‬ ‫ﻳ‬ ‫ﺎ‬ ‫ﺩ‬ ‫ﺓ‬ ‫ﺗ‬ ‫ﻘ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﺮ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﲡ‬ ‫ﺔ‬ . ‫ﻳ‬ ‫ﺴ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺪ‬ ‫ﻡ‬ ‫ﺃ‬ ‫ﻛ‬ ‫ﺜ‬ ‫ﺮ‬ ‫ﻣ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﺩ‬ ‫ﻗ‬ ‫ﻴ‬ ‫ﻖ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﻤ‬ ‫ﻼ‬ ‫ﺋ‬ ‫ﻤ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﻧ‬ ‫ﺔ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﺭ‬ ‫ﺟ‬ ‫ﺤ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻵ‬ ‫ﺧ‬ ‫ﺮ‬ ‫ﻯ‬ . ‫ﻗ‬ ‫ﻴ‬ ‫ﻤ‬ ‫ﺘ‬ ‫ﻪ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺔ‬ ‫ﺗ‬ ‫ﺪ‬ ‫ﻝ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ ‫ﺃ‬ ‫ﻥ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺫ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻗ‬ ‫ﻞ‬ ‫ﻫ‬ ‫ﻲ‬ ‫ﺍ‬ ‫ﳊ‬ ‫ﻞ‬ . ‫ﺍ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﺧ‬ ‫ﻠ‬ ‫ﺔ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺬ‬ ‫ﻱ‬ ‫ﻳ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﻥ‬ ‫ﺑ‬ ‫ﲔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﺎ‬ ‫ﻭ‬ ‫ﺭ‬ ‫ﺓ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﻡ‬ ‫ﻃ‬ ‫ﺮ‬ ‫ﻳ‬ ‫ﻘ‬ ‫ﺔ‬ Bootstrap sample . 𝐿𝑅 = −2{𝑙𝑜𝑔𝐿 * 𝜑! − 𝑙𝑜𝑔𝐿( - 𝜑(!#$))} ‫ﺍ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﻧ‬ ‫ﺴ‬ ‫ﺒ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﺭ‬ ‫ﺟ‬ ‫ﺤ‬ ‫ﻴ‬ ‫ﺔ‬ BLRT ‫ﻣ‬ ‫ﻌ‬ ‫ﺪ‬ ‫ﻝ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺨ‬ ‫ﻔ‬ ‫ﺾ‬ ‫ﺑ‬ ‫ﺸ‬ ‫ﻜ‬ ‫ﻞ‬ ‫ﻋ‬ ‫ﺎ‬ ‫ﻡ‬ ‫ﰲ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺸ‬ ‫ﻒ‬ ‫ﻋ‬ ‫ﻦ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﻣ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﻧ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﻊ‬ SABIC. ‫ﻫ‬ ‫ﻮ‬ ‫ﺍ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﻗ‬ ‫ﻮ‬ ‫ﻱ‬ ‫ﻭ‬ ‫ﻳ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﻨ‬ ‫ﺐ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺮ‬ ‫ﺝ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻔ‬ ‫ﺮ‬ ‫ﻁ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﻣ‬ ‫ﻊ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﻃ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﺔ‬ ، ‫ﻣ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﻧ‬ ‫ﺔ‬ ‫ﺏ‬ BLRT ‫ﻭ‬ BIC . ‫ﻗ‬ ‫ﻴ‬ ‫ﻤ‬ ‫ﺘ‬ ‫ﻪ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺔ‬ ‫ﺗ‬ ‫ﺪ‬ ‫ﻝ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ ‫ﺃ‬ ‫ﻥ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺫ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻗ‬ ‫ﻞ‬ ‫ﻫ‬ ‫ﻲ‬ ‫ﺍ‬ ‫ﳊ‬ ‫ﻞ‬ . ‫ﺍ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﺧ‬ ‫ﻠ‬ ‫ﺔ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺬ‬ ‫ﻱ‬ ‫ﻳ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﻥ‬ ‫ﺑ‬ ‫ﲔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﺎ‬ ‫ﻭ‬ ‫ﺭ‬ ‫ﺓ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﻡ‬ ‫ﳎ‬ ‫ﻤ‬ ‫ﻮ‬ ‫ﻉ‬ ‫ﺃ‬ ‫ﻭ‬ ‫ﺯ‬ ‫ﺍ‬ ‫ﻥ‬ ‫ﻣ‬ ‫ﺮ‬ ‫ﺑ‬ ‫ﻊ‬ ‫ﻛ‬ ‫ﺎ‬ ‫ﻱ‬ . LR adjusted = 𝐿𝑅 1 + 𝑝 − 𝑞 log 𝑛!" ‫ﺍ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺪ‬ ‫ﻝ‬ ‫ﻭ‬ ‫ﺭ‬ ‫ﻭ‬ ‫ﺑ‬ ‫ﲔ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻌ‬ ‫ﺪ‬ ‫ﻝ‬ ALMR
‫ﺍ‬ ‫ﻟ‬ ‫ﺴ‬ ‫ﻠ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺕ‬ Disadvantages ‫ﺍ‬ ‫ﻹ‬ ‫ﳚ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺕ‬ Advantages ‫ﻣ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺭ‬ Choice criteria ‫ﺧ‬ ‫ﺼ‬ ‫ﺎ‬ ‫ﺋ‬ ‫ﺼ‬ ‫ﻪ‬ Characterization ‫ﻣ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﺩ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻪ‬ Formula ‫ﺍ‬ ‫ﳌ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ indicator ‫ﻣ‬ ‫ﻦ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻤ‬ ‫ﻜ‬ ‫ﻦ‬ ‫ﺃ‬ ‫ﻥ‬ ‫ﻳ‬ ‫ﻔ‬ ‫ﺮ‬ ‫ﻁ‬ ‫ﰲ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﲡ‬ ‫ﺔ‬ . ‫ﺇ‬ ‫ﱃ‬ ‫ﺣ‬ ‫ﺪ‬ ‫ﻣ‬ ‫ﺎ‬ ‫ﻫ‬ ‫ﻮ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺐ‬ ‫ﻟ‬ ‫ﻼ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﻡ‬ ‫ﰲ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺼ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺓ‬ > 500 . ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﻮ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺫ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻘ‬ ‫ﻴ‬ ‫ﻤ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻗ‬ ‫ﻞ‬ ‫ﻫ‬ ‫ﻮ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻓ‬ ‫ﺾ‬ ‫ﻣ‬ ‫ﻼ‬ ‫ﺋ‬ ‫ﻤ‬ ‫ﺔ‬ . ‫ﻣ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﻤ‬ ‫ﻌ‬ ‫ﻠ‬ ‫ﻮ‬ ‫ﻣ‬ ‫ﺎ‬ ‫ﺕ‬ ، ‫ﻳ‬ ‫ﻌ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺪ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ ‫ﺃ‬ ‫ﺭ‬ ‫ﺟ‬ ‫ﺤ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺫ‬ ‫ﺝ‬ ، ‫ﻭ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﻣ‬ ‫ﱰ‬ ‫ﺍ‬ ‫ﺕ‬ ، ‫ﻭ‬ ‫ﻻ‬ ‫ﻳ‬ ‫ﺄ‬ ‫ﺧ‬ ‫ﺬ‬ ‫ﺣ‬ ‫ﺠ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﰲ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﻋ‬ ‫ﺘ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﺭ‬ . AIC= 𝐺& + 2𝑝 AIC ‫ﺍ‬ ‫ﻹ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﻁ‬ ‫ﰲ‬ ‫ﺗ‬ ‫ﻘ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﺮ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﺬ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﻣ‬ ‫ﻊ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﻃ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﺔ‬ . ‫ﻭ‬ ‫ﻋ‬ ‫ﻜ‬ ‫ﺲ‬ ‫ﺫ‬ ‫ﻟ‬ ‫ﻚ‬ ‫ﻣ‬ ‫ﻊ‬ ‫ﺣ‬ ‫ﺠ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺼ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺓ‬ . ‫ﻣ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﺟ‬ ‫ﻴ‬ ‫ﺪ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﺪ‬ ‫ﻗ‬ ‫ﺔ‬ ، ‫ﻭ‬ ‫ﺗ‬ ‫ﺰ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﺩ‬ ‫ﻗ‬ ‫ﺘ‬ ‫ﻪ‬ ‫ﰲ‬ ‫ﺍ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﻮ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺫ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺣ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ ‫ﺑ‬ ‫ﺰ‬ ‫ﻳ‬ ‫ﺎ‬ ‫ﺩ‬ ‫ﺓ‬ ‫ﺣ‬ ‫ﺠ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺔ‬ . ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﻮ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺫ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻘ‬ ‫ﻴ‬ ‫ﻤ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻗ‬ ‫ﻞ‬ ‫ﻫ‬ ‫ﻮ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻓ‬ ‫ﺾ‬ ‫ﻣ‬ ‫ﻼ‬ ‫ﺋ‬ ‫ﻤ‬ ‫ﺔ‬ . ‫ﻣ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﻤ‬ ‫ﻌ‬ ‫ﻠ‬ ‫ﻮ‬ ‫ﻣ‬ ‫ﺎ‬ ‫ﺕ‬ ، ‫ﻳ‬ ‫ﻌ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺪ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ ‫ﺃ‬ ‫ﺭ‬ ‫ﺟ‬ ‫ﺤ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺫ‬ ‫ﺝ‬ ، ‫ﻭ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﻣ‬ ‫ﱰ‬ ‫ﺍ‬ ‫ﺕ‬ ، ‫ﻭ‬ ‫ﺣ‬ ‫ﺠ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺔ‬ . BIC= 𝐺# + 𝑙𝑜𝑜𝑔 𝑛 [𝑝] BIC ‫ﺍ‬ ‫ﻹ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﻁ‬ ‫ﰲ‬ ‫ﺗ‬ ‫ﻘ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﺮ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﺬ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﻣ‬ ‫ﻊ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﻃ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﺔ‬ . ‫ﻣ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﺟ‬ ‫ﻴ‬ ‫ﺪ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﺪ‬ ‫ﻗ‬ ‫ﺔ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﳌ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﻧ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﻊ‬ BIC ‫ﻭ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺬ‬ ‫ﻱ‬ ‫ﻳ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﻗ‬ ‫ﺐ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ ‫ﺣ‬ ‫ﺠ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺔ‬ . ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﻮ‬ ‫ﺫ‬ ‫ﺝ‬ ‫ﺫ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻘ‬ ‫ﻴ‬ ‫ﻤ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻗ‬ ‫ﻞ‬ ‫ﻫ‬ ‫ﻮ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻓ‬ ‫ﺾ‬ ‫ﻣ‬ ‫ﻼ‬ ‫ﺋ‬ ‫ﻤ‬ ‫ﺔ‬ . ‫ﳏ‬ ‫ﻚ‬ ‫ﺑ‬ ‫ﻴ‬ ‫ﺰ‬ ‫ﻳ‬ ‫ﺎ‬ ‫ﻥ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﻤ‬ ‫ﻌ‬ ‫ﻠ‬ ‫ﻮ‬ ‫ﻣ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺬ‬ ‫ﻱ‬ ‫ﻳ‬ ‫ﻀ‬ ‫ﺒ‬ ‫ﻂ‬ ‫ﺣ‬ ‫ﺠ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺔ‬ . SABIC= −2𝐿𝐿 + 𝑝 log 𝑁 + 2 /24 SABIC
‫ﳏ‬ ‫ﺎ‬ ‫ﻛ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺗ‬ ‫ﺴ‬ ‫ﻤ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﲡ‬ ‫ﺔ‬ : 1 Њ ‫ﺑ‬ ‫ﺎ‬ ‫ﻻ‬ ‫ﻋ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺩ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺆ‬ ‫ﺷ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺕ‬ . 2 Њ ‫ﺑ‬ ‫ﺎ‬ ‫ﻛ‬ ‫ﺘ‬ ‫ﺸ‬ ‫ﺎ‬ ‫ﻑ‬ ‫ﺟ‬ ‫ﻮ‬ ‫ﻫ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ . 3 Њ ‫ﺗ‬ ‫ﺮ‬ ‫ﻗ‬ ‫ﻴ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺇ‬ ‫ﺫ‬ ‫ﺍ‬ ‫ﻛ‬ ‫ﺎ‬ ‫ﻥ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﻫ‬ ‫ﺎ‬ ‫ﻛ‬ ‫ﺒ‬ ‫ﲑ‬ .
‫ﻣ‬ ‫ﻦ‬ ‫ﺧ‬ ‫ﻼ‬ ‫ﻝ‬ ‫ﺇ‬ ‫ﺩ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺝ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺸ‬ ‫ﱰ‬ ‫ﻛ‬ ‫ﺔ‬ Covariates . ‫ﺍ‬ ‫ﳉ‬ ‫ﻨ‬ ‫ﺲ‬ ، ‫ﺍ‬ ‫ﳌ‬ ‫ﺴ‬ ‫ﺘ‬ ‫ﻮ‬ ‫ﻯ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺪ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺳ‬ ‫ﻲ‬ . ‫ﻋ‬ ‫ﺪ‬ ‫ﻡ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﺲ‬ ‫؟‬ ‫؟‬
‫ﻣ‬ ‫ﻦ‬ ‫ﺧ‬ ‫ﻼ‬ ‫ﻝ‬ ‫ﺇ‬ ‫ﺩ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺝ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺸ‬ ‫ﱰ‬ ‫ﻛ‬ ‫ﺔ‬ Covariates . ‫ﺍ‬ ‫ﳉ‬ ‫ﻨ‬ ‫ﺲ‬ ، ‫ﺍ‬ ‫ﳌ‬ ‫ﺴ‬ ‫ﺘ‬ ‫ﻮ‬ ‫ﻯ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺪ‬ ‫ﺭ‬ ‫ﺍ‬ ‫ﺳ‬ ‫ﻲ‬ . ‫ﻋ‬ ‫ﺪ‬ ‫ﻡ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﺲ‬ ‫؟‬ ‫؟‬
- ‫ﻫ‬ ‫ﻞ‬ ‫ﻫ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﻙ‬ ‫ﻓ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺃ‬ ‫ﻭ‬ ‫ﺑ‬ ‫ﺮ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﻛ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﻪ‬ ‫ﺍ‬ ‫ﻋ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺩ‬ ‫ﺍ‬ ً ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻰ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻔ‬ ‫ﺮ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﺕ‬ ‫؟‬ - ‫ﻛ‬ ‫ﻢ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺃ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻮ‬ ‫ﺟ‬ ‫ﻮ‬ ‫ﺩ‬ ‫ﺓ‬ ‫ﰲ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﺎ‬ ‫ﺕ‬ ‫؟‬ - ‫ﻣ‬ ‫ﺎ‬ ‫ﻫ‬ ‫ﻮ‬ ‫ﺣ‬ ‫ﺠ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺃ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ) Prevalence ( ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ‫؟‬ Њ ‫ﻛ‬ ‫ﻴ‬ ‫ﻒ‬ ‫ﲣ‬ ‫ﺘ‬ ‫ﻠ‬ ‫ﻒ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﺘ‬ ‫ﺎ‬ ‫ﺋ‬ ‫ﺞ‬ ‫ﻋ‬ ‫ﱪ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺨ‬ ‫ﺘ‬ ‫ﻠ‬ ‫ﻔ‬ ‫ﺔ‬ ‫؟‬ Њ ‫ﺇ‬ ‫ﺫ‬ ‫ﺍ‬ ‫ﺍ‬ ‫ﻓ‬ ‫ﱰ‬ ‫ﺿ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺃ‬ ‫ﻥ‬ ‫ﺃ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﳝ‬ ‫ﻜ‬ ‫ﻦ‬ ‫ﺗ‬ ‫ﺼ‬ ‫ﻨ‬ ‫ﻴ‬ ‫ﻔ‬ ‫ﻬ‬ ‫ﻢ‬ ‫ﺇ‬ ‫ﱃ‬ ‫ﻓ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺃ‬ ‫ﻭ‬ ‫ﺑ‬ ‫ﺮ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﻛ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ، ‫ﻛ‬ ‫ﻴ‬ ‫ﻒ‬ ‫ﳝ‬ ‫ﻜ‬ ‫ﻨ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺇ‬ ‫ﺛ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﻫ‬ ‫ﺬ‬ ‫ﻩ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺮ‬ ‫ﺿ‬ ‫ﻴ‬ ‫ﺔ‬ ‫؟‬ Њ ‫ﻫ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺃ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻼ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﻗ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﻠ‬ ‫ﺔ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﺘ‬ ‫ﻜ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺭ‬ ‫ﻋ‬ ‫ﱪ‬ ‫ﻋ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﳐ‬ ‫ﺘ‬ ‫ﻠ‬ ‫ﻔ‬ ‫ﺔ‬ ‫ﳑ‬ ‫ﻴ‬ ‫ﺰ‬ ‫ﺓ‬ ، ‫ﺃ‬ ‫ﻭ‬ ‫ﻋ‬ ‫ﱪ‬ ‫ﻧ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﻁ‬ ‫ﺯ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﺘ‬ ‫ﻌ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﺓ‬ ‫؟‬ - ‫ﺑ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻈ‬ ‫ﺮ‬ ‫ﺇ‬ ‫ﱃ‬ ‫ﳕ‬ ‫ﻂ‬ ‫ﺍ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﺔ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﺩ‬ ‫ﻣ‬ ‫ﻌ‬ ‫ﲔ‬ ، ‫ﻣ‬ ‫ﺎ‬ ‫ﻫ‬ ‫ﻲ‬ ‫ﺍ‬ ‫ﺣ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻧ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺅ‬ ‫ﻩ‬ ‫ﺇ‬ ‫ﱃ‬ ‫ﺑ‬ ‫ﺮ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺃ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺌ‬ ‫ﺔ‬ ‫ﻛ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺔ‬ ‫؟‬ - ‫ﻫ‬ ‫ﻞ‬ ‫ﳝ‬ ‫ﻜ‬ ‫ﻦ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻨ‬ ‫ﺒ‬ ‫ﺆ‬ ‫ﺑ‬ ‫ﻌ‬ ‫ﻀ‬ ‫ﻮ‬ ‫ﻳ‬ ‫ﺔ‬ ‫ﺑ‬ ‫ﺮ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﻣ‬ ‫ﻌ‬ ‫ﲔ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﺧ‬ ‫ﻼ‬ ‫ﻝ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺍ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺸ‬ ‫ﱰ‬ ‫ﻛ‬ ‫ﺔ‬ ‫؟‬
13 . ‫ﻣ‬ ‫ﺜ‬ ‫ﺎ‬ ‫ﻝ‬ ‫ﲝ‬ ‫ﺜ‬ ‫ﻲ‬
14 . ‫ﳎ‬ ‫ﺎ‬ ‫ﻻ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﻣ‬ ‫ﻪ‬ ‫ﻭ‬ ‫ﺗ‬ ‫ﻄ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﺗ‬ ‫ﻪ‬
- ‫ﻟ‬ ‫ﺘ‬ ‫ﻘ‬ ‫ﺴ‬ ‫ﻴ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﺇ‬ ‫ﱃ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﺍ‬ ƒ ‫ﻤ‬ ‫ﻮ‬ ‫ﻋ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﺮ‬ ‫ﻋ‬ ‫ﻴ‬ ‫ﺔ‬ . - ‫ﻛ‬ ‫ﺎ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ﺭ‬ ‫ﺗ‬ ‫ﺸ‬ ‫ﺨ‬ ‫ﻴ‬ ‫ﺼ‬ ‫ﻲ‬ ‫ﻷ‬ ‫ﻏ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺽ‬ ‫ﻃ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﺜ‬ ‫ﻞ‬ : ‫ﺗ‬ ‫ﻘ‬ ‫ﻴ‬ ‫ﻴ‬ ‫ﻢ‬ ‫ﺻ‬ ‫ﺪ‬ ‫ﻕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺪ‬ ‫ﺭ‬ ‫ﺟ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺄ‬ ‫ﺧ‬ ‫ﻮ‬ ‫ﺫ‬ ‫ﺓ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻘ‬ ‫ﻴ‬ ‫ﻴ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﻌ‬ ‫ﺮ‬ ‫ﻓ‬ ‫ﻴ‬ ‫ﺔ‬ Cognitive assessment - ‫ﻟ‬ ‫ﺘ‬ ‫ﺼ‬ ‫ﻨ‬ ‫ﻴ‬ ‫ﻒ‬ ‫ﺍ‬ ‫ﻷ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺩ‬ ‫ﺇ‬ ‫ﱃ‬ ‫ﳎ‬ ‫ﻤ‬ ‫ﻮ‬ ‫ﻋ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﻓ‬ ‫ﺮ‬ ‫ﻋ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﻋ‬ ‫ﻨ‬ ‫ﺪ‬ ‫ﻣ‬ ‫ﺎ‬ ‫ﻻ‬ ‫ﻳ‬ ‫ﻮ‬ ‫ﺟ‬ ‫ﺪ‬ ‫ﻣ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺭ‬ " ‫ﺩ‬ ‫ﺭ‬ ‫ﺟ‬ ‫ﺔ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻘ‬ ‫ﻄ‬ ‫ﻊ‬ " Cut score . - ‫ﻟ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﺪ‬ ‫ﻭ‬ ‫ﺿ‬ ‫ﺒ‬ ‫ﻂ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻐ‬ ‫ﲑ‬ ‫ﺻ‬ ‫ﺎ‬ ‫ﺩ‬ ‫ﻗ‬ ‫ﺔ‬ ‫ﺃ‬ ‫ﻭ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻴ‬ ‫ﺰ‬ ‫ﺓ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﻤ‬ ‫ﺴ‬ ‫ﺘ‬ ‫ﺠ‬ ‫ﻴ‬ ‫ﺒ‬ ‫ﲔ‬ . ‫ﳎ‬ ‫ﺎ‬ ‫ﻻ‬ ‫ﺕ‬ ‫ﺍ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺪ‬ ‫ﺍ‬ ‫ﻣ‬ ‫ﻪ‬ : ‫ﺗ‬ ‫ﻄ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﺗ‬ ‫ﻪ‬ : - ‫ﺍ‬ ‫ﻟ‬ ‫ﻄ‬ ‫ﺐ‬ ، ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻌ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻢ‬ ، ‫ﻋ‬ ‫ﻠ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻔ‬ ‫ﺲ‬ ، ‫ﻋ‬ ‫ﻠ‬ ‫ﻢ‬ ‫ﺍ‬ ‫ﻻ‬ ‫ﺟ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﻉ‬ ، ‫ﺍ‬ ‫ﻷ‬ ‫ﲝ‬ ‫ﺎ‬ ‫ﺙ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻨ‬ ‫ﻈ‬ ‫ﻴ‬ ‫ﻤ‬ ‫ﻴ‬ ‫ﺔ‬ .
15 . ‫ﻣ‬ ‫ﺎ‬ ‫ﳉ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﺪ‬ ‫؟‬ ‫؟‬
‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﻣ‬ ‫ﺘ‬ ‫ﻌ‬ ‫ﺪ‬ ‫ﺩ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺴ‬ ‫ﺘ‬ ‫ﻮ‬ ‫ﻳ‬ ‫ﺎ‬ ‫ﺕ‬ MLPA . ‫ﺍ‬ ‫ﳉ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﺪ‬ ‫ﰲ‬ ‫ﲢ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﻭ‬ ‫ﻓ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﻞ‬ ‫ﺑ‬ ‫ﻌ‬ ‫ﺪ‬ ‫ﻋ‬ ‫ﺎ‬ ‫ﻡ‬ 2010 :
16 . ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﺍ‬ ‫ﻣ‬ ‫ﺞ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺴ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺪ‬ ‫ﻣ‬ ‫ﺔ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬
Њ Latent Gold (Vermunt & Magidson, 2005). Њ Mplus (Muthén & Muthén, 2010). Њ SAS (SAS Institute, 2004). Њ R (Ross& Robert, 1993). ‫ﺍ‬ ‫ﻟ‬ ‫ﱪ‬ ‫ﺍ‬ ‫ﻣ‬ ‫ﺞ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺴ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺪ‬ ‫ﻣ‬ ‫ﺔ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻞ‬ :
17. ‫ﻣ‬ ‫ﺜ‬ ‫ﺎ‬ ‫ﻝ‬ ‫ﺗ‬ ‫ﻄ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﻘ‬ ‫ﻲ‬ Mplus
18. ‫ﺍ‬ ‫ﳌ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺟ‬ ‫ﻊ‬
‫ﺍ‬ ‫ﳌ‬ ‫ﺮ‬ ‫ﺍ‬ ‫ﺟ‬ ‫ﻊ‬ ‫ﺍ‬ ‫ﳌ‬ ‫ﺴ‬ ‫ﺘ‬ ‫ﺨ‬ ‫ﺪ‬ ‫ﻣ‬ ‫ﺔ‬ References :

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