Latent transition model for mixed variables with applications to youth’s study habits and academic achievement<sup>†</sup>
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(2) 650. Kyuhyoung Kim · Miyoung Sung · Byungtae Seo. ᄌᄌ ᆷ ᅡ ᅢᄌ ᆫᄋ ᅥ ᅵᄆ ᅩᄒ ᆼ (Latent Transition Model, LTM; Collinsᄋ ᅧ ᅪ Wugalter, 1992; Collins ᄃ ᆼ, 1991)ᄋ ᅳ ᆫᄋ ᅳ ᅵᄅ ᅥ ᆫᄌ ᅡ ᄒ ᆷᄌ ᅡ ᅢᄀ ᅨᄎ ᆼᄆ ᅳ ᅩᄒ ᆼᄋ ᅧ ᆯᄌ ᅳ ᆼᄃ ᅩ ᆫᄒ ᅡ ᆼᄌ ᅧ ᅡᄅ ᅭᄋ ᅴᄀ ᆼᄋ ᅧ ᅮᄅ ᅩᄒ ᆨᄌ ᅪ ᆼᅡ ᅡ ᆫ ᄒᄆ ᅩᄒ ᆼᄋ ᅧ ᅳᄅ ᅩᄀ ᆨᄉ ᅡ ᅵᄌ ᆷᄆ ᅥ ᅡᄃ ᅡᄀ ᆫᄎ ᅪ ᆨᄀ ᅳ ᅢᄎ ᅦᄃ ᆯᄋ ᅳ ᅵᄋ ᅥᄂ ᅳᄒ ᅡᄋ ᅱᄌ ᆸᄃ ᅵ ᆫ ᅡ ᅦᄉ ᄋ ᆨᄒ ᅩ ᅡᄂ ᆫᄌ ᅳ ᅵᅪ ᄋᄉ ᅵᄌ ᆷᄋ ᅥ ᅵᄇ ᅡᄁ ᆯᄄ ᅱ ᅢᄆ ᅡᄃ ᅡᄋ ᅥᄄ ᆫᄒ ᅥ ᅡᄋ ᅱᄌ ᆸᄃ ᅵ ᆫᄋ ᅡ ᅳᄅ ᅩᄇ ᅡᄁ ᅱᄂ ᆫᄌ ᅳ ᅵᄅ ᆯᄒ ᅳ ᆨᄅ ᅪ ᆯᄌ ᅲ ᆨᄋ ᅥ ᅳᄅ ᅩᄀ ᅨᄉ ᆫᅡ ᅡ ᆯ ᄒᄉ ᅮᄋ ᆻᄀ ᅵ ᅦᄒ ᆫᄆ ᅡ ᅩᄒ ᆼ ᅧ ᅵᄃ ᄋ ᅡ. ᄋ ᅨᄅ ᆯᄃ ᅳ ᆯᄋ ᅳ ᅥᄑ ᅢᄂ ᆯᄉ ᅥ ᆯᄆ ᅥ ᆫᄌ ᅮ ᅩᄉ ᅡᄋ ᅦᄉ ᅥᄉ ᅵᄀ ᆫᄋ ᅡ ᅵᄀ ᆼᄀ ᅧ ᅪᅡ ᆷ ᄒᄋ ᅦᄄ ᅡᄅ ᅡᄋ ᅲᄒ ᆼᄋ ᅢ ᅴᄐ ᅳᄅ ᆫᄃ ᅢ ᅳᄂ ᅡᄉ ᅡᄅ ᆷᄃ ᅡ ᆯᄋ ᅳ ᅴᄉ ᆼᄒ ᅥ ᆼᄋ ᅣ ᅵᄋ ᅥᄄ ᇂᄀ ᅥ ᅦᄇ ᅡ ᅱᄋ ᄁ ᅥᄀ ᅡᄂ ᆫᄌ ᅳ ᅵᄇ ᆫᄉ ᅮ ᆨᄒ ᅥ ᆯᄉ ᅡ ᅮᄋ ᆻᄀ ᅵ ᅩᄋ ᅵᄅ ᆯᄐ ᅳ ᆼᄒ ᅩ ᅢᄉ ᅥᄉ ᅡᄅ ᆷᄃ ᅡ ᆯᄋ ᅳ ᅴᄎ ᅱᄒ ᆼᄋ ᅣ ᅵᄋ ᅥᄄ ᇂᄀ ᅥ ᅦᄇ ᆫᄒ ᅧ ᅡᄂ ᆫᄌ ᅳ ᅵᄅ ᆯᄀ ᅳ ᅩᄅ ᅧᄒ ᅡᄋ ᅧᄉ ᅩᄇ ᅵᄌ ᅡᄃ ᆯᅳ ᅳ ᆯ ᄋᄃ ᅢᄉ ᆼ ᅡ ᅳᄅ ᄋ ᅩᅡ ᄆᄏ ᅦᄐ ᆼᄋ ᅵ ᅦᄒ ᆯᄋ ᅪ ᆼᄒ ᅭ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᄐ ᆨᄒ ᅳ ᅵ Lanzaᄋ ᅪ Collins (2008)ᄂ ᆫᄃ ᅳ ᅦᄋ ᅵᄐ ᅳᅪ ᄋᄉ ᆼᄌ ᅥ ᆨᄋ ᅥ ᆫᄋ ᅵ ᅱᄒ ᆷᄒ ᅥ ᆼᄃ ᅢ ᆼᄋ ᅩ ᅦᄀ ᆫᄒ ᅪ ᆫᄂ ᅡ ᅦ ᅡᄌ ᄀ ᅵᆯ ᅵᄆ ᄌ ᆫᄃ ᅮ ᆯᄋ ᅳ ᅦᄃ ᅢᄒ ᆫᄋ ᅡ ᆼᄃ ᅳ ᆸᄌ ᅡ ᅡᄅ ᅭᄅ ᆯᄉ ᅳ ᅡᄋ ᆼᄒ ᅭ ᅢᄃ ᅡᄉ ᆺᄀ ᅥ ᅡᄌ ᅵᄌ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄅ ᆯᄃ ᅳ ᅩᄎ ᆯᄒ ᅮ ᅢᄂ ᅢᄀ ᅩᄉ ᅵᄀ ᆫᄋ ᅡ ᅵᄌ ᅵᄂ ᆯᄄ ᅡ ᅢᄆ ᅡᄃ ᅡᄀ ᆨᄌ ᅡ ᆷᄌ ᅡ ᅢᄉ ᆼ ᅡ ᅢᄃ ᄐ ᆯᅵ ᅳ ᄋᄋ ᅥᄄ ᇂᄀ ᅥ ᅦᄇ ᆫᄒ ᅧ ᅡᄂ ᆫᄌ ᅳ ᅵᄇ ᆫᄉ ᅮ ᆨᄒ ᅥ ᅡᄋ ᆻᄃ ᅧ ᅡ. LCMᄀ ᅪ LTMᄋ ᆫᄀ ᅳ ᆫᄎ ᅪ ᆨᄀ ᅳ ᅢᄎ ᅦᄃ ᆯᄋ ᅳ ᅵᄇ ᆷᄌ ᅥ ᅮᄒ ᆼᄌ ᅧ ᅡᄅ ᅭᄋ ᆯᄄ ᅵ ᅢᄉ ᅡᄋ ᆼᄒ ᅭ ᆯᄉ ᅡ ᅮᄋ ᆻᄂ ᅵ ᆫᄆ ᅳ ᅩᄒ ᆼᄋ ᅧ ᅵᄃ ᅡ. ᄒ ᅡᄌ ᅵᄆ ᆫᄋ ᅡ ᅮᄅ ᅵᄀ ᅡᄋ ᆯᄇ ᅵ ᆫᄌ ᅡ ᆨᄋ ᅥ ᅳ ᅩᄌ ᄅ ᆸᅡ ᅥ ᄒᄂ ᆫᄌ ᅳ ᅡᄅ ᅭᄃ ᆯᄋ ᅳ ᅴᄀ ᅮᄌ ᅩᄂ ᆫᄇ ᅳ ᆷᄌ ᅥ ᅮᄒ ᆼᅧ ᅧ ᆫ ᄇᄉ ᅮᄈ ᆫᄆ ᅮ ᆫᄋ ᅡ ᅡᄂ ᅵᄅ ᅡᄋ ᆫᄉ ᅧ ᆨᄒ ᅩ ᆼ/ᄋ ᅧ ᅵᄉ ᆫᄒ ᅡ ᆼᅧ ᅧ ᆫ ᄇᄉ ᅮᄃ ᅩᄑ ᅩᄒ ᆷᄒ ᅡ ᅡᄂ ᆫᄀ ᅳ ᆼᄋ ᅧ ᅮᄀ ᅡᄆ ᆭᄃ ᅡ ᅡ. ᄋ ᅵᄅ ᅥ ᆫᄀ ᅡ ᄒ ᆼᅮ ᅧ ᄋᄋ ᅦᄇ ᆷᄌ ᅥ ᅮᄒ ᆼᄇ ᅧ ᆫᄉ ᅧ ᅮᄀ ᅡᄋ ᅡᄂ ᆫᄇ ᅵ ᆫᄉ ᅧ ᅮᄃ ᆯᅳ ᅳ ᆯ ᄋᄌ ᅦᄀ ᅥᄒ ᅡᄀ ᅥᄂ ᅡᄇ ᆷᄌ ᅥ ᅮᄒ ᅪᄒ ᅡᄋ ᅧᄋ ᇁᄉ ᅡ ᅥᄋ ᆫᄀ ᅥ ᆸᄒ ᅳ ᆫᄆ ᅡ ᅩᄒ ᆼᄋ ᅧ ᅦᄌ ᆨᄋ ᅥ ᆼᄒ ᅭ ᅡᄂ ᆫᄀ ᅳ ᆺᄋ ᅥ ᆫᄋ ᅳ ᆫᄉ ᅧ ᆨ ᅩ ᆼ/ᄋ ᅧ ᄒ ᅵᄉ ᆫᄒ ᅡ ᆼᅧ ᅧ ᆫ ᄇᄉ ᅮᄃ ᆯᄋ ᅳ ᅵᄀ ᅡᄌ ᅵᄀ ᅩᄋ ᆻᄂ ᅵ ᆫᄌ ᅳ ᆼᄇ ᅥ ᅩᄋ ᅴᄉ ᆫᄉ ᅩ ᆯᄋ ᅵ ᆯᄀ ᅳ ᅡᄌ ᅧᄋ ᆯᄉ ᅩ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᄇ ᆫᄋ ᅩ ᆫᄀ ᅧ ᅮᄋ ᅦᄉ ᅥᄂ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄌ ᆫᄋ ᅥ ᅵᄆ ᅩᄒ ᆼᄋ ᅧ ᆯᄀ ᅳ ᆨᄀ ᅡ ᆨ ᅡ ᅴᄇ ᄋ ᆫᅮ ᅧ ᄉᄃ ᆯᄋ ᅳ ᅵᄀ ᅡᄌ ᅵᄀ ᅩᄋ ᆻᄂ ᅵ ᆫᄌ ᅳ ᆼᄇ ᅥ ᅩᄃ ᆯᅳ ᅳ ᆯ ᄋᄆ ᅩᄃ ᅮᄑ ᅩᄒ ᆷᄒ ᅡ ᅡᄂ ᆫᄆ ᅳ ᅩᄒ ᆼᄋ ᅧ ᅳᄅ ᅩᄒ ᆨᄌ ᅪ ᆼᄒ ᅡ ᅡᄀ ᅩᄋ ᅵᄅ ᆯᄇ ᅳ ᅡᄐ ᆼᄋ ᅡ ᅳᄅ ᅩᄎ ᅩ·ᄌ ᆼᄉ ᅮ ᆼᄋ ᅢ ᅴᅡ ᆨ ᄒᄉ ᆸᄉ ᅳ ᆸᄀ ᅳ ᆫ ᅪ ᆾᄒ ᅵ ᄆ ᆨᅥ ᅡ ᆸ 어 ᆼ ᄉᄎ ᅱᄃ ᅩᄋ ᅴᄇ ᆫᄒ ᅧ ᅪᄎ ᅮᄋ ᅵᄅ ᆯᅮ ᅳ ᆫ ᄇᄉ ᆨᄒ ᅥ ᅡᄀ ᅩᄌ ᅡᄒ ᆫᄃ ᅡ ᅡ. ᆫ ᅩ ᅩ ᄇ ᆫ ᄂᄆ ᆫᄋ ᅮ ᅴ ᄀ ᅮᄉ ᆼᄋ ᅥ ᆫ ᄆ ᅳ ᆫᄌ ᅥ ᅥ 2ᄌ ᆼᄋ ᅡ ᅦᄉ ᅥ LCMᄀ ᅪ LTMᄋ ᆯ ᄉ ᅳ ᅩᄀ ᅢᄒ ᅡᄀ ᅩ LTMᄋ ᅦ ᄃ ᅢᄒ ᆫ ᄆ ᅡ ᅩᄉ ᅮ ᄎ ᅮᄌ ᆼ ᄇ ᅥ ᆼᄉ ᅡ ᆨᄋ ᅵ ᆯ ᄉ ᅳ ᆯᄆ ᅥ ᆼᄒ ᅧ ᆫ ᅡ ᅡ. 3ᄌ ᄃ ᆼᄋ ᅡ ᅦᄉ ᅥᄂ ᆫ LTMᄋ ᅳ ᅦᄉ ᅥᄇ ᆷᄌ ᅥ ᅮᄒ ᆼᅧ ᅧ ᆫ ᄇᄉ ᅮᄆ ᆫᄀ ᅡ ᅡᄌ ᅵᄂ ᆫᄌ ᅳ ᅡᄅ ᅭᄀ ᅡᄋ ᅡᄂ ᆫᄋ ᅵ ᅵᄉ ᆫᄒ ᅡ ᆼ, ᄋ ᅧ ᆫᄉ ᅧ ᆨᄒ ᅩ ᆼᅧ ᅧ ᆫ ᄇᄉ ᅮᄀ ᅡᄑ ᅩᄒ ᆷᄃ ᅡ ᆫᄌ ᅬ ᅡᄅ ᅭᄋ ᅦᄉ ᅥᄋ ᅴ LTMᄋ ᆯᄉ ᅳ ᆯᅧ ᅥ ᆼ ᄆᄒ ᆫᄒ ᅡ ᅮᄆ ᅩᄉ ᅮᄅ ᆯᄎ ᅳ ᅮᄌ ᆼᄒ ᅥ ᅡᄂ ᆫᄇ ᅳ ᆼᄇ ᅡ ᆸᄀ ᅥ ᅪᄌ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄋ ᅴᄀ ᅢᄉ ᅮᄅ ᆯᄉ ᅳ ᆫᅢ ᅥ ᆨ ᄐᄒ ᅢᄆ ᅩᄒ ᆼᄋ ᅧ ᆯᄉ ᅳ ᆫᅢ ᅥ ᆨ ᄐᄒ ᅡᄂ ᆫᄇ ᅳ ᆼᄇ ᅡ ᆸᄋ ᅥ ᆯᄉ ᅳ ᆯᄆ ᅥ ᆼᄒ ᅧ ᅡᄀ ᅩ 4ᄌ ᆼᄋ ᅡ ᅦᄉ ᅥᄂ ᆫᄉ ᅳ ᆯᄌ ᅵ ᅦᄃ ᅦᄋ ᅵᄐ ᅥᄅ ᆯᄌ ᅳ ᅦᄋ ᆫᅡ ᅡ ᆫ ᄒᄆ ᅩᄒ ᆼᄋ ᅧ ᆯᄉ ᅳ ᅡᄋ ᆼᄒ ᅭ ᅢᄇ ᆫᄉ ᅮ ᆨᄒ ᅥ ᆫᄃ ᅡ ᅡ. ᄆ ᅡᄌ ᅵᄆ ᆨᄋ ᅡ ᅳᄅ ᅩ 5ᄌ ᆼᄋ ᅡ ᅦᄉ ᅥᄂ ᆫᅩ ᅳ ᆫ ᄇᄋ ᆫᄀ ᅧ ᅮᄋ ᅴᄀ ᆯᄅ ᅧ ᆫᅳ ᅩ ᆯ ᄋᄉ ᅥ ᆯᄒ ᅮ ᄉ ᆫᅡ ᅡ ᄃ.. 2. 문헌 연구 2.1. 잠재범주 모형 LCMᄋ ᆫᄀ ᅳ ᆫᄎ ᅪ ᆨᄀ ᅳ ᅡᄂ ᆼᄒ ᅳ ᆫᄇ ᅡ ᆷᄌ ᅥ ᅮᄒ ᆼᄇ ᅧ ᆫᄉ ᅧ ᅮ, ᄌ ᆨᄃ ᅳ ᅡᄒ ᆼᄇ ᅡ ᆫᄑ ᅮ ᅩᄅ ᆯᄄ ᅳ ᅡᄅ ᅳᄂ ᆫᄃ ᅳ ᅡᄇ ᆫᄅ ᅧ ᆼᄇ ᅣ ᆫᄉ ᅧ ᅮᅪ ᄋᄀ ᆫᄎ ᅪ ᆨᄒ ᅳ ᆯᄉ ᅡ ᅮᄋ ᆹᄂ ᅥ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄇ ᆫᄉ ᅧ ᅮᄅ ᆯ ᅳ ᄑᄒ ᅩ ᆷᅡ ᅡ ᄒᄂ ᆫᄆ ᅳ ᅩᄒ ᆼᄋ ᅧ ᅳᄅ ᅩᄀ ᆨᄀ ᅡ ᆫᄎ ᅪ ᆨᄀ ᅳ ᅡᄂ ᆼᄒ ᅳ ᆫᄀ ᅡ ᅢᄎ ᅦᄃ ᆯᄋ ᅳ ᅵᄋ ᅥᄄ ᆫᄒ ᅥ ᅡᄋ ᅱᄇ ᆫᄑ ᅮ ᅩᄋ ᅦᄉ ᆨᄒ ᅩ ᅡᄂ ᆫᄌ ᅳ ᅵᄎ ᅮᄌ ᆼᄒ ᅥ ᆯᄉ ᅡ ᅮᄋ ᆻᄀ ᅵ ᅦᄒ ᅢᄌ ᅮᄂ ᆫᄐ ᅳ ᆼᄀ ᅩ ᅨᄌ ᆨ ᅥ ᅩᄒ ᄆ ᆼᅵ ᅧ ᄋᄃ ᅡ. ᄋ ᅵᄅ ᆯᄉ ᅳ ᆯᄆ ᅥ ᆼᄒ ᅧ ᅡᄀ ᅵᄋ ᅱᄒ ᅢᄆ ᆫᄌ ᅥ ᅥ Jᄀ ᅢᄋ ᅴᄋ ᆼᄃ ᅳ ᆸᄇ ᅡ ᆫᄉ ᅧ ᅮᄅ ᆯᄀ ᅳ ᅡᄌ ᅵᄂ ᆫ iᄇ ᅳ ᆫᄍ ᅥ ᅢᄀ ᆫᄎ ᅪ ᆨᄇ ᅳ ᆨᄐ ᅦ ᅥᄅ ᆯ Yi = (Yi1 , ..., YiJ ) ᄅ ᅳ ᅡ ᅩᄒ ᄀ ᅡᄌ ᅡ. ᄄ ᅩᄒ ᆫ, ᄋ ᅡ ᅵᄀ ᆫᄎ ᅪ ᆨᄇ ᅳ ᆨᄐ ᅦ ᅥᄀ ᅡᄉ ᆨᄒ ᅩ ᅡᄂ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄇ ᆷᄌ ᅥ ᅮᄅ ᆯᄂ ᅳ ᅡᄐ ᅡᄂ ᅢᄂ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄇ ᆫᄉ ᅧ ᅮᄅ ᆯ Li ᄅ ᅳ ᅡᄀ ᅩᄒ ᅡᄀ ᅩᄑ ᆫᄋ ᅧ ᅴᄉ ᆼ Li ᄋ ᅡ ᆫ 1ᄇ ᅳ ᅮᄐ ᅥ Cᄁ ᅡᄌ ᅵᅴ ᄋᄌ ᆼᄉ ᅥ ᅮᄀ ᆹᄋ ᅡ ᆯᄀ ᅳ ᅡᄌ ᅵᄂ ᆫᄒ ᅳ ᆨᄅ ᅪ ᆯᄇ ᅲ ᆫᄉ ᅧ ᅮᄅ ᅡᄀ ᅩᄒ ᅡᄌ ᅡ. ᄋ ᅵᄄ ᅢ Yi ᄀ ᅡ lᄇ ᆫᄍ ᅥ ᅢᄌ ᆷᄌ ᅡ ᅢᄇ ᆷᄌ ᅥ ᅮᄋ ᅦᄉ ᆨᄒ ᅩ ᆯᄒ ᅡ ᆨᄅ ᅪ ᆯᅳ ᅲ ᆯ ᄋ γl = P (Li = l)ᄋ ᅵᄅ ᅡᅩ ᄀᄒ ᅡᄆ ᆫ iᄇ ᅧ ᆫᄍ ᅥ ᅢᄀ ᆫᄎ ᅪ ᆨᄇ ᅳ ᆨᄐ ᅦ ᅥᄋ ᅴᄒ ᆨᄅ ᅪ ᆯᅮ ᅲ ᆫ ᄇᄑ ᅩᄒ ᆷᄉ ᅡ ᅮᄂ ᆫ ᅳ. P (Yi = yi ) =. C X l=1. P (Li = l)P (Yi = yi |Li = l) =. C X. γl P (Yi = yi |Li = l). (2.1). l=1. ᄅᄑ ᅩ ᅭᄒ ᆫᄒ ᅧ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ. P ᅵᅢ ᄋ ᄄᄀ ᆨᄀ ᅡ ᆫᄎ ᅪ ᆨᄀ ᅳ ᅢᄎ ᅦᄃ ᆯᄋ ᅳ ᆫᄒ ᅳ ᅡᄂ ᅡᄋ ᅴᄌ ᆷᄌ ᅡ ᅢᄇ ᆷᄌ ᅥ ᅮᄋ ᅦᄉ ᆨᄒ ᅩ ᅢᄋ ᅣᄒ ᅡᄆ ᅳᄅ ᅩ C ᆯᄆ ᅳ ᆫᄌ ᅡ ᆨᄒ ᅩ ᅡᄋ ᅧᄋ ᅣᄒ ᆫᄃ ᅡ ᅡ. ᄄ ᅩᄒ ᆫ, ᄀ ᅡ ᆨ ᅡ l=1 γl = 1ᄋ ᆼᄃ ᅳ ᄋ ᆸᄇ ᅡ ᆫᄉ ᅧ ᅮ Yij ᄂ ᆫ 1ᄇ ᅳ ᅮᄐ ᅥ Mj ᄁ ᅡᄌ ᅵᄋ ᅴᄀ ᆹᄋ ᅡ ᆯᄀ ᅳ ᅡᄌ ᆫᄃ ᅵ ᅡᄀ ᅩᄒ ᅡᄆ ᆫᄀ ᅧ ᆨᄋ ᅡ ᆼᄃ ᅳ ᆸᄇ ᅡ ᆫᄉ ᅧ ᅮᄃ ᆯᄋ ᅳ ᆫᄃ ᅳ ᅡᄒ ᆼᄇ ᅡ ᆫᄑ ᅮ ᅩᄅ ᆯᄄ ᅳ ᅡᄅ ᅳᄀ ᅦᄃ ᆫᄃ ᅬ ᅡ. ᄋ ᅵ ᅢ lᄇ ᄄ ᆫᅢ ᅥ ᄍᄒ ᅡᄋ ᅱᄇ ᆫᄑ ᅮ ᅩᄋ ᆫᄋ ᅡ ᅴ jᄇ ᆫᄍ ᅥ ᅢᄋ ᆼᄃ ᅳ ᆸᄇ ᅡ ᆫᄉ ᅧ ᅮᄀ ᅡ mᄋ ᅵᄅ ᅡᄀ ᅩᄃ ᆸᄒ ᅡ ᆯᄒ ᅡ ᆨᄅ ᅪ ᆯᅳ ᅲ ᆯ ᄋ ρjm|l = P (Yij = m|Li = l)ᄅ ᅡᄀ ᅩ PMj ᅡᄆ ᄒ ᆫᄋ ᅧ ᆼᄃ ᅳ ᆸᄇ ᅡ ᆫᄉ ᅧ ᅮᄃ ᆯᄋ ᅳ ᅵᄃ ᆸᄒ ᅡ ᆯᄉ ᅡ ᅮᄋ ᆻᄂ ᅵ ᆫᄋ ᅳ ᆼᄃ ᅳ ᆸᄋ ᅡ ᆫᄒ ᅳ ᆫᄀ ᅡ ᅡᄌ ᅵᄆ ᆫᄀ ᅡ ᅡᄂ ᆼᄒ ᅳ ᅡᄆ ᅳᄅ ᅩ ρ = 1ᄋ ᆯ ᅳ ᆫ ᅡ ᄆ ᆨ ᅩ ᄌ ᅡ ᄒ ᅧ ᄋ ᅣ ᄋ ᆫ ᅡ ᄒ ᅡ ᄃ . jm|l m=1 LCMᄋ ᅦᄉ ᅥᄂ ᆫᄇ ᅳ ᅩᄐ ᆼᄌ ᅩ ᅵᄋ ᆨᄃ ᅧ ᆨᄅ ᅩ ᆸᅥ ᅵ ᆼ ᄉᄀ ᅡᄌ ᆼ (local independence), ᄌ ᅥ ᆨ, ᄌ ᅳ ᆷᄌ ᅡ ᅢᄇ ᆷᄌ ᅥ ᅮ Li ᄀ ᅡᄌ ᅮᄋ ᅥᄌ ᆻᄋ ᅧ ᆯᄄ ᅳ ᅢᄀ ᆨᄀ ᅡ ᆫᄎ ᅪ ᆨᄇ ᅳ ᆫᄉ ᅧ ᅮ ᆯᄉ ᅳ ᄃ ᅡᅵ ᄋᄋ ᅴᄃ ᆨᄅ ᅩ ᆸᄋ ᅵ ᆯᄀ ᅳ ᅡᄌ ᆼᄒ ᅥ ᅡᄂ ᆫᄃ ᅳ ᅦ (Lazarsfeldᄋ ᅪ Henry, 1968) ᄋ ᅵᄌ ᅩᄀ ᆫᄋ ᅥ ᆯᄉ ᅳ ᅡᄋ ᆼᄒ ᅭ ᅡᄆ ᆫᄉ ᅧ ᆨ (2.1)ᄋ ᅵ ᆫᄃ ᅳ ᅡᄉ ᅵᄃ ᅡᄋ ᆷᄀ ᅳ ᅪ ᇀᄋ ᅡ ᄀ ᅵᄂ ᅡᄐ ᅡᄂ ᆯᄉ ᅢ ᅮᄋ ᆻᄃ ᅵ ᅡ..
(3) Latent transition model for mixed variable with applications to youth’s study habits and academic achievement651. P (Yi = yi ) =. C X. γl. l=1. Mj J Y Y. I(y. ρjm|lij. =m). .. j=1 m=1. 2.2. 잠재전이 모형 LTMᄋ ᆫᄀ ᅳ ᆨᄀ ᅡ ᆫᄎ ᅪ ᆨᄀ ᅳ ᅢᄎ ᅦᄀ ᅡᄋ ᅥᄂ ᅳᄒ ᆫᄉ ᅡ ᅵᄌ ᆷᄋ ᅥ ᅦᄉ ᅥᄆ ᆫᄀ ᅡ ᆫᄎ ᅪ ᆨᄃ ᅳ ᆫᄀ ᅬ ᆺᄋ ᅥ ᅵᄋ ᅡᄂ ᆫᄋ ᅵ ᅧᄅ ᅥᄉ ᅵᄌ ᆷᄋ ᅥ ᅦᄉ ᅥᄇ ᆫᄇ ᅡ ᆨᄎ ᅩ ᆨᄌ ᅳ ᆼᄃ ᅥ ᆫᄌ ᅬ ᅡᄅ ᅭ, ᄌ ᆨᄌ ᅳ ᆼ ᅩ ᆫᄒ ᅡ ᄃ ᆼᅡ ᅧ ᄌᄅ ᅭᄋ ᆯᄄ ᅵ ᅢᄉ ᅡᄋ ᆼᄒ ᅭ ᆯᄉ ᅡ ᅮᄋ ᆻᄂ ᅵ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄀ ᅨᄎ ᆼᄆ ᅳ ᅩᄒ ᆼᄋ ᅧ ᅵᄃ ᅡ. LTMᄋ ᆫ LCMᄀ ᅳ ᅪᄃ ᅡᄅ ᅳᄀ ᅦᄀ ᆫᄎ ᅪ ᆨᄀ ᅳ ᆹᄋ ᅡ ᅵᄉ ᆨᄒ ᅩ ᅡᄂ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄇ ᆷᄌ ᅥ ᅮ ᅡᄀ ᄀ ᆫᄎ ᅪ ᆨᄉ ᅳ ᅵᄌ ᆷᄋ ᅥ ᅦᄄ ᅡᄅ ᅡᄇ ᅡᄁ ᆯᄉ ᅱ ᅮᄋ ᆻᄋ ᅵ ᅳᄆ ᅳᄅ ᅩᄇ ᅩᄐ ᆼᄌ ᅩ ᆷᄌ ᅡ ᅢᄀ ᅨᄎ ᆼᄋ ᅳ ᅵᄅ ᅡᄀ ᅩᄑ ᅭᄒ ᆫᄒ ᅧ ᅡᄌ ᅵᄋ ᆭᄀ ᅡ ᅩᄌ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢ (latent status)ᄅ ᅡ ᅩᄑ ᄀ ᅭᄒ ᆫᄒ ᅧ ᆫᄃ ᅡ ᅡ. LTMᄋ ᅦᄉ ᅥ tᄉ ᅵᄌ ᆷᄋ ᅥ ᅦᄉ ᅥ Jᄀ ᅢᄋ ᅴᄋ ᆼᄃ ᅳ ᆸᄇ ᅡ ᆫᄉ ᅧ ᅮᄅ ᆯᄀ ᅳ ᅡᄌ ᅵᄂ ᆫᄀ ᅳ ᆫᄎ ᅪ ᆨᄇ ᅳ ᆨᄐ ᅦ ᅥᄅ ᆯ Yit = (Yi1t , ..., YiJt )ᄅ ᅳ ᅡᄀ ᅩᄒ ᅡ ᅡ. ᄋ ᄌ ᅵᄄ ᅢᄎ ᅥᄋ ᆷᄉ ᅳ ᅵᄌ ᆷt=1ᄇ ᅥ ᅮᄐ ᅥᄆ ᅡᄌ ᅵᄆ ᆨᄉ ᅡ ᅵᄌ ᆷt=T ᄁ ᅥ ᅡᄌ ᅵᄌ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄅ ᆯᄂ ᅳ ᅡᄐ ᅡᄂ ᅢᄂ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄇ ᆫᄉ ᅧ ᅮᄅ ᆯ L1 , ...LT ᄅ ᅳ ᅡᄀ ᅩ ᅡᄆ ᄒ ᆫ iᄇ ᅧ ᆫᄍ ᅥ ᅢᄀ ᅢᄎ ᅦᄋ ᅴᄌ ᆷᄌ ᅡ ᅢᄇ ᆫᄉ ᅧ ᅮᄃ ᆯᄋ ᅳ ᅴᄇ ᆨᄐ ᅦ ᅥᄅ ᆯ Li = (Li1 , ..., LiT )ᄅ ᅳ ᅩᄑ ᅭᄒ ᆫᄒ ᅧ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᄀ ᆨᄉ ᅡ ᅵᄌ ᆷᄆ ᅥ ᅡᄃ ᅡᄋ ᅴᄌ ᆷᄌ ᅡ ᅢᄇ ᆫᄉ ᅧ ᅮ ᅡᄎ ᄀ ᆼ Cᄀ ᅩ ᅢᄋ ᅴᅡ ᆼ ᄉᄐ ᅢᄅ ᆯᄀ ᅳ ᅡᄌ ᆯᄉ ᅵ ᅮᄋ ᆻᄃ ᅵ ᅡᄀ ᅩᄒ ᅡᄆ ᆫ, iᄇ ᅧ ᆫᄍ ᅥ ᅢᄀ ᆫᄎ ᅪ ᆨᄀ ᅳ ᅢᄎ ᅦ Yi = (Yi1 , ..., YiT )ᄋ ᅴᄒ ᆨᄅ ᅪ ᆯᅮ ᅲ ᆫ ᄇᄑ ᅩᄒ ᆷᄉ ᅡ ᅮᄂ ᆫᄃ ᅳ ᅡ ᆷᄀ ᅳ ᄋ ᅪᄀ ᇀᄋ ᅡ ᅵᄑ ᅭᄒ ᆫᄒ ᅧ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ.. P (Yi1 = yi1 , ..., YiT = yiT ) =. C X. ···. l1 =1. C X. P (Li1 = l1 , ..., LiT = lT )P (Yi1 = yi1 , ..., YiT = yiT |Li1 = l1 , ..., LiT = lT ). (2.2). lT =1. LTMᄋ ᅦᄉ ᅥᄂ ᆫᄉ ᅳ ᅵᄌ ᆷᄋ ᅥ ᅵᄀ ᆼᄀ ᅧ ᅪᅡ ᆷ ᄒᄋ ᅦᄄ ᅡᄅ ᅡᄀ ᆫᄎ ᅪ ᆨᄀ ᅳ ᅢᄎ ᅦᄃ ᆯᄋ ᅳ ᅴᄌ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄋ ᅴᄌ ᆫᄋ ᅥ ᅵᄒ ᆨᄅ ᅪ ᆯᄃ ᅲ ᆯᄋ ᅳ ᅵ 1ᄎ ᅡ Markov Chainᄋ ᆯᄋ ᅳ ᅵ ᆫᄃ ᅮ ᄅ ᅡᄀ ᅩᄀ ᅡᄌ ᆼᄒ ᅥ ᅡᄂ ᆫᄃ ᅳ ᅦᄋ ᅵᄅ ᅥᄒ ᆫᄀ ᅡ ᅡᄌ ᆼᄒ ᅥ ᅡᄋ ᅦᄉ ᅥ Li ᄋ ᅴᄀ ᆯᄒ ᅧ ᆸᄒ ᅡ ᆨᄅ ᅪ ᆯᄋ ᅲ ᆫ ᅳ. P (L1 = l1 , ..., LT = lT ) = P (L1 = l1 ). T Y. P (Lt = lt |Lt−1 = lt−1 ) = δl1. T Y. τlt |lt−1. t=2. t=2. ᄋᄅ ᅳ ᅩᅭ ᄑᄒ ᆫᄒ ᅧ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᄃ ᆫ, ᄋ ᅡ ᅧᄀ ᅵᄉ ᅥ δlt = P (Lt = lt )ᄋ ᅵᄀ ᅩ τlt |lt −1 = P (Lt = lt |Lt−1 = lt−1 )ᄋ ᅵᄃ ᅡ. ᄋ ᅵᄅ ᆯ ᅳ ᆼᄒ ᅩ ᄐ ᅢᄉ ᆨ (2.2)ᄂ ᅵ ᆫ ᅳ. P (Yi1 = yi1 , ..., YiT = yiT ) =. X 1≤l1 ,...,lT ≤C. δl1. T Y. ! τlt |lt−1 P (Yi1 = yi1 , ..., YiT = yiT |Li1 = l1 , ..., LiT = lT ). (2.3). t=2. ᄅᄑ ᅩ ᅭᄒ ᆫᄒ ᅧ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᄋ ᅵᄄ ᅢ, LCMᄀ ᅪᄆ ᅡᄎ ᆫᄀ ᅡ ᅡᄌ ᅵᄅ ᅩᄀ ᆨᄉ ᅡ ᅵᄌ ᆷᄋ ᅥ ᅦᄉ ᅥᄀ ᆫᄎ ᅪ ᆨᄀ ᅳ ᅢᄎ ᅦᄃ ᆯᄋ ᅳ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄃ ᆯᄌ ᅳ ᆼᄋ ᅮ ᅦᄒ ᆫᄀ ᅡ ᅢᄋ ᅴᄌ ᆷ ᅡ P = 1ᄋ ᆯ ᅳ ᆫ ᅡ ᄆ ᆨ ᅩ ᄌ ᅡ ᄒ ᅧ ᄋ ᅣ ᄋ ᅡ ᄒ ᅧ ᄆ ᅵ ᄉ ᆷ ᅥ ᄌ tᄋ ᅦ ᅥ ᄉ ᆷ ᅡ ᄌ ᅢ ᄌ ᆼ ᅡ ᄉ ᅢ ᄐ ᅡ ᄀ l ᆫ ᅵ ᄋ iᄇ ᆫ ᅥ ᅢ ᄍ ᅢ ᄀ ᅦ ᄎ ᅢᄉ ᄌ ᆼᅢ ᅡ ᄐᄋ ᅦᄉ ᆨᄒ ᅩ ᅢᄋ ᅣᄒ ᅡᄀ ᅵᄄ ᅢᄆ ᆫᄋ ᅮ ᅦ C δ t l t lt =1 ᅴ jᄇ ᄋ ᆫᄍ ᅥ ᅢᄋ ᆼᄃ ᅳ ᆸᄇ ᅡ ᆫᄉ ᅧ ᅮᄀ ᅡ mᄋ ᅵᄅ ᅡᄀ ᅩᄃ ᆸᅡ ᅡ ᆯ ᄒᄒ ᆨᄅ ᅪ ᆯᅳ ᅲ ᆯ ᄋ ρjmt|lt = P (Yijt = m|Lt = lt )ᄅ ᅡᄀ ᅩᄒ ᅡᄆ ᆫᄌ ᅧ ᅵᄋ ᆨᄃ ᅧ ᆨᄅ ᅩ ᆸᅥ ᅵ ᆼ ᄉᄀ ᅡᄌ ᆼ ᅥ ᅡᄋ ᄒ ᅦᅥ ᄉᄉ ᆨ (2.3)ᄋ ᅵ ᆫᄃ ᅳ ᅡᄉ ᅵᄃ ᅡᄋ ᆷᄀ ᅳ ᅪᄀ ᇀᄋ ᅡ ᅵᄂ ᅡᄐ ᅡᄂ ᆯᄉ ᅢ ᅮᄋ ᆻᄃ ᅵ ᅡ.. P (Yi1 = yi1 , ..., YiT = yiT ) =. X 1≤l1 ,...,lT ≤C. Mj Y T T Y J Y Y I(yijt =m) δl1 τlt |lt−1 × ρjmt|lt . t=2. t=1 j=1 m=1. (2.4).
(4) 652. Kyuhyoung Kim · Miyoung Sung · Byungtae Seo. LTMᄋ ᅦᄉ ᅥᄂ ᆫ ᄇ ᅳ ᅩᄐ ᆼ ᄀ ᅩ ᆨ ᄉ ᅡ ᅵᄌ ᆷᄋ ᅥ ᅦᄉ ᅥ ᄌ ᆫᄌ ᅩ ᅢᄒ ᅡᄂ ᆫ ᄌ ᅳ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄃ ᆯᄋ ᅳ ᅴ ᄀ ᅢᄉ ᅮᄂ ᆫ ᄀ ᅳ ᇀᄃ ᅡ ᅡᄂ ᆫ ᄌ ᅳ ᅦᄋ ᆨ ᄀ ᅣ ᅳᄅ ᅵᄀ ᅩ ᄀ ᆨ ᄉ ᅡ ᅵᄌ ᆷᄃ ᅥ ᆯᄋ ᅳ ᅦᄉ ᅥᄋ ᅴ ᆨᄌ ᅡ ᄀ ᆷᅢ ᅡ ᄌᄉ ᆼᄐ ᅡ ᅢᄃ ᆯᄋ ᅳ ᅴᅡ ᆼ ᄒᄆ ᆨ-ᄋ ᅩ ᆼᄃ ᅳ ᆸᄒ ᅡ ᆨᄅ ᅪ ᆯᄀ ᅲ ᆹᄋ ᅡ ᅵᄃ ᆼᄋ ᅩ ᅵ ᆯᄒ ᅡᄃ ᅡᄂ ᆫᄌ ᅳ ᅦᄋ ᆨ, ᄌ ᅣ ᆨ, ᄌ ᅳ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢ lt ᄀ ᅡᄌ ᅮᄋ ᅥᄌ ᆻᄋ ᅧ ᆯᄄ ᅳ ᅢ, ᄆ ᅩᄃ ᆫ tᄋ ᅳ ᅦᄃ ᅢᄒ ᅢᄉ ᅥ ρjm|lt = ρjmt|lt ᄋ ᆯᄆ ᅳ ᆫᄌ ᅡ ᆨᄒ ᅩ ᆫᄃ ᅡ ᅡᄂ ᆫᄌ ᅳ ᅦᄋ ᆨᄋ ᅣ ᆯᄃ ᅳ ᆫᄃ ᅮ ᅡ. ᄋ ᅵᄅ ᆫᄌ ᅥ ᅦᄋ ᆨᄋ ᅣ ᆯᄃ ᅳ ᅮᄂ ᆫᄋ ᅳ ᅵᄋ ᅲᄂ ᆫᄎ ᅳ ᆺᅥ ᅥ ᆫ ᄇᄍ ᅢᄅ ᅩᄉ ᅵᄌ ᆷᄋ ᅥ ᅵᄌ ᅵᄂ ᆯᄉ ᅡ ᅮᄅ ᆨᄌ ᅩ ᆷᄌ ᅡ ᅢ ᆫᄉ ᅧ ᄇ ᅮᅳ ᆯ ᄃᄋ ᅴᄀ ᅢᄉ ᅮᄀ ᅡᄃ ᆯᄅ ᅡ ᅡᄌ ᅵᄀ ᅩ ρjmt|lt ᄅ ᆯᄆ ᅳ ᅩᄃ ᅮᄎ ᅮᄌ ᆼᄒ ᅥ ᅢᄋ ᅣᄒ ᆫᄃ ᅡ ᅡᄆ ᆫᄆ ᅧ ᅩᄉ ᅮᄃ ᆯᄋ ᅳ ᅴᄉ ᅮᄀ ᅡᄂ ᅥᄆ ᅮᄆ ᆭᄋ ᅡ ᅡᄌ ᅧᄋ ᆫᄌ ᅡ ᆼᄌ ᅥ ᆨᄋ ᅥ ᆫᄎ ᅵ ᅮᄌ ᆼᄋ ᅥ ᆯ ᅳ ᆯᄉ ᅡ ᄒ ᅮᅡ ᄀᄋ ᆹᄃ ᅥ ᅡ. ᄀ ᅳᄅ ᅵᄀ ᅩᄃ ᅮᄇ ᆫᄍ ᅥ ᅢᄅ ᅩᄆ ᅩᄒ ᆼᄒ ᅧ ᅢᄉ ᆨᄋ ᅥ ᅦᄋ ᆻᄋ ᅵ ᅥᄉ ᅥᄒ ᆼᄆ ᅡ ᆨ-ᄋ ᅩ ᆼᄃ ᅳ ᆸᄒ ᅡ ᆨᄅ ᅪ ᆯᄀ ᅲ ᆹᄋ ᅡ ᆫᄀ ᅳ ᆨᄌ ᅡ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄅ ᆯᄐ ᅳ ᆨᄌ ᅳ ᆼᄋ ᅵ ᆯᄉ ᅳ ᆯᅧ ᅥ ᆼ ᄆᄒ ᅢ ᅮᄂ ᄌ ᆫᅡ ᅳ ᆹ ᄀᄋ ᆫᄃ ᅵ ᅦᄉ ᅵᄌ ᆷᄋ ᅥ ᅵᄇ ᆫᄒ ᅧ ᆯᄄ ᅡ ᅢᄆ ᅡᄃ ᅡᄀ ᆨᄌ ᅡ ᆷᄌ ᅡ ᅢᄇ ᆫᄉ ᅧ ᅮᄅ ᆯᄉ ᅳ ᆯᅧ ᅥ ᆼ ᄆᄒ ᅢᄌ ᅮᄂ ᆫᄀ ᅳ ᆹᄋ ᅡ ᅵᄃ ᆯᄅ ᅡ ᅡᄌ ᆫᄃ ᅵ ᅡᄆ ᆫᄆ ᅧ ᅩᄒ ᆼᄒ ᅧ ᅢᄉ ᆨᄋ ᅥ ᅦᄋ ᅥᄅ ᅧᄋ ᆷᅳ ᅮ ᆯ ᄋᄀ ᆽᄀ ᅡ ᅵ ᅢᄆ ᄄ ᆫᅵ ᅮ ᄋᄃ ᅡ. 2.3. LTM의 추정 LTMᄋ ᅦᄉ ᅥ ᄎ ᅮᄌ ᆼᄒ ᅥ ᅢᄋ ᅣ ᄒ ᆯ ᄆ ᅡ ᅩᄉ ᅮᄂ ᆫ ᄎ ᅳ ᆺ ᄇ ᅥ ᆫᄍ ᅥ ᅢ ᄎ ᆨᄌ ᅳ ᆼᄃ ᅥ ᆫ ᄉ ᅬ ᅵᄌ ᆷᄋ ᅥ ᅦᄉ ᅥ ᄌ ᆷᄌ ᅡ ᅢᄇ ᆫᄉ ᅧ ᅮ L1 ᄋ ᅵ ᄉ ᆼᄐ ᅡ ᅢ l1 ᄋ ᅦ ᄉ ᆨᄒ ᅩ ᆯ ᄒ ᅡ ᆨᄅ ᅪ ᆯ δl1 , ᅲ t − 1ᄉ ᅵᄌ ᆷᄋ ᅥ ᅦᄎ ᆨᄌ ᅳ ᆼᄃ ᅥ ᅬᄋ ᆻᄋ ᅥ ᆯᄄ ᅳ ᅢᄌ ᆷᄌ ᅡ ᅢᄇ ᆫᄉ ᅧ ᅮ Lt−1 ᄋ ᅵ lt−1 ᄋ ᆯᄄ ᅵ ᅢᄃ ᅡᄋ ᆷᄉ ᅳ ᅵᄌ ᆷᄋ ᅥ ᆫ tᄉ ᅵ ᅵᄌ ᆷᄋ ᅥ ᅦᄉ ᅥᄎ ᆨᄌ ᅳ ᆼᄃ ᅥ ᅬᄋ ᆻᄋ ᅥ ᆯᄄ ᅳ ᅢᄌ ᆷᄌ ᅡ ᅢᄇ ᆫᄉ ᅧ ᅮ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢ lt ᄀ ᅡᄌ ᅮᄋ ᅥᄌ ᆻᄋ ᅧ ᆯᄄ ᅳ ᅢᄇ ᆷᄌ ᅥ ᅮᄒ ᆼᄀ ᅧ ᆫᄎ ᅪ ᆯᄇ ᅡ ᆫᄉ ᅧ ᅮ jᄀ ᅡ mᄋ ᅵᄅ ᅡᄀ ᅩᄋ ᆼᄃ ᅳ ᆸᄒ ᅡ ᆯᄒ ᅡ ᆨᄅ ᅪ ᆯ ρjm|lt ᄋ ᅲ ᅵ Lt ᄀ ᅡ lt ᄋ ᆯᄒ ᅵ ᆨᄅ ᅪ ᆯ τlt |lt−1 , ᄌ ᅲ ᅡ. ᄎ ᄃ ᅮᄌ ᆼᄇ ᅥ ᆼᄇ ᅡ ᆸᄋ ᅥ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄆ ᅩᄒ ᆼᄋ ᅧ ᅦᄉ ᅥᄌ ᅮᄅ ᅩᄉ ᅡᄋ ᆼᄒ ᅭ ᅡᄂ ᆫ EM ᄋ ᅳ ᆯᄀ ᅡ ᅩᄅ ᅵᄌ ᆷ (Expectation Maximization Algorithm; ᅳ Dempster ᄃ ᆼ, 1977)ᄋ ᅳ ᆯᄉ ᅳ ᅡᄋ ᆼᄒ ᅭ ᅡᄂ ᆫᄃ ᅳ ᅦ EM ᄋ ᆯᄀ ᅡ ᅩᄅ ᅵᄌ ᆷᄋ ᅳ ᆯᄉ ᅳ ᅡᄋ ᆼᄒ ᅭ ᅡᄀ ᅵᄋ ᅱᄒ ᅢᄉ ᅥᄂ ᆫᄆ ᅳ ᆫᄌ ᅥ ᅥᄀ ᆫᄎ ᅪ ᆨᄇ ᅳ ᆫᄉ ᅧ ᅮᄋ ᅪᄌ ᆷᄌ ᅡ ᅢᄇ ᆫᄉ ᅧ ᅮᄀ ᆫᄋ ᅡ ᅴ ᆯᄒ ᅧ ᄀ ᆸᆯ ᅡ ᅵᄃ ᄆ ᅩᄒ ᆨᄅ ᅪ ᆯᄋ ᅲ ᆯᄀ ᅳ ᅮᄒ ᅢᄋ ᅣᄒ ᆫᄃ ᅡ ᅡ. ᄌ ᆷᄌ ᅡ ᅢᄇ ᆫᄉ ᅧ ᅮ Lᄋ ᆫᄀ ᅳ ᆨᄎ ᅡ ᆨᄌ ᅳ ᆼᄉ ᅥ ᅵᄌ ᆷᄋ ᅥ ᅦᄉ ᅥᄌ ᆷᄌ ᅡ ᅢᄇ ᆫᄉ ᅧ ᅮᄃ ᆯᄋ ᅳ ᅵᄀ ᆽᄂ ᅡ ᆫᄇ ᅳ ᆷᄌ ᅥ ᅮᄃ ᆯᄋ ᅳ ᅴᄇ ᆨᄐ ᅦ ᅥᄅ ᅡᄀ ᅩ ᅡᄆ ᄒ ᆫᄀ ᅧ ᆨᄇ ᅡ ᆨᄐ ᅦ ᅥᄋ ᅴᄉ ᆼᄇ ᅥ ᆫᄃ ᅮ ᆯᄋ ᅳ ᆫ 1ᄇ ᅳ ᅮᄐ ᅥ Cᄁ ᅡᄌ ᅵᄋ ᅴᄀ ᆹᄋ ᅡ ᆯᄀ ᅳ ᅡᄌ ᆯᄉ ᅵ ᅮᄋ ᆻᄃ ᅵ ᅡ. l = (l1 , . . . , lT )ᄅ ᅡᄀ ᅩᄒ ᅡᄆ ᆫ (2.4)ᄋ ᅧ ᅴᄉ ᆨᄋ ᅵ ᆯᄉ ᅳ ᅡ ᆼᄒ ᅭ ᄋ ᅡᄋ ᅧ Yi ᄋ ᅪ Li ᄋ ᅴᄀ ᆯᄒ ᅧ ᆸᄆ ᅡ ᆯᄃ ᅵ ᅩᄒ ᆷᄉ ᅡ ᅮᄂ ᆫ ᅳ P (Yi = yi , Li = l) =. T Y. . Y. δl1. 1≤l1 ,...,lT ≤C. . τlt |lt−1 ×. Mj T Y J Y Y. t=2. I(Li =l) I(y. ρjm|lijtt. =m). . t=1 j=1 m=1. ᅪᄀ ᄋ ᇀᅵ ᅡ ᄋᄑ ᅭᄒ ᆫᄒ ᅧ ᆯᄉ ᅡ ᅮᄋ ᆻᄀ ᅵ ᅩ (Y1 , L1 ), . . . , (Yn , Ln )ᄋ ᅵᄌ ᅮᄋ ᅥᄌ ᆻᄋ ᅧ ᆯᄄ ᅳ ᅢᄋ ᅴᄅ ᅩᄀ ᅳᄀ ᅡᄂ ᆼᄃ ᅳ ᅩᄒ ᆷᄉ ᅡ ᅮ ℓ(θ|Y, L)ᄂ ᆫ ᅳ. ℓ(θ|Y, L) =. n X. . Mj T T Y J Y Y Y I(yijt =m) I(Li = l) log δl1 τlt |lt−1 × ρjm|lt. X. i=1 1≤l1 ,...,lT ≤C. t=2. (2.5). t=1 j=1 m=1. ᄋᄅ ᅳ ᅩᅭ ᄑᄒ ᆫᄒ ᅧ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᄋ ᅵᄄ ᅢ, ᄌ ᆷᄌ ᅡ ᅢᄇ ᆫᄉ ᅧ ᅮ Li ᄂ ᆫᄀ ᅳ ᆫᄎ ᅪ ᆨᄒ ᅳ ᆯᄉ ᅡ ᅮᄋ ᆹᄂ ᅥ ᆫᄇ ᅳ ᆫᄉ ᅧ ᅮᄋ ᅵᄆ ᅳᄅ ᅩᅬ ᄎᄃ ᅢᄋ ᅮᄃ ᅩᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯᄀ ᅳ ᅮᄒ ᅡᄀ ᅵᄋ ᅱᄒ ᅢ ᅡᄋ ᄃ ᆷᅴ ᅳ ᄋ EM ᄋ ᆯᄀ ᅡ ᅩᄅ ᅵᄌ ᆷᅳ ᅳ ᆯ ᄋᄋ ᅵᄋ ᆼᄒ ᅭ ᆫᄃ ᅡ ᅡ. [E-Step] E-stepᄋ ᅦᄉ ᅥᄂ ᆫ ᄆ ᅳ ᅩᄉ ᅮᄃ ᆯᄋ ᅳ ᅴ ᄎ ᅩᄀ ᅵᄀ ᆹᄀ ᅡ ᅪ ᄀ ᆫᄎ ᅪ ᆨᄒ ᅳ ᆯ ᄉ ᅡ ᅮ ᄋ ᆻᄂ ᅵ ᆫ ᄇ ᅳ ᆫᄉ ᅧ ᅮᄃ ᆯᄋ ᅳ ᅵ ᄌ ᅮᄋ ᅥᄌ ᆻᄋ ᅧ ᆯ ᄄ ᅳ ᅢ ᄀ ᆫᄎ ᅪ ᆨ ᅮ ᅳ ᆯ ᄇᄀ ᅡᄂ ᆼᄒ ᅳ ᆫ ᄌ ᅡ ᆷᄌ ᅡ ᅢᄇ ᆫᄉ ᅧ ᅮ ᆯᄀ ᅳ ᄃ ᅪ ᄀ ᆫᄎ ᅪ ᆨ ᄀ ᅳ ᅢᄎ ᅦᄃ ᆯᄋ ᅳ ᅴ ᄀ ᆯᄒ ᅧ ᆸ ᄇ ᅡ ᆫᄑ ᅮ ᅩᄋ ᅴ ᄅ ᅩᄀ ᅳ ᄀ ᅡᄂ ᆼᄃ ᅳ ᅩ ᄒ ᆷᄉ ᅡ ᅮᄋ ᅴ ᄀ ᅵᄃ ᆺᄀ ᅢ ᆹᄋ ᅡ ᆯ ᄀ ᅳ ᅮᄒ ᅡᄂ ᆫ ᄃ ᅳ ᆫᄀ ᅡ ᅨᄋ ᅵᄃ ᅡ. θᄀ ᅡ ᄋ ᅮᄅ ᅵᄀ ᅡ ᄎ ᆽ ᅡ ᅡᄋ ᄋ ᅣ ᅡ ᄒᄂ ᆫ ᄆ ᅳ ᅩᄉ ᅮᄃ ᆯᄋ ᅳ ᅴ ᄇ ᆨᄐ ᅦ ᅥᄅ ᅡᄀ ᅩ ᄒ ᅡᄀ ᅩ θ′ ᄋ ᆯ ᄋ ᅳ ᅵᄌ ᆫ ᄉ ᅥ ᅵᄒ ᆼ ᄃ ᅢ ᆫᄀ ᅡ ᅨᄋ ᅦᄉ ᅥ ᄎ ᆽᄋ ᅡ ᆫ ᄆ ᅳ ᅩᄉ ᅮ ᄇ ᆨᄐ ᅦ ᅥᄅ ᅡᄀ ᅩ ᄒ ᅡᄀ ᅩ Q(θ|θ ′ ) = E(l(θ|Y, Y)|Y, θ ′ )ᄅ ᅡᄀ ᅩ ᄌ ᆼᄋ ᅥ ᅴᄒ ᅡᄌ ᅡ. ᄉ ᆨ (2.5)ᄋ ᅵ ᅴ ᄌ ᅩᄀ ᆫᄇ ᅥ ᅮ ᄀ ᅵᄃ ᆺᄀ ᅢ ᆹᄋ ᅡ ᆯ ᄀ ᅳ ᅮᄒ ᅡᄀ ᅵ ᄋ ᅱᄒ ᅢ ᄆ ᆫᄌ ᅥ ᅥ Zˆil = E(I(Li = ′ ′ l)|Y, θ ) = P (Li = l|Yi = yi , θ )ᄋ ᆯᄀ ᅳ ᅨᄉ ᆫᄒ ᅡ ᅡᄆ ᆫᄃ ᅧ ᅡᄋ ᆷᄀ ᅳ ᅪᄀ ᇀᄃ ᅡ ᅡ. Mj T T Y J Y Y Y I(y =m) δl1 τlt |lt−1 × ρjm|lijtt t=2. Zˆil = X 1≤l1 ,...,lT ≤C. t=1 j=1 m=1. . Mj Y T T Y J Y Y I(yijt =m) δl 1 τlt |lt−1 × ρjm|lt t=2. t=1 j=1 m=1.
(5) Latent transition model for mixed variable with applications to youth’s study habits and academic achievement653. ᅵᄅ ᄋ ᆯᅵ ᅳ ᄋᄋ ᆼᄒ ᅭ ᅡᄆ ᆫ Q(θ|θ ′ )ᄂ ᅧ ᆫ ᅳ. Q(θ|θ ′ ) =. n X. X. Zˆil log(δl1 ) +. i=1 1≤l1 ,...,lT ≤C. T X. log(τlt |lt−1 ) +. t=2. Mj T X J X X. I(yijt = m) log(ρjm|lt ). t=1 j=1 m=1. ᅩᄀ ᄅ ᅨᄉ ᆫᄒ ᅡ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ. [M-step] ᅡᄋ ᄃ ᆷ ᄃ ᅳ ᆫᄀ ᅡ ᅨᄋ ᆫ M-stepᄋ ᅵ ᅦᄉ ᅥᄂ ᆫ E-stepᄋ ᅳ ᅦᄉ ᅥ ᄀ ᅮᄒ ᆫ Qᄅ ᅡ ᆯ ᄎ ᅳ ᅬᄃ ᅢᄒ ᅪᄉ ᅵᄏ ᅵᄂ ᆫ ᄆ ᅳ ᅩᄉ ᅮᄅ ᅩ ᄋ ᆸᄃ ᅥ ᅦᄋ ᅵᄐ ᅳᄒ ᅡᄂ ᆫ ᄀ ᅳ ᅪᄌ ᆼᄋ ᅥ ᅵᄃ ᅡ. ′ ′ Q(θ|θ )ᄅ ᆯ ᄀ ᅳ ᆨᄀ ᅡ ᆨᄋ ᅡ ᅴ ᄆ ᅩᄉ ᅮᄀ ᆹᄃ ᅡ ᆯᄅ ᅳ ᅩ ᄑ ᆫᄆ ᅧ ᅵᄇ ᆫᄒ ᅮ ᅡᄋ ᅧ Q(θ|θ )ᄅ ᆯ ᄎ ᅳ ᅬᄃ ᅢᄒ ᅪᄉ ᅵᄏ ᅵᄂ ᆫ ᄆ ᅳ ᅩᄉ ᅮᄅ ᆯ ᄎ ᅳ ᆽᄂ ᅡ ᆫᄃ ᅳ ᅡ. ᄃ ᅡᄋ ᆷ ᄀ ᅳ ᅪᄌ ᆼᄋ ᅥ ᆯ ᄀ ᅳ ᅥᄎ ᅧ ᆸᄃ ᅥ ᄋ ᅦᄋ ᅵᄐ ᅳᄉ ᅵᄏ ᆯᄆ ᅵ ᅩᄉ ᅮᄋ ᅴᄀ ᆹᄋ ᅡ ᆫᄃ ᅳ ᅡᄋ ᆷᄀ ᅳ ᅪᄀ ᇀᄃ ᅡ ᅡ. n X C X. δˆl1 =. ···. i=1 l2 =1. C X lT =1. n. n X C X. Zˆil ,. τˆlt |lt−1 =. C X. ···. i=1 l1 =1 n X C X. ρˆjm|l =. t=1 i=1 l1 =1. ···. C X. C X. lt−1 =1 lt+1 =1. T X n X C X t=1 i=1 l1 =1. ···. C X. ···. ···. lt−2 =1 lt+1 =1 C C X X. ···. i=1 l1 =1. T X n X C X. C X. lt−2 =1 lt =1. C X. lt−1 =1 lt+1 =1. Zˆil. lT =1 C X. ,. Zˆil. lT =1. Zˆil I(yijt = m). lT =1 C X. ···. C X. ···. C X. . Zˆil. lT =1. ᅵᄅ ᄋ ᅥᄒ ᆫ E-stepᄋ ᅡ ᅪ M-stepᄋ ᆯᄋ ᅳ ᅮᄃ ᅩᄒ ᆷᄉ ᅡ ᅮᄀ ᅡᄉ ᅮᄅ ᆷᄒ ᅧ ᆯᄄ ᅡ ᅢᄁ ᅡᄌ ᅵᄇ ᆫᄇ ᅡ ᆨᄒ ᅩ ᅡᄋ ᅧ LTMᄋ ᅴᄆ ᅩᄉ ᅮᄋ ᅴ MLEᄅ ᆯᄀ ᅳ ᅮᄒ ᆫᄃ ᅡ ᅡ.. 3. 혼합변수를 포함하는 잠재전이 모형 3.1. 모형 ᇁᄋ ᅡ ᄋ ᅦᄉ ᅥᄉ ᅩᄀ ᅢᄒ ᆫ LCMᄀ ᅡ ᅪ LTMᄋ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄇ ᆫᄉ ᅧ ᅮᄀ ᅡᄌ ᅮᄋ ᅥᄌ ᆻᄋ ᅧ ᆯᄄ ᅳ ᅢᄋ ᅴᄇ ᆫᄑ ᅮ ᅩᄅ ᆯᄀ ᅳ ᆨᄀ ᅡ ᅵᄃ ᅡᄅ ᆫᄃ ᅳ ᅡᄒ ᆼᄇ ᅡ ᆫᄑ ᅮ ᅩᄅ ᆯᄄ ᅳ ᅡᄅ ᅳᄂ ᆫᄀ ᅳ ᆺᄋ ᅥ ᅳ ᄅᄀ ᅩ ᅡᄌ ᆼᅢ ᅥ ᆻ ᄒᄌ ᅵᄆ ᆫᅡ ᅡ ᆫ ᄆᄋ ᆨᄃ ᅣ ᅦᄋ ᅵᄐ ᅥᄋ ᅦᄇ ᆷᄌ ᅥ ᅮᄒ ᆼᅧ ᅧ ᆫ ᄇᄉ ᅮᄈ ᆫᄆ ᅮ ᆫᄋ ᅡ ᅵᄋ ᅡᄂ ᅵᄅ ᅡᄋ ᅵᄉ ᆫᄒ ᅡ ᆼᅧ ᅧ ᆫ ᄇᄉ ᅮᄄ ᅩᄂ ᆫᄋ ᅳ ᆫᄉ ᅧ ᆨᄒ ᅩ ᆼᅧ ᅧ ᆫ ᄇᄉ ᅮᄀ ᅡᄌ ᆫᄌ ᅩ ᅢᄒ ᆯᄄ ᅡ ᅢᄂ ᆫ ᅳ ᇁᄉ ᅡ ᄋ ᅥᄉ ᆯᅧ ᅥ ᆼ ᄆᄒ ᆫ LCMᄀ ᅡ ᅪ LTMᄋ ᆯᄉ ᅳ ᅡᄋ ᆼᄒ ᅭ ᅡᄋ ᅧᄒ ᆨᄅ ᅪ ᆯᄆ ᅲ ᅩᄒ ᆼᄋ ᅧ ᆯᄆ ᅳ ᆫᄃ ᅡ ᆯᄉ ᅳ ᅮᄋ ᆹᄃ ᅥ ᅡ. ᄋ ᅵᄅ ᆯᄒ ᅳ ᅢᄀ ᆯᄒ ᅧ ᅡᄀ ᅵᄋ ᅱᅡ ᆫ ᄒᄀ ᅡᄌ ᆼᄀ ᅡ ᆫᅡ ᅡ ᆫ 다 ᆫ ᄒᄇ ᆼᄇ ᅡ ᆸ ᅥ ᅳᄅ ᄋ ᅩᄂ ᆫᄋ ᅳ ᅵᄅ ᅥᄒ ᆫᄋ ᅡ ᅵᄉ ᆫᄒ ᅡ ᆼᄒ ᅧ ᆨᄋ ᅩ ᆫᄋ ᅳ ᆫᄉ ᅧ ᆨᄒ ᅩ ᆼᅧ ᅧ ᆫ ᄇᄉ ᅮᄅ ᆯᄇ ᅳ ᆷᄌ ᅥ ᅮᄒ ᅪᄉ ᅵᄏ ᅧᄇ ᆫᄉ ᅮ ᆨᄒ ᅥ ᆯᄉ ᅡ ᅮᄋ ᆻᄂ ᅵ ᆫᄃ ᅳ ᅦᄋ ᅵᄂ ᆫᄋ ᅳ ᅵᄉ ᆫᄒ ᅡ ᆼᅧ ᅧ ᆫ ᄇᄉ ᅮᄂ ᅡᄋ ᆫᄉ ᅧ ᆨᄒ ᅩ ᆼᅧ ᅧ ᆫ ᄇ ᅮᄀ ᄉ ᅡᅥ ᆷ ᄇᄌ ᅮᄒ ᅪᄃ ᅬᄆ ᆫᄉ ᅧ ᅥᄉ ᆼᄀ ᅢ ᅵᄂ ᆫᄌ ᅳ ᆼᄇ ᅥ ᅩᄋ ᅴᄉ ᆫᄉ ᅩ ᆯᄋ ᅵ ᆯᄎ ᅳ ᅩᄅ ᅢᄒ ᆫᄃ ᅡ ᅡ. Everitt (1988, 1993)ᄂ ᆫᄇ ᅳ ᆷᄌ ᅥ ᅮᄒ ᆼᅧ ᅧ ᆫ ᄇᄉ ᅮᄆ ᆫᄌ ᅡ ᆫᄌ ᅩ ᅢᄒ ᅡᄂ ᆫ ᅳ ᆯᄇ ᅵ ᄋ ᆫᅥ ᅡ ᆨ ᄌᄋ ᆫ LCMᄋ ᅵ ᅦᄉ ᅥᄒ ᆨᄌ ᅪ ᆼᄒ ᅡ ᅡᄋ ᅧᄋ ᅵᄉ ᆫᄒ ᅡ ᆼ, ᄋ ᅧ ᆫᄉ ᅧ ᆨᄒ ᅩ ᆼᄇ ᅧ ᆫᄑ ᅮ ᅩᄅ ᆯᄄ ᅳ ᅡᄅ ᅳᄂ ᆫᄀ ᅳ ᆫᄎ ᅪ ᆯᄇ ᅡ ᆫᄉ ᅧ ᅮᄅ ᆯᄑ ᅳ ᅩᄒ ᆷᄒ ᅡ ᅡᄂ ᆫᄃ ᅳ ᅦᄋ ᅵᄐ ᅥᄋ ᅦᄉ ᅥᄀ ᆫᄌ ᅮ ᆸᄒ ᅵ ᅪ ᆯᄀ ᅳ ᄅ ᅩᅧ ᄅᄒ ᅡᄋ ᆻᄀ ᅧ ᅩ, ᄋ ᅵᄅ ᆯᄇ ᅳ ᅡᄐ ᆼᄋ ᅡ ᅳᄅ ᅩ Sammel ᄃ ᆼ (1997)ᄋ ᅳ ᆫ LCMᄋ ᅳ ᅳᄅ ᅩᄒ ᆨᄌ ᅪ ᆼᄒ ᅡ ᅡᄋ ᅧ LCMM (Latent Class Model for Mixed variable)ᄋ ᆯᄌ ᅳ ᅦᄉ ᅵᄒ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᄋ ᅵᄀ ᆼᄋ ᅧ ᅮᄇ ᆷᄌ ᅥ ᅮᄒ ᆼᅧ ᅧ ᆫ ᄇᄉ ᅮᄂ ᆫ LCMᄀ ᅳ ᅪᄆ ᅡᄎ ᆫᄀ ᅡ ᅡᄌ ᅵᄅ ᅩᄃ ᅡᄒ ᆼᄇ ᅡ ᆫᄑ ᅮ ᅩᄅ ᅩᄀ ᅡᄌ ᆼᄋ ᅥ ᆯᄒ ᅳ ᅡ ᅵᄆ ᄌ ᆫᄇ ᅡ ᆷᄌ ᅥ ᅮᄒ ᆼᅧ ᅧ ᆫ ᄇᄉ ᅮᄀ ᅡᄋ ᅡᄂ ᆫᅧ ᅵ ᆫ ᄇᄉ ᅮᄃ ᆯᄋ ᅳ ᅦᄃ ᅢᄒ ᅢᄉ ᅥᄂ ᆫᄀ ᅳ ᆨᄇ ᅡ ᆫᄉ ᅧ ᅮᄃ ᆯᄋ ᅳ ᅴᄉ ᆼᄌ ᅥ ᆯᄋ ᅵ ᅦᄄ ᅡᄅ ᅡᄉ ᅥᄑ ᅩᄋ ᅡᄉ ᆼᅮ ᅩ ᆫ ᄇᄑ ᅩ, ᄋ ᆷᄋ ᅳ ᅵᄒ ᆼᄇ ᅡ ᆫᄑ ᅮ ᅩ, ᄌ ᆼ ᅥ ᅲᄇ ᄀ ᆫᅩ ᅮ ᄑ, tᄇ ᆫᄑ ᅮ ᅩᄃ ᆼᄋ ᅳ ᅳᄅ ᅩᄀ ᅡᄌ ᆼᄒ ᅥ ᅡᄋ ᅧᄇ ᆫᄉ ᅮ ᆨᄒ ᅥ ᆯᄉ ᅡ ᅮᄋ ᆻᄂ ᅵ ᆫᄃ ᅳ ᅦ Shinᄋ ᅪ Seo (2019)ᄂ ᆫᄇ ᅳ ᆷᄌ ᅥ ᅮᄒ ᆼᄇ ᅧ ᆫᄉ ᅧ ᅮᄈ ᆫᄆ ᅮ ᆫᄋ ᅡ ᅡᄂ ᅵᄅ ᅡᄐ ᆨᄉ ᅦ ᅳᄐ ᅳ ᅡᄑ ᄀ ᅩᄒ ᆷᄃ ᅡ ᆫᄌ ᅬ ᅡᄅ ᅭᄋ ᅴᄋ ᆨᄑ ᅣ ᆷᄒ ᅮ ᅮᄀ ᅵᄌ ᅡᄅ ᅭᄅ ᆯ LCMMᄋ ᅳ ᆯᄐ ᅳ ᆼᄒ ᅩ ᅢᄇ ᆫᄉ ᅮ ᆨᄒ ᅥ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᅵᄅ ᄋ ᆯ LTMᄋ ᅳ ᅦ ᄌ ᆨᄋ ᅥ ᆼᄒ ᅭ ᅡᄀ ᅵ ᄋ ᅱᄒ ᅢ ᄆ ᆫᄌ ᅥ ᅥ iᄇ ᆫᄍ ᅥ ᅢ ᄀ ᆫᄎ ᅪ ᆯ ᄀ ᅡ ᅢᄎ ᅦ Yi ᄀ ᅡ ᄎ ᆼ Tᄇ ᅩ ᆫ ᄇ ᅥ ᆫᄇ ᅡ ᆨᄒ ᅩ ᅢᄉ ᅥ ᄎ ᆨᄌ ᅳ ᆼᄃ ᅥ ᅬᄋ ᆻᄋ ᅥ ᆯ ᄄ ᅳ ᅢ Yi = (Yi1 , ..., YiT )ᄅ ᅩ ᄑ ᅭᄒ ᆫᄒ ᅧ ᆯ ᄉ ᅡ ᅮ ᄋ ᆻᄃ ᅵ ᅡ. tᄉ ᅵᄌ ᆷᄋ ᅥ ᅦᄉ ᅥ ᄎ ᆨᄌ ᅳ ᆼᄃ ᅥ ᆫ iᄇ ᅬ ᆫᄍ ᅥ ᅢ ᄀ ᆫᄎ ᅪ ᆨ ᄀ ᅳ ᅢᄎ ᅦᄀ ᅡ Jᄀ ᅢᄋ ᅴ ᄀ ᆫᄎ ᅪ ᆨᄇ ᅳ ᆫᄉ ᅧ ᅮᄅ ᆯ ᄑ ᅳ ᅩᄒ ᆷᄒ ᅡ ᆯ ᅡ.
(6) 654. Kyuhyoung Kim · Miyoung Sung · Byungtae Seo. ᄄ, Yit = (Yi1t , ..., YiJt )ᄅ ᅢ ᅩ ᄑ ᅭᄒ ᆫ ᄀ ᅧ ᅡᄂ ᆼᄒ ᅳ ᆫᄃ ᅡ ᅦ, ᄋ ᅧᄀ ᅵᄉ ᅥ Jᄀ ᅢᄋ ᅴ ᄀ ᆫᄎ ᅪ ᆨᄇ ᅳ ᆫᄉ ᅧ ᅮᄃ ᆯᄋ ᅳ ᆫ Rᄀ ᅳ ᅢᄋ ᅴ ᄇ ᆷᄌ ᅥ ᅮᄒ ᆼ ᅧ ᅧ ᆫ ᄇᄉ ᅮ Wit = (Wi1t , ..., WiRt )ᄋ ᅵᄅ ᅡᄂ ᆫᄒ ᅳ ᆨᄅ ᅪ ᆯᄇ ᅲ ᆨᄐ ᅦ ᅥᄅ ᅩᄑ ᅭᄒ ᆫᄒ ᅧ ᅡᄀ ᅩ Sᄀ ᅢᄋ ᅴᄇ ᅵᄇ ᆷᄌ ᅥ ᅮᄒ ᆼᅧ ᅧ ᆫ ᄇᄉ ᅮᄃ ᆯᄋ ᅳ ᆫ Vit = (Vi1t , ...ViSt )ᄋ ᅳ ᅵᄅ ᅡᄂ ᆫᄒ ᅳ ᆨ ᅪ ᆯᄇ ᅲ ᄅ ᆨᅥ ᅦ ᄐᄅ ᅩᄂ ᅡᄐ ᅡᄂ ᅢᄆ ᆫ iᄇ ᅧ ᆫᄍ ᅥ ᅢᄀ ᆫᄎ ᅪ ᆨᄀ ᅳ ᅢᄎ ᅦᄂ ᆫ Yit = (Wit , Vit )ᄅ ᅳ ᅩᄃ ᅡᄉ ᅵᄑ ᅭᄒ ᆫᄒ ᅧ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᄋ ᅧᄀ ᅵᄉ ᅥᄌ ᆷᄌ ᅡ ᅢᄇ ᆫᄉ ᅧ ᅮᄀ ᅡ ᅮᄋ ᄌ ᅥᅧ ᆻ ᄌᄋ ᆯᄄ ᅳ ᅢ 1ᄇ ᅮᄐ ᅥ Rᄇ ᆫᄍ ᅥ ᅢᄁ ᅡᄌ ᅵᄋ ᅴᄇ ᆷᄌ ᅥ ᅮᄒ ᆼᅧ ᅧ ᆫ ᄇᄉ ᅮᄃ ᆯᄋ ᅳ ᆫᄃ ᅳ ᅡᄒ ᆼᄇ ᅡ ᆫᄑ ᅮ ᅩᄅ ᆯᄄ ᅳ ᅡᄅ ᆫᄃ ᅳ ᅡᄀ ᅩᄀ ᅡᄌ ᆼᄒ ᅥ ᆯᄉ ᅡ ᅮᄋ ᆻᄀ ᅵ ᅩ R + 1ᄇ ᆫᄍ ᅥ ᅢᄇ ᅮᄐ ᅥ Jᄇ ᆫᄍ ᅥ ᅢᄁ ᅡᄌ ᅵᄋ ᅴᄇ ᆫᄉ ᅧ ᅮᄃ ᆯᄋ ᅳ ᆫᄄ ᅳ ᅩᄃ ᅡᄅ ᆫᅮ ᅳ ᆫ ᄇᄑ ᅩᄅ ᆯᄄ ᅳ ᅡᄅ ᆫᄃ ᅳ ᅡᄀ ᅩᄀ ᅡᄌ ᆼᄒ ᅥ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ. 2.2ᄌ ᆯᄋ ᅥ ᅦᄉ ᅥᄉ ᅩᄀ ᅢᄒ ᆫ LTMᄋ ᅡ ᅦᄉ ᅥᄉ ᅡᄋ ᆼᄒ ᅭ ᆫ ᅡ ᅡᄌ ᄀ ᆼᅳ ᅥ ᆯ 드 ᆯ ᄋᄆ ᅩᄃ ᅮᄉ ᅡᄋ ᆼᄒ ᅭ ᅡᄋ ᅧ LTM ᄆ ᅩᄒ ᆼᄉ ᅧ ᆨ (2.4)ᄅ ᅵ ᆯᄒ ᅳ ᆨᄌ ᅪ ᆼᄒ ᅡ ᅢᄇ ᆫᄃ ᅩ ᅡᄆ ᆫᄃ ᅧ ᅡᄋ ᆷᄀ ᅳ ᅪᄀ ᇀᄃ ᅡ ᅡ.. P (Yi1 = yi1 , ..., YiT = yiT ) " Y # T T Y J X Y = δl1 τlt |lt−1 × P (Yijt = yijt |Lit = lt ) 1≤l1 ,...,lT ≤C. =. t=2. ". X. δl1. 1≤l1 ,...,lT ≤C. T Y. t=1 j=1. ×. τlt |lt−1. t=2. Y Mr T Y R Y t=1. P (Wirt = m|Lit = lt )I(wirt =m). r=1 m=1 S Y. ×. P (Vist = vist |Lit = lt ). # . s=1. =. ". X. δl 1. 1≤l1 ,...,lT ≤C. T Y. τlt |lt−1. ×. t=2. Y Mr T Y R Y t=1. I(w. ρrm|lirt t. =m). r=1 m=1 S Y. ×. P (Vist. # = vist |Lit = lt ) ,. s=1. ᄋᄀ ᅧ ᅵᅥ ᄉᄇ ᆷᄌ ᅥ ᅮᄒ ᆼᄇ ᅧ ᆫᄉ ᅧ ᅮᄅ ᆯᄀ ᅳ ᆽᄌ ᅡ ᅵᄋ ᆭᄂ ᅡ ᆫᄀ ᅳ ᆫᄎ ᅪ ᆨᄇ ᅳ ᆫᄉ ᅧ ᅮᄃ ᆯᄋ ᅳ ᆫᄒ ᅵ ᆨᄅ ᅪ ᆯᄇ ᅲ ᆨᄐ ᅦ ᅥ Vi ᄋ ᅴᄒ ᆨᄅ ᅪ ᆯᅮ ᅲ ᆫ ᄇᄑ ᅩ P (Vist = vist |Lit = lit )ᄂ ᆫ ᅳ Vist ᄋ ᅴ ᄐ ᆨᄉ ᅳ ᆼᄋ ᅥ ᅦ ᄄ ᅡᄅ ᅡ ᄌ ᆨᄃ ᅥ ᆼᅡ ᅡ ᆫ ᄒ ᄆ ᅩᄉ ᅮᄌ ᆨ ᄇ ᅥ ᆫᄑ ᅮ ᅩᄅ ᅩ ᄀ ᅡᄌ ᆼᄒ ᅥ ᆯ ᄉ ᅡ ᅮ ᄋ ᆻᄃ ᅵ ᅡ. ᄋ ᅵᄒ ᅮᄅ ᅩ ᄇ ᆫ ᄂ ᅩ ᆫᅮ ᅩ ᆫ ᄆᄋ ᅦᄉ ᅥᄂ ᆫ ᄋ ᅳ ᅵᄅ ᇂᄀ ᅥ ᅦ ᄒ ᆨᄌ ᅪ ᆼᄃ ᅡ ᆫ ᅬ LTMᄋ ᆯ LTMM (Latent Transition Model for Mixed Variable)ᄋ ᅳ ᅳᄅ ᅩᄆ ᆼᅧ ᅧ ᆼ ᄆᄒ ᅡᄀ ᅵᄅ ᅩᄒ ᅡᄀ ᆻᄃ ᅦ ᅡ. 3.2. 모수 추정 LTMMᄋ ᅦᄉ ᅥᄋ ᅴᄎ ᅮᄌ ᆼᄒ ᅥ ᅢᄋ ᅣᄒ ᆯᄆ ᅡ ᅩᄉ ᅮᄂ ᆫᄎ ᅳ ᆺᄇ ᅥ ᆫᄍ ᅥ ᅢᄎ ᆨᄌ ᅳ ᆼᄃ ᅥ ᆫᄉ ᅬ ᅵᄌ ᆷᄋ ᅥ ᅦᄉ ᅥᄌ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢ l1 ᄋ ᅦᄉ ᆨᄒ ᅩ ᆯᄒ ᅡ ᆨᄅ ᅪ ᆯ δl1 , t − 1ᄉ ᅲ ᅵᄌ ᆷ ᅥ ᄋᄎ ᅦ ᆨᄌ ᅳ ᆼᄃ ᅥ ᆫᄀ ᅬ ᅢᄎ ᅦᄀ ᅡᄌ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢ lt−1 ᄋ ᅦᄉ ᆨᄒ ᅩ ᆻᄋ ᅢ ᆯᄄ ᅳ ᅢᄃ ᅡᄋ ᆷᄉ ᅳ ᅵᄌ ᆷᄋ ᅥ ᆫ tᄉ ᅵ ᅵᄌ ᆷᄋ ᅥ ᅦᄉ ᅥᄎ ᆨᄌ ᅳ ᆼᄃ ᅥ ᆫᄀ ᅬ ᅢᄎ ᅦᄀ ᅡᄌ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢ lt ᄋ ᅦᄉ ᆨᄒ ᅩ ᅡ ᅦᄃ ᄀ ᆯᄒ ᅬ ᆨᄅ ᅪ ᆯ τlt |lt−1 , tᄉ ᅲ ᅵᄌ ᆷᄋ ᅥ ᅦᄉ ᅥᄌ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢ lt ᄀ ᅡᄌ ᅮᄋ ᅥᄌ ᆻᄋ ᅧ ᆯᄄ ᅳ ᅢᄇ ᆷᄌ ᅥ ᅮᄒ ᆼᄀ ᅧ ᆫᄎ ᅪ ᆯᄇ ᅡ ᆫᄉ ᅧ ᅮ rᄀ ᅡ mᄋ ᅵᄅ ᅡᄀ ᅩᄋ ᆼᄃ ᅳ ᆸᅡ ᅡ ᆯ ᄒᄒ ᆨᄅ ᅪ ᆯ ᅲ ρrmt|lt ᄋ ᅵᄃ ᅡ. ᄒ ᅡᄌ ᅵᄆ ᆫ LTMMᄋ ᅡ ᅦᄉ ᅥᄂ ᆫᄄ ᅳ ᅩᄃ ᅡᄅ ᆫᄇ ᅳ ᆫᄑ ᅮ ᅩᄅ ᆯᄄ ᅳ ᅡᄅ ᅳᄂ ᆫᄇ ᅳ ᆫᄉ ᅧ ᅮᄀ ᅡᄎ ᅮᄀ ᅡᄃ ᅬᄋ ᆻᄀ ᅥ ᅵᄄ ᅢᄆ ᆫᄋ ᅮ ᅦᄀ ᅳᄋ ᅦᄆ ᆽᄂ ᅡ ᆫᅮ ᅳ ᆫ ᄇᄑ ᅩᄀ ᅡ ᅡᄌ ᄀ ᅵᄂ ᆫᄆ ᅳ ᅩᄉ ᅮᄃ ᆯᄃ ᅳ ᅩᄎ ᆽᄋ ᅡ ᅡᄋ ᅣᄒ ᆫᄃ ᅡ ᅡ. ᆫᅥ ᅥ ᄆ ᄌ (Y1 , L1 ), . . . , (Yn , Ln )ᄋ ᅵᄌ ᅮᄋ ᅥᄌ ᆻᄋ ᅧ ᆯᄄ ᅳ ᅢᄋ ᅴᄅ ᅩᄀ ᅳᄀ ᅡᄂ ᆼᄃ ᅳ ᅩᄒ ᆷᄉ ᅡ ᅮ ℓ(θ|Y, L)ᄂ ᆫ ᅳ. l(θ|Y, L) =. n X. X. i=1 1≤l1 ,...,lT ≤C. " I(Li = l) log. δl1. T Y. τlt |lt−1. ×. Y Mr T Y R Y. t=2. t=1. ×. S Y s=1. I(w. ρrm|lirt t. =m). r=1 m=1. P (Vist = vist |Lit = lt ). # . (3.1).
(7) Latent transition model for mixed variable with applications to youth’s study habits and academic achievement655. ᅵᄀ ᄋ ᅩ Zˆil = P (Li = l|Yi = yi )ᄋ ᆫ ᅳ. δl1. T Y. ×. τlt |lt−1. Y Mr T Y R Y t=1. t=2. Zˆil =. ". X. δl1. 1≤l1 ,...,lT ≤C. T Y. ×. τlt |lt−1. I(w. ρrm|lirt t. =m). r=1 m=1. t=1. P (Vist = vist |Lit = lt ). . s=1. Y Mr T Y R Y. t=2. S Y. I(w =m) ρrm|lirt t. r=1 m=1. S Y. P (Vist = vist |Lit = lt ). # . s=1. ᅪᄀ ᄀ ᇀᅵ ᅡ ᄋᄀ ᅨᄉ ᆫᄃ ᅡ ᆫᄃ ᅬ ᅡ. ᅵᅦ ᄋ ᄌ LTMᄋ ᅴᄎ ᅮᄌ ᆼᄀ ᅥ ᅪᄋ ᅲᄉ ᅡᄒ ᆫᄇ ᅡ ᆼᄉ ᅡ ᆨᄋ ᅵ ᅳᄅ ᅩᄋ ᅡᄅ ᅢᅪ ᄋᄀ ᇀᄋ ᅡ ᅵ E-stepᄀ ᅪ M-stepᄋ ᆯᄋ ᅳ ᅲᄃ ᅩᄒ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ. [E-Step] Q(θ|θ ′ ) = E(l(θ|Y, L)|, Y, θ ′ )ᄅ ᅡᄀ ᅩᄌ ᆼᄋ ᅥ ᅴᄒ ᅡᄆ ᆫᄉ ᅧ ᆨ (3.1)ᄋ ᅵ ᅴᄌ ᅩᄀ ᆫᄇ ᅥ ᅮᄀ ᅵᄃ ᆺᄀ ᅢ ᆹᄋ ᅡ ᆫ ᅳ. Q(θ|θ ′ ) =. n X. T X Zˆil log δl1 + log(τlt |lt−1 ). X. i=1 1≤l1 ,...,lT ≤C. t=2. +. Mr T hX R X X t=1. log(ρrm|lt ) +. r=1 m=1. S X. log(P (Vist. i = vist |Lit = lt )). s=1. ᅩᄀ ᄅ ᅨᄉ ᆫᅡ ᅡ ᆯ ᄒᄉ ᅮᄋ ᆻᄃ ᅵ ᅡ. [M-step] ᅡᄋ ᄃ ᆷᄃ ᅳ ᆫᄀ ᅡ ᅨᄋ ᆫ M-stepᄋ ᅵ ᅦᄉ ᅥᄂ ᆫ E-stepᄋ ᅳ ᅦᄉ ᅥᄀ ᅮᄒ ᆫ Qᄅ ᅡ ᆯᄎ ᅳ ᅬᄃ ᅢᄒ ᅪᄉ ᅵᄏ ᅵᄂ ᆫᄆ ᅳ ᅩᄉ ᅮᄅ ᅩᄋ ᆸᄃ ᅥ ᅦᄋ ᅵᄐ ᅳᄒ ᅡᄂ ᆫᄀ ᅳ ᅪᄌ ᆼᄋ ᅥ ᆫᄃ ᅵ ᅦ δˆl1 , τˆlt |lt−1 , ρˆrm|l ᄋ ᆫ 2.3ᄌ ᅳ ᆯᄋ ᅥ ᅴ M-stepᄋ ᅪ ᄃ ᆼᄋ ᅩ ᆯᄒ ᅵ ᅡᄀ ᅦ ᄀ ᅮᄒ ᆯ ᄉ ᅡ ᅮ ᄋ ᆻᄃ ᅵ ᅡ. ᄄ ᅩᄒ ᆫ P (Vist = vist |Lit = lit )ᄋ ᅡ ᅦ ᄑ ᅩᄒ ᆷ ᅡ ᆫᄆ ᅬ ᄃ ᅩᄉ ᅮᄂ ᆫ Q(θ|θ ′ )ᄅ ᅳ ᆯᄒ ᅳ ᅢᄃ ᆼᄆ ᅡ ᅩᄉ ᅮᄋ ᅦᄃ ᅢᄒ ᅢᅬ ᄎᄃ ᅢᄒ ᅪᄒ ᅡᄂ ᆫᄆ ᅳ ᅩᄉ ᅮᄅ ᆯᄎ ᅳ ᆽᄋ ᅡ ᆷᄋ ᅳ ᅳᄅ ᅩᄊ ᅥᄋ ᆮᄋ ᅥ ᅥᄌ ᆯᄉ ᅵ ᅮᄋ ᆻᄂ ᅵ ᆫᄃ ᅳ ᅦ, ᄋ ᅨᄅ ᆯᄃ ᅳ ᆯᄋ ᅳ ᅥ ˆ s|l ᄋ P (Vist = vist |Lit = lit )ᄀ ᅡᄑ ᆼᄀ ᅧ ᆫ λs|l ᄋ ᅲ ᆯᄄ ᅳ ᅡᄅ ᅳᄂ ᆫᄑ ᅳ ᅩᄋ ᅡᄉ ᆼᄒ ᅩ ᆨᄅ ᅪ ᆯᄌ ᅲ ᆯᄅ ᅵ ᆼᅡ ᅣ ᆷ ᄒᄉ ᅮᄋ ᆯᄄ ᅵ ᅢλ ᆫ ᅳ PT ˆ s|l = λ. t=1. PT. Pn. t=1. i=1. Pn. PC. i=1. l1 =1. PC. ···. l1 =1. PC. ···. lt−1 =1. PC. PC. lt−1 =1. lt+1 =1. PC. ···. lt+1 =1. PC. ···. lT =1. PC. Zˆil vist. lT =1. Zˆil. ᅩᄎ ᄅ ᅮᄌ ᆼᄒ ᅥ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ.. 4. 실증 자료 분석 4.1. 자료 소개 ᆫᄋ ᅩ ᄇ ᆫᄀ ᅧ ᅮᄋ ᅦᄉ ᅥᄋ ᅴᄒ ᆫᄀ ᅡ ᆨᄎ ᅮ ᆼᄉ ᅥ ᅩᄂ ᆫᄌ ᅧ ᆼᅢ ᅥ ᆨ 쳐 ᆫ ᄋᄀ ᅮᆫ ᄋ ᅯᄋ ᅦᄉ ᅥᄌ ᅩᄉ ᅡᄒ ᆫᄒ ᅡ ᆫᄀ ᅡ ᆨᄋ ᅮ ᅡᄃ ᆼ·ᄎ ᅩ ᆼᄉ ᅥ ᅩᄂ ᆫᄑ ᅧ ᅢᄂ ᆯᄌ ᅥ ᅩᄉ ᅡ (2010-2016)ᄅ ᆯᄉ ᅳ ᅡᄋ ᆼᄒ ᅭ ᅡ ᄋᄀ ᅧ ᆨᅡ ᅡ ᆨ ᄀ LTMᄀ ᅪ LTMMᄋ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᅧᄇ ᆫᄉ ᅮ ᆨᄒ ᅥ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᄋ ᅵᄌ ᅡᄅ ᅭᄂ ᆫᄎ ᅳ ᅩ1 ᄏ ᅩᄒ ᅩᄐ ᅳ, ᄎ ᅩ4 ᄏ ᅩᄒ ᅩᄐ ᅳ, ᄌ ᆼ1 ᄏ ᅮ ᅩᄒ ᅩᄐ ᅳᄋ ᅦᄃ ᅢ ᅡᄋ ᄒ ᅧ 7ᄂ ᆫᄀ ᅧ ᆫᄌ ᅡ ᅩᄉ ᅡᄃ ᆫᄌ ᅬ ᅡᄅ ᅭᄅ ᆯᄑ ᅳ ᅩᄒ ᆷᄒ ᅡ ᅡᄀ ᅩᄋ ᆻᄃ ᅵ ᅡ. ᄇ ᆫᄋ ᅩ ᆫᄀ ᅧ ᅮᄋ ᅦᄉ ᅥᄂ ᆫᄌ ᅳ ᆫᄎ ᅥ ᅦᄌ ᅡᄅ ᅭᄌ ᆼᄎ ᅮ ᅩ4 ᄏ ᅩᄒ ᅩᄐ ᅳᄅ ᆯᄃ ᅳ ᅢᄉ ᆼᄋ ᅡ ᅳᄅ ᅩᄉ ᅵᄒ ᆼᄃ ᅢ ᆫ ᅬ 3ᄎ ᅡᄌ ᅩᅡ ᄉ (2012)ᄇ ᅮᄐ ᅥ 5ᄎ ᅡᄌ ᅩᄉ ᅡ (2014)ᄁ ᅡᄌ ᅵᄋ ᅴᄌ ᅡᄅ ᅭ, ᄌ ᆨ, ᄎ ᅳ ᅩᄃ ᆼᄒ ᅳ ᆨᄀ ᅡ ᅭ 6ᄒ ᆨᅧ ᅡ ᆫ ᄂ, ᄌ ᆼᄒ ᅮ ᆨᄀ ᅡ ᅭ 1ᄒ ᆨᅧ ᅡ ᆫ ᄂ, ᄌ ᆼᄒ ᅮ ᆨᄀ ᅡ ᅭ 2ᄒ ᆨᅧ ᅡ ᆫ ᄂᄋ ᅦ ᅩᄉ ᄌ ᅡᄃ ᆫᄌ ᅬ ᅡᄅ ᅭᄅ ᆯᄀ ᅳ ᅩᄅ ᅧᄒ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᄀ ᅩᄅ ᅧᄃ ᆫᄌ ᅬ ᅡᄅ ᅭᄂ ᆫᄎ ᅳ ᆼ 2378ᄆ ᅩ ᆼᄋ ᅧ ᆯᄃ ᅳ ᅢᄉ ᆼᄋ ᅡ ᅳᄅ ᅩᄉ ᆯᄉ ᅵ ᅵᄃ ᆫᄌ ᅬ ᅩᄉ ᅡᄀ ᆯᄀ ᅧ ᅪᄅ ᆯᄑ ᅳ ᅩᄒ ᆷᄒ ᅡ ᅡᄂ ᆫᄃ ᅳ ᅦᄋ ᅵᄌ ᆼ ᅮ ᆯᄎ ᅧ ᄀ ᆨᅵ ᅳ ᄎᄅ ᆯᄌ ᅳ ᅦᄀ ᅥᄒ ᅡᄋ ᅧ 1715ᄆ ᆼᄋ ᅧ ᅴᄌ ᅡᄅ ᅭᄆ ᆫᄋ ᅡ ᆯᄇ ᅳ ᆫᄉ ᅮ ᆨᄋ ᅥ ᅦᄋ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᄌ ᆯᄆ ᅵ ᆫᄋ ᅮ ᆼᄋ ᅧ ᆨᄋ ᅧ ᆫᄀ ᅳ ᅪᄆ ᆨᄇ ᅩ ᆯᄉ ᅧ ᆼᄌ ᅥ ᆨᄋ ᅥ ᅴᄌ ᅮᄀ ᆫᄌ ᅪ ᆨᄑ ᅥ ᆼᄀ ᅧ ᅡ, ᄉ ᆼ ᅢ ᆯᄉ ᅪ ᄒ ᅵᄀ ᆫᄌ ᅡ ᆼᄒ ᅮ ᆨᅥ ᅡ ᆸ ᄋᄀ ᆫᄅ ᅪ ᆫᄉ ᅧ ᅵᄀ ᆫ, ᄒ ᅡ ᆨᄀ ᅡ ᅭᄌ ᆨᄋ ᅥ ᆼ (ᄒ ᅳ ᆨᄉ ᅡ ᆸᄒ ᅳ ᆯᄃ ᅪ ᆼ) ᄉ ᅩ ᅦᄀ ᅢᄅ ᅩᄂ ᅡᄂ ᅱᄆ ᅧᄀ ᆨᄀ ᅡ ᆨᄋ ᅡ ᅴᄋ ᆼᄋ ᅧ ᆨᄆ ᅧ ᅡᄃ ᅡᄌ ᆯᄆ ᅵ ᆫᄋ ᅮ ᆫ 3ᄀ ᅳ ᅢ, 4ᄀ ᅢ, 4ᄀ ᅢᄅ ᅩ.
(8) 656. Kyuhyoung Kim · Miyoung Sung · Byungtae Seo. ᄀᄉ ᅮ ᆼᄃ ᅥ ᅬᄋ ᅥᄋ ᆻᄃ ᅵ ᅡ. ᄐ ᆨᄒ ᅳ ᅵᄋ ᆼᄃ ᅳ ᆸᄆ ᅡ ᆫᄒ ᅮ ᆼᄌ ᅡ ᆼᄒ ᅮ ᆨᅥ ᅡ ᆸ ᄋᄀ ᆫᄅ ᅪ ᆫᄉ ᅧ ᅵᄀ ᆫᄋ ᅡ ᆼᄋ ᅧ ᆨᄋ ᅧ ᅦᄉ ᅥᄂ ᆫᄋ ᅳ ᆼᄃ ᅳ ᆸᄋ ᅡ ᅵᄇ ᆷᄌ ᅥ ᅮᄒ ᆼᄌ ᅧ ᅡᄅ ᅭᄀ ᅡᄋ ᅡᄂ ᆫᄌ ᅵ ᅮᄀ ᆫᄉ ᅪ ᆨᄋ ᅵ ᅳᄅ ᅩᄉ ᅵ ᆫᄋ ᅡ ᄀ ᆯᅵ ᅳ ᄀᄋ ᆸᄒ ᅵ ᅡᄋ ᅧᄋ ᆮᄋ ᅥ ᅥᄌ ᆫᄌ ᅵ ᅡᄅ ᅭᄋ ᅵᄃ ᅡ. ᆫᄉ ᅮ ᄇ ᆨᄋ ᅥ ᆯ ᄋ ᅳ ᅱᄒ ᅢ ᄉ ᆼᄌ ᅥ ᆨᄋ ᅥ ᅴ ᄌ ᅮᄀ ᆫᄌ ᅪ ᆨ ᅧ ᅥ ᆼ ᄑᄀ ᅡᄋ ᆼᄋ ᅧ ᆨᄋ ᅧ ᅦᄉ ᅥᄂ ᆫ ᄀ ᅳ ᆨ ᅡ ᅡ ᆨ 해 ᆼ ᄉᄋ ᅵ ᄀ ᆨᄋ ᅮ ᅥ, ᄋ ᆼᄋ ᅧ ᅥ, ᄉ ᅮᄒ ᆨᄋ ᅡ ᅦ ᄃ ᅢᄒ ᅡᄋ ᅧ “ᄆ ᅢᄋ ᅮ ᄌ ᆯᄒ ᅡ ᆻ ᅢ ᅡ”, “ ᄌ ᄃ ᆯᅡ ᅡ ᆫ ᄒᄑ ᆫᄋ ᅧ ᅵᄃ ᅡ”, “ᄇ ᅩᄐ ᆼᄋ ᅩ ᅵᄃ ᅡ”, “ᄆ ᆺᄒ ᅩ ᆫ ᅧ ᅡ ᆫ ᄑᄋ ᅵᄃ ᅡ”, “ᄆ ᅢᄋ ᅮ ᄆ ᆺᄒ ᅩ ᆻᄃ ᅢ ᅡ”ᄋ ᅴ ᄃ ᅡᄉ ᆺ ᄆ ᅥ ᆫᄒ ᅮ ᆼᄌ ᅡ ᆼ ᄒ ᅮ ᅡᄂ ᅡᄋ ᅦ ᄃ ᆸᄒ ᅡ ᅡᄋ ᆻᄂ ᅧ ᆫ ᅳ ᅦ ᄇ ᄃ ᆫ ᄋ ᅩ ᆫᄀ ᅧ ᅮᄋ ᅦᄉ ᅥᄂ ᆫ ᄋ ᅳ ᅵᄅ ᆯ “ᄌ ᅳ ᆯᄒ ᅡ ᆻᄃ ᅢ ᅡ”, “ᄇ ᅩᄐ ᆼᄋ ᅩ ᅵᄃ ᅡ”, “ᄆ ᆺᄒ ᅩ ᆻᄃ ᅢ ᅡ”ᄋ ᅴ ᄉ ᅦᄀ ᅢᄋ ᅴ ᄇ ᆷᄌ ᅥ ᅮᄅ ᅩ ᄆ ᆩᄋ ᅮ ᅥ ᄋ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᄄ ᅩᄒ ᆫ ᅡ ᆨᄉ ᅡ ᄒ ᆸ ᄒ ᅳ ᆯᄃ ᅪ ᆼᄋ ᅩ ᅦ ᄃ ᅢᄒ ᅡᄋ ᅧᄉ ᅥᄂ ᆫ ᄒ ᅳ ᆨᄀ ᅡ ᅭᄉ ᅮᄋ ᆸᄋ ᅥ ᅴ ᄒ ᆼᄆ ᅳ ᅵ, ᄒ ᆨᄀ ᅡ ᅭᄉ ᆨᄌ ᅮ ᅦᄋ ᅴ ᄎ ᆼᄉ ᅮ ᆯᅥ ᅵ ᆼ ᄉ, ᄉ ᅮᄋ ᆸᄂ ᅥ ᅢᄋ ᆼᄋ ᅭ ᅦ ᄃ ᅢᄒ ᆫ ᄋ ᅡ ᅵᄒ ᅢ, ᄆ ᅩᄅ ᅳᄂ ᆫ ᄀ ᅳ ᆺᄋ ᅥ ᅦ ᅢᄒ ᄃ ᆫ ᅥ ᅡ ᆨ ᄌᄀ ᆨᄌ ᅳ ᆨ ᄌ ᅥ ᆯᄆ ᅵ ᆫᄋ ᅮ ᅦ ᄃ ᅢᄒ ᅡᄋ ᅧ “ᄆ ᅢᄋ ᅮ ᄀ ᅳᄅ ᇂᄃ ᅥ ᅡ”, “ᄀ ᅳᄅ ᇂᄃ ᅥ ᅡ”, “ᄀ ᅳᄅ ᇂᄌ ᅥ ᅵ ᄋ ᆭᄋ ᅡ ᆫ ᄑ ᅳ ᆫᄋ ᅧ ᅵᄃ ᅡ”, “ᄌ ᆫᄒ ᅥ ᅧ ᄀ ᅳᄅ ᇂᄌ ᅥ ᅵ ᄋ ᆭᄃ ᅡ ᅡ” ᅴ ᄂ ᄋ ᅦ ᄆ ᆫᄒ ᅮ ᆼᄌ ᅡ ᆼ ᄒ ᅮ ᅡᄂ ᅡᄅ ᆯ ᄃ ᅳ ᆸᄒ ᅡ ᅡᄋ ᆻᄂ ᅧ ᆫᄃ ᅳ ᅦ ᄋ ᅵᄌ ᆼ “ᄆ ᅮ ᅢᄋ ᅮ ᄀ ᅳᄅ ᇂᄃ ᅥ ᅡ”ᄋ ᅪ “ᄀ ᅳᄅ ᇂᄃ ᅥ ᅡ”ᄅ ᆯ “ᄀ ᅳ ᅳᄅ ᇂᄃ ᅥ ᅡ”ᄋ ᅴ ᄇ ᆷᄌ ᅥ ᅮᄅ ᅩ ᄆ ᆩᄀ ᅮ ᅩ “ᄀ ᅳᄅ ᇂ ᅥ ᅵ ᄋ ᄌ ᆭᅳ ᅡ ᆫ ᄋ ᄑ ᆫᄋ ᅧ ᅵᄃ ᅡ”ᄋ ᅪ “ᄌ ᆫᄒ ᅥ ᅧ ᄀ ᅳᄅ ᇂᄌ ᅥ ᅵ ᄋ ᆭᄃ ᅡ ᅡ”ᄅ ᆯ “ᄀ ᅳ ᅳᄅ ᇂᄌ ᅥ ᅵ ᄋ ᆭᄃ ᅡ ᅡ”ᄋ ᅴ ᄇ ᆷᄌ ᅥ ᅮᄅ ᅩ ᄆ ᆩᄋ ᅮ ᅥᄉ ᅥ ᄇ ᆫᄉ ᅮ ᆨᄋ ᅥ ᆯ ᄌ ᅳ ᆫᄒ ᅵ ᆼᄒ ᅢ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᄒ ᆨ ᅡ ᆸ ᄀ ᅥ ᄋ ᆫᄅ ᅪ ᆫ ᄉ ᅧ ᅵᄀ ᆫᄋ ᅡ ᅴ ᄃ ᆸᄇ ᅡ ᆫᄋ ᅧ ᆫ ᄑ ᅳ ᆼᄋ ᅧ ᆯᄋ ᅵ ᅦ ᄇ ᅩᄂ ᆫᄉ ᅢ ᅵᄀ ᆫᄀ ᅡ ᅪ ᄌ ᅮᄆ ᆯᄋ ᅡ ᅦ ᄇ ᅩᄂ ᆫᄉ ᅢ ᅵᄀ ᆫᄋ ᅡ ᅦ ᄃ ᅢᄒ ᅢ ᄃ ᆸᄇ ᅡ ᆫᄒ ᅧ ᅡᄀ ᅦ ᅬ ᄃᄋ ᅥ ᄋ ᆻᄃ ᅵ ᅡ. ᄒ ᆨᄋ ᅡ ᆫᄒ ᅯ ᆨᄉ ᅡ ᆸ ᅳ ᅵᄀ ᄉ ᆫ, ᄒ ᅡ ᆨᄀ ᅡ ᅭᄉ ᆨᄌ ᅮ ᅦᄉ ᅵᄀ ᆫ, ᄒ ᅡ ᆨᄋ ᅡ ᆫᄉ ᅯ ᆨᄌ ᅮ ᅦᄉ ᅵᄀ ᆫ, ᄒ ᅡ ᆨᆫ ᅡ ᄋ ᅯᄀ ᅪ ᅡ ᆨ ᄒᄀ ᅭ ᄋ ᅵᅬ ᄋᄋ ᅴ ᄀ ᆼᄇ ᅩ ᅮᄉ ᅵᄀ ᆫᄋ ᅡ ᅦ ᄃ ᅢᄒ ᆫ ᄀ ᅡ ᆨ ᄋ ᅡ ᆼᄃ ᅳ ᆸ ᄉ ᅡ ᅵᄀ ᆫᄋ ᅡ ᅦ ᄃ ᅢᄒ ᅡᄋ ᅧ ᄒ ᆨ ᅡ ᅭ ᄀ ᄀ ᅡᄂ ᆫ ᄂ ᅳ ᆯᄋ ᅡ ᅴ ᄑ ᆼᄀ ᅧ ᆫ ᄉ ᅲ ᅵᄀ ᆫᄀ ᅡ ᅪ ᅡ ᆨ ᄒᄀ ᅭ ᄀ ᅡᄌ ᅵ ᄋ ᆭᄂ ᅡ ᆫ ᄂ ᅳ ᆯᄋ ᅡ ᅴ ᄑ ᆼᄀ ᅧ ᆫᄉ ᅲ ᅵᄀ ᆫᄋ ᅡ ᆯ ᄒ ᅳ ᆸᄎ ᅡ ᅵᄀ ᅵ ᄋ ᅱᄒ ᅢ ᄒ ᆨᄀ ᅡ ᅭ ᄀ ᅡᄂ ᆫ ᄂ ᅳ ᆯᄋ ᅡ ᆯ ᄑ ᅳ ᆼᄋ ᅧ ᆯ, ᄒ ᅵ ᆨ ᅡ ᅭ ᄀ ᄀ ᅡᅵ ᄌ ᄋ ᆭᄂ ᅡ ᆫ ᄂ ᅳ ᆯᄋ ᅡ ᆯ ᄌ ᅳ ᅮᄆ ᆯᄅ ᅡ ᅩ ᄉ ᆼᄀ ᅢ ᆨᄒ ᅡ ᅡᄋ ᅧ ᄒ ᅡᄅ ᅮ ᄑ ᆼᄀ ᅧ ᆫ ᄒ ᅲ ᅢᄃ ᆼ ᄌ ᅡ ᆯᄆ ᅵ ᆫᄋ ᅮ ᅴ ᄃ ᅢᄃ ᆸᄋ ᅡ ᅦ ᄃ ᅢᄒ ᆫ ᄋ ᅡ ᆼᄃ ᅳ ᆸᄋ ᅡ ᆯ ᄒ ᅳ ᅡᄅ ᅮᄑ ᆼᄀ ᅧ ᆫᄉ ᅲ ᅵᄀ ᆫ = ᅡ (ᄒ ᆨᄀ ᅡ ᅭᄀ ᅡᄂ ᆫᄂ ᅳ ᆯᄑ ᅡ ᆼᄀ ᅧ ᆫᄉ ᅲ ᅵᄀ ᆫ×5+ᄒ ᅡ ᆨᄀ ᅡ ᅭᄀ ᅡᄌ ᅵᄋ ᆭᄂ ᅡ ᆫᄂ ᅳ ᆯᄑ ᅡ ᆼᄀ ᅧ ᆫᄉ ᅲ ᅵᄀ ᆫ × 2) /7ᄅ ᅡ ᅩ ᄀ ᅨᄉ ᆫᅡ ᅡ ᆫ ᄒ ᄒ ᅮ ᄇ ᆫᄋ ᅡ ᆯᄅ ᅩ ᆷᄒ ᅵ ᅢ ᄌ ᆼᄉ ᅥ ᅮᄀ ᆹᄋ ᅡ ᆯ ᄆ ᅳ ᆫᄃ ᅡ ᆯ ᅳ ᅥᄉ ᄋ ᅡᅭ ᆼ ᄋᄒ ᅡᄋ ᆻᄃ ᅧ ᅡ. 4.2. LTM 분석 ᅡᄅ ᄌ ᅭᄋ ᅴ ᄇ ᆫᄉ ᅮ ᆨᄋ ᅥ ᆯ ᄋ ᅳ ᅱᄒ ᅢ ᄆ ᆫᄌ ᅥ ᅥ 4.1ᄌ ᆯᄋ ᅥ ᅦᄉ ᅥ ᄉ ᆯᅧ ᅥ ᆼ ᄆᄒ ᆫ ᄌ ᅡ ᅡᄅ ᅭᄌ ᆼ ᄒ ᅮ ᆨᅥ ᅡ ᆸ ᄋᄉ ᅵᄀ ᆫᄋ ᅡ ᅦ ᄀ ᆫᄒ ᅪ ᆫ ᄌ ᅡ ᆯᄆ ᅵ ᆫᅳ ᅮ ᆯ ᄋ ᄌ ᅦᅬ ᄋᄒ ᅡᄀ ᅩ LTM ᄇ ᆫᄉ ᅮ ᆨᄋ ᅥ ᆯ ᅳ ᄉᄉ ᆯ ᅵ ᅵᄒ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᄌ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄋ ᅴ ᄉ ᅮᄅ ᆯ ᄀ ᅳ ᆯᅥ ᅧ ᆼ ᄌᄒ ᅡᄀ ᅵ ᄋ ᅱᄒ ᅢ 2ᄀ ᅢᄇ ᅮᄐ ᅥ 8ᄀ ᅢᄋ ᅴ ᄌ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄅ ᆯ ᄀ ᅳ ᅡᄌ ᅵᄂ ᆫ ᄆ ᅳ ᅩᄒ ᆼᄋ ᅧ ᅦ ᄃ ᅢᄒ ᅡᄋ ᅧ AIC (Akaike Information Criterion; Akaike, 1973), BIC (Bayesian Information Criterion; Schwarz, 1978), CAIC (Consistent AIC; Bozdogan; 1987)ᄅ ᆯ Table 4.1ᄀ ᅳ ᅪᄀ ᇀᄋ ᅡ ᅵᄀ ᅨᄉ ᆫᄒ ᅡ ᅡᄋ ᆻᄂ ᅧ ᆫᄃ ᅳ ᅦ AICᄂ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄋ ᅴᄉ ᅮᄀ ᅡ 8ᄀ ᅢᆯ ᅵᄄ ᄋ ᅢ, BIC, CAICᄂ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄋ ᅴᄉ ᅮᄀ ᅡ 6ᄀ ᅢᄋ ᆯᄄ ᅵ ᅢᄀ ᅡᄌ ᆼᄂ ᅡ ᆽᄋ ᅡ ᆻᄃ ᅡ ᅡ. AICᄂ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄋ ᅴᄉ ᅮᄀ ᅡᄆ ᆭᄀ ᅡ ᅦᄉ ᆫᅢ ᅥ ᆨ ᄐᄒ ᅡ ᅧᅪ ᄋ ᄀᄌ ᆨᄒ ᅥ ᆸᄒ ᅡ ᅡᄂ ᆫᄀ ᅳ ᆼᄒ ᅧ ᆼᄋ ᅣ ᅵᄋ ᆻᄋ ᅵ ᅳᄆ ᅳᄅ ᅩᄌ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄋ ᅴᄉ ᅮᄀ ᅡᄌ ᆨᄋ ᅥ ᆯᄄ ᅳ ᅢᄒ ᅢᄉ ᆨᄋ ᅥ ᅵᄀ ᆫᄀ ᅡ ᆯᄒ ᅧ ᅢᄌ ᆷᄋ ᅵ ᆯᄉ ᅳ ᆼᄀ ᅢ ᆨᄒ ᅡ ᅡᄋ ᅧ BICᄋ ᅪ CAICᄅ ᆯ ᅳ ᅩᄅ ᄀ ᅧᅡ ᄒᄋ ᅧᄆ ᅩᄃ ᆯᄋ ᅦ ᆯᄉ ᅳ ᆫᅢ ᅥ ᆨ ᄐᄒ ᅡᄋ ᆻᄃ ᅧ ᅡ. BICᄋ ᅪ CAICᄂ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄋ ᅴᄉ ᅮᄀ ᅡ 5ᄀ ᅢ, 6ᄀ ᅢ, 7ᄀ ᅢᄋ ᆯᄄ ᅵ ᅢᄏ ᆫᄎ ᅳ ᅡᄋ ᅵᄀ ᅡᄋ ᆹᄋ ᅥ ᅳᄆ ᅳᄅ ᅩ ᅢᄉ ᄒ ᆨᅴ ᅥ ᄋᄀ ᆫᄀ ᅡ ᆯᄒ ᅧ ᆷᄋ ᅡ ᆯᄋ ᅳ ᅱᄒ ᅢᄌ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄋ ᅴᄉ ᅮᄀ ᅡ 5ᄀ ᅢᄋ ᆫᄆ ᅵ ᅩᄒ ᆼᄋ ᅧ ᆯᄉ ᅳ ᆫᅢ ᅥ ᆨ ᄐᄒ ᅡᄋ ᅧ LTM ᄌ ᆨᄒ ᅥ ᆸᄒ ᅡ ᅮᄆ ᅩᄉ ᅮᄃ ᆯᄋ ᅳ ᅴᄎ ᅮᄌ ᆼᄀ ᅥ ᆹᄋ ᅡ ᆯ Table ᅳ 4.2ᄋ ᅪ 4.3ᄋ ᅦᄌ ᆼᄅ ᅥ ᅵᄒ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᄀ ᅳᄅ ᅵᄀ ᅩᄒ ᅢᄉ ᆨᄋ ᅥ ᅴᄑ ᆫᄅ ᅧ ᅵᄒ ᆷᄋ ᅡ ᆯᄋ ᅳ ᅱᄒ ᅢᄆ ᅩᄉ ᅮᄎ ᅮᄌ ᆼᄀ ᅥ ᆹᄋ ᅡ ᆯᄇ ᅳ ᅡᄐ ᆼᄋ ᅡ ᅳᄅ ᅩᄀ ᆨᄉ ᅡ ᆼᄐ ᅡ ᅢᄋ ᅴᄐ ᆨᄌ ᅳ ᆼᄋ ᅵ ᆯ Table ᅳ 4.4ᄋ ᅦᄌ ᆼᄅ ᅥ ᅵᄒ ᅡᄋ ᆻᄃ ᅧ ᅡ. Table 4.1 AIC, BIC, and CAIC for different number of latent status in LTM. AIC BIC CAIC. 2 49059 49195 49220. 3 47309 47549 47593. Number 4 46556 46921 46988. of latent 5 46002 46514 46608. status 6 45673 46354 46479. 7 45533 46405 46565. 8 45495 46579 46778. 가 ᆨ ᅡ ᆼ ᄉᄐ ᅢᄋ ᅴᄌ ᆯᄆ ᅵ ᆫᄒ ᅮ ᆼᄆ ᅡ ᆨᄋ ᅩ ᅴᄋ ᆼᄃ ᅳ ᆸᄇ ᅡ ᅵᄋ ᆯᅳ ᅲ ᆯ ᄋᄒ ᆨᄋ ᅪ ᆫᄒ ᅵ ᅡᄆ ᆫᄉ ᅧ ᆼᄐ ᅡ ᅢ 2, 3, 4ᄂ ᆫ “ᄉ ᅳ ᅮᄋ ᆸᄉ ᅥ ᅵᄀ ᆫᄋ ᅡ ᅦᄃ ᅢᄒ ᆫᄒ ᅡ ᆼᄆ ᅳ ᅵᄃ ᅩ”ᄋ ᅪ “ᄆ ᅩᄅ ᅳᄂ ᆫᄀ ᅳ ᆺ ᅥ ᅦᄃ ᄋ ᅢᄒ ᆫᄌ ᅡ ᆯᄆ ᅵ ᆫ”ᄋ ᅮ ᅦᄉ ᅥᄀ ᆼᄌ ᅳ ᆼᄌ ᅥ ᆨᄋ ᅥ ᆫᄃ ᅵ ᆸᄇ ᅡ ᆫᄋ ᅧ ᅴᄋ ᆼᄃ ᅳ ᆸᄇ ᅡ ᅵᄋ ᆯᄋ ᅲ ᅵᄂ ᇁᄋ ᅩ ᆫᄀ ᅳ ᆺᄋ ᅥ ᅳᄅ ᅩᄇ ᅩᄋ ᅡᄒ ᆨᄀ ᅡ ᅭᄉ ᆼᄒ ᅢ ᆯᄋ ᅪ ᅦᄌ ᆨᄀ ᅥ ᆨᄌ ᅳ ᆨᄋ ᅥ ᅳᄅ ᅩᄎ ᆷᄋ ᅡ ᅧᄒ ᅡᄂ ᆫᄌ ᅳ ᆸ ᅵ ᆫᄋ ᅡ ᄃ ᅳᄅ ᅩᄑ ᆫᄃ ᅡ ᆫᅡ ᅡ ᆯ ᄒᄉ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᄒ ᅡᄌ ᅵᄆ ᆫᅡ ᅡ ᆨ 허 ᆸ 어 ᆼ ᄉᄎ ᅱᄃ ᅩᄂ ᆫᄉ ᅳ ᆼᄐ ᅡ ᅢ 2ᄀ ᅡᄀ ᅡᄌ ᆼᄂ ᅡ ᇁᄀ ᅩ ᅩᄉ ᆼᄐ ᅡ ᅢ 4ᄂ ᆫᄇ ᅳ ᅩᄐ ᆼᄀ ᅩ ᅳᄅ ᅵᄀ ᅩᄉ ᆼᄐ ᅡ ᅢ 3ᄋ ᆫᄂ ᅳ ᆽ ᅡ ᆫᄌ ᅳ ᄋ ᆸᄃ ᅵ ᆫᄋ ᅡ ᅳᄅ ᅩᄉ ᆼᄀ ᅢ ᆨᅡ ᅡ ᆯ ᄒᄉ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᄉ ᆼᄐ ᅡ ᅢ 1ᄋ ᆫᄃ ᅳ ᅢᄇ ᅮᄇ ᆫᄋ ᅮ ᅴᄌ ᆯᄆ ᅵ ᆫᄋ ᅮ ᅦᄃ ᅢᄒ ᅡᄋ ᅧᄇ ᅮᄌ ᆼᄌ ᅥ ᆨᄋ ᅥ ᅵᄌ ᅵᄃ ᅩᄀ ᆼᄌ ᅳ ᆼᄌ ᅥ ᆨᄋ ᅥ ᅵᄌ ᅵᄃ ᅩᄋ ᆭᄋ ᅡ ᆫᄃ ᅳ ᆸᄇ ᅡ ᆫ ᅧ ᆯᄒ ᅳ ᄋ ᆫᆸ ᅡ ᅵᄃ ᄌ ᆫᄋ ᅡ ᅵᄀ ᅩᄉ ᆼᄐ ᅡ ᅢ 5ᄂ ᆫᄇ ᅳ ᅮᄌ ᆼᄌ ᅥ ᆨᄃ ᅥ ᆸᄇ ᅡ ᆫᄋ ᅧ ᅴᄋ ᆼᄃ ᅳ ᆸᄇ ᅡ ᅵᄋ ᆯᄋ ᅲ ᅵᄂ ᇁᄋ ᅩ ᆫᄌ ᅳ ᆸᄃ ᅵ ᆫᄋ ᅡ ᅵᄅ ᅡᄀ ᅩᄉ ᆼᄀ ᅢ ᆨᅡ ᅡ ᆯ ᄒᄉ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᅵᅥ ᄋ ᄅᄒ ᆫᄃ ᅡ ᅡᄉ ᆺᄀ ᅥ ᅡᄌ ᅵᄉ ᆼᄐ ᅡ ᅢᄋ ᅴᄌ ᆫᄋ ᅥ ᅵᄒ ᆼᅧ ᅢ ᆯ ᄅᄋ ᆯᄇ ᅳ ᅩᄆ ᆫ, ᄎ ᅧ ᅩᄃ ᆼᄒ ᅳ ᆨᄀ ᅡ ᅭ 4ᄒ ᆨᅧ ᅡ ᆫ ᄂᄋ ᅦᄉ ᅥ 5ᄒ ᆨᅧ ᅡ ᆫ ᄂᄋ ᅳᄅ ᅩᄒ ᆨᅧ ᅡ ᆫ ᄂᄋ ᅵᄋ ᆯᄅ ᅩ ᅡᄀ ᆯᄀ ᅡ ᆼᄋ ᅧ ᅮ, ᄃ ᅢᄇ ᅮ ᆫᄋ ᅮ ᄇ ᅵᄌ ᆫᄉ ᅥ ᆼᄐ ᅡ ᅢᄋ ᅦᄆ ᅥᄆ ᅮᄅ ᅳᄂ ᆫᄀ ᅳ ᆼᄒ ᅧ ᆼᄋ ᅣ ᆯᄇ ᅳ ᅩᄋ ᅵᄌ ᅵᄆ ᆫᄉ ᅡ ᆼᄐ ᅡ ᅢ 4ᄋ ᅦᄉ ᅥᄉ ᆼᄐ ᅡ ᅢ 3ᄋ ᅳᄅ ᅩᄋ ᅵᄃ ᆼᄒ ᅩ ᅡᄅ ᅧᄂ ᆫᄒ ᅳ ᆨᅢ ᅡ ᆼ ᄉᄋ ᅵᄉ ᆼᅡ ᅡ ᆼ ᄃᄉ ᅮᄋ ᆻᄂ ᅵ ᆫᄀ ᅳ ᆺᄋ ᅥ ᅳ ᅩᄇ ᄅ ᅩᅵ ᄋᄃ ᆫ ᅡ. ᄋ ᅵᄅ ᆯᄐ ᅳ ᆼᄒ ᅩ ᅢᄇ ᆯᄄ ᅩ ᅢᄒ ᆨᄀ ᅡ ᅭᄉ ᆼᄒ ᅢ ᆯᄋ ᅪ ᅦᄌ ᆨᄀ ᅥ ᆨᄌ ᅳ ᆨᄋ ᅥ ᅵᄀ ᅩᄒ ᆨᅥ ᅡ ᆸ ᄋᄉ ᆼᄎ ᅥ ᅱᄃ ᅩᄂ ᆫᄇ ᅳ ᅩᄐ ᆼᄋ ᅩ ᅵᄋ ᆻᄃ ᅥ ᆫᄎ ᅥ ᅩᄃ ᆼᄒ ᅳ ᆨᅢ ᅡ ᆼ ᄉᄃ ᆯᄋ ᅳ ᅵᄒ ᆨᅧ ᅡ ᆫ ᄂᄋ ᅵᄋ ᆯ ᅩ.
(9) Latent transition model for mixed variable with applications to youth’s study habits and academic achievement657. Table 4.2 Estimated item-response probabilities in LTM Status prevalence at time 1 well done Korean medium poor well done Math medium poor well done English medium poor Interest level did well in class did not well Achievement level did well of school homework did not well Understanding level did well in class did not well Actively asking did well questions did not well. Status 1 0.236 0.418 0.493 0.089 0.339 0.402 0.259 0.457 0.390 0.154 0.393 0.607 0.494 0.506 0.445 0.555 0.609 0.391. Status 2 0.563 0.847 0.130 0.023 0.815 0.143 0.042 0.867 0.103 0.030 0.877 0.123 0.929 0.071 0.974 0.026 0.934 0.066. Status 3 0.042 0.208 0.293 0.499 0.127 0.145 0.728 0.101 0.118 0.780 0.769 0.231 0.767 0.233 0.790 0.210 0.889 0.111. Status 4 0.154 0.176 0.789 0.035 0.137 0.724 0.139 0.187 0.697 0.116 0.882 0.118 0.852 0.148 0.894 0.106 0.929 0.071. Status 5 0.032 0.059 0.192 0.749 0.035 0.085 0.880 0.014 0.077 0.908 0.254 0.746 0.182 0.818 0.049 0.951 0.417 0.583. Table 4.3 Estimated transition probabilities in LTM. Transition probability at time 1 to time 2. Transition probability at time 2 to time 3 Status prevalence Status prevalence Status prevalence. Status 1 Status 2 Status 3 Status 4 Status 5 Status 1 Status 2 Status 3 Status 4 Status 5 at time 1 at time 2 at time 3. Status 1 0.391 0.117 0.000 0.092 0.000 0.554 0.073 0.082 0.069 0.070 0.236 0.169 0.155. Status 2 0.020 0.566 0.000 0.060 0.000 0.179 0.804 0.025 0.169 0.006 0.536 0.318 0.327. Status 3 0.201 0.099 0.735 0.416 0.148 0.167 0.000 0.519 0.254 0.125 0.042 0.200 0.198. Status 4 0.153 0.205 0.000 0.394 0.098 0.048 0.118 0.218 0.476 0.049 0.154 0.210 0.194. Status 5 0.235 0.013 0.265 0.037 0.753 0.051 0.005 0.156 0.033 0.750 0.032 0.104 0.126. Table 4.4 Interpretation of each latent status from LTM Status Status Status Status Status. 1 2 3 4 5. Academic achievement Medium High Low Medium Low. Positiveness in school Medium High High High High. ᄅᄀ ᅡ ᆯᄉ ᅡ ᅮᄅ ᆨᄒ ᅩ ᆨᅥ ᅡ ᆸ 어 ᆼ ᄉᄎ ᅱᄃ ᅩᄀ ᅡᄂ ᆽᄋ ᅡ ᆫᄌ ᅳ ᆸᄃ ᅵ ᆫᄋ ᅡ ᅳᄅ ᅩᄆ ᆭᄋ ᅡ ᅵᄋ ᅵᄃ ᆼᄒ ᅩ ᆻᄃ ᅢ ᅡᄀ ᅩᄑ ᆫᅡ ᅡ ᆫ ᄃᄒ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᄄ ᅩᄒ ᆫᄌ ᅡ ᆼᄒ ᅮ ᆨᄀ ᅡ ᅭ 1ᄒ ᆨᅧ ᅡ ᆫ ᄂᄋ ᅦᄉ ᅥ 2ᄒ ᆨᅧ ᅡ ᆫ ᄂ ᅳᄅ ᄋ ᅩᄋ ᆯᄅ ᅩ ᅡᄀ ᆯᄄ ᅡ ᅢᄀ ᅡᄎ ᅩᄃ ᆼᄒ ᅳ ᆨᄀ ᅡ ᅭ 6ᄒ ᆨᅧ ᅡ ᆫ ᄂᄋ ᅦᄉ ᅥᄌ ᆼᄒ ᅮ ᆨᄀ ᅡ ᅭ 1ᄒ ᆨᅧ ᅡ ᆫ ᄂᄋ ᅳᄅ ᅩᄋ ᆯᄅ ᅩ ᅡᄀ ᅡᄂ ᆫᄄ ᅳ ᅢᄇ ᅩᄃ ᅡᄌ ᆫᄇ ᅥ ᆫᄌ ᅡ ᆨᄋ ᅥ ᅳᄅ ᅩᄉ ᆼᄐ ᅡ ᅢᄃ ᆯᄋ ᅳ ᅴᄌ ᆫᄋ ᅥ ᅵᄀ ᅡ ᆯᄋ ᅥ ᄃ ᆯᄋ ᅵ ᅥᄂ ᆷᄋ ᅡ ᆯᄋ ᅳ ᆯᄉ ᅡ ᅮᄋ ᆻᄋ ᅵ ᅳᄆ ᅧ, ᄎ ᅩᄃ ᆼᄒ ᅳ ᆨᄀ ᅡ ᅭ 6ᄒ ᆨᅧ ᅡ ᆫ ᄂᄄ ᅢᄂ ᆫᄉ ᅳ ᆼᄐ ᅡ ᅢ 2ᄋ ᅦᄆ ᅥᄆ ᆯᄅ ᅮ ᆻᅥ ᅥ ᆫ ᄃᄌ ᆸᄃ ᅵ ᆫᄋ ᅡ ᅵ 50% ᄋ ᅵᄉ ᆼᄀ ᅡ ᅳᄅ ᅵᄀ ᅩᄉ ᆼᄐ ᅡ ᅢ 5ᄋ ᅦ ᆨᄒ ᅩ ᄉ ᆻᅥ ᅢ ᆫ ᄃᄌ ᆸᄃ ᅵ ᆫᄋ ᅡ ᅵ 5% ᄋ ᅵᄒ ᅡᄋ ᆻᅥ ᅧ ᆫ ᄃᄀ ᆺᄋ ᅥ ᅦᄇ ᅵᄒ ᅢᄌ ᆼᄒ ᅮ ᆨᄀ ᅡ ᅭ 2ᄒ ᆨᅧ ᅡ ᆫ ᄂᄄ ᅢᄂ ᆫᄆ ᅳ ᅩᄃ ᆫᄉ ᅳ ᆼᄐ ᅡ ᅢᄋ ᅦᄇ ᅵᄀ ᅭᄌ ᆨᄀ ᅥ ᅩᄅ ᅮᄇ ᆫᄑ ᅮ ᅩᅬ ᄃᄋ ᅥᄋ ᆻᄋ ᅵ ᆷᅳ ᅳ ᆯ ᄋᄋ ᆯ ᅡ ᅮᄋ ᄉ ᆻᅡ ᅵ ᄃ..
(10) 658. Kyuhyoung Kim · Miyoung Sung · Byungtae Seo. 4.3. LTMM 분석 LTMᄋ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᆫ 4.2ᄌ ᅡ ᆯᄋ ᅥ ᅦᄉ ᅥᄋ ᅴᄇ ᆫᄉ ᅮ ᆨᄋ ᅥ ᅦᄉ ᅥᄂ ᆫᄒ ᅳ ᆨᅥ ᅡ ᆸ ᄋᄀ ᆫᄅ ᅪ ᆫᄉ ᅧ ᅵᄀ ᆫᄋ ᅡ ᅦᄃ ᅢᄒ ᆫᅥ ᅡ ᆼ ᄌᄇ ᅩᄅ ᆯᄉ ᅳ ᅡᄋ ᆼᄒ ᅭ ᆯᄉ ᅡ ᅮᄋ ᆹᄋ ᅥ ᅥᄉ ᅥᄋ ᅵᄅ ᆯᄌ ᅳ ᅦᅬ 아 ᆫ ᄒ ᄇᄌ ᆷ ᅥ ᅮᄒ ᆼᄌ ᅧ ᅡᄅ ᅭᄆ ᆫᄋ ᅡ ᆯᄀ ᅳ ᅡᄌ ᅵᄀ ᅩᄇ ᆫᄉ ᅮ ᆨᄋ ᅥ ᆯᄒ ᅳ ᅡᄋ ᆻᄂ ᅧ ᆫᄃ ᅳ ᅦᄇ ᆫᄌ ᅩ ᆯᄋ ᅥ ᅦᄉ ᅥᄂ ᆫᄒ ᅳ ᆨᅥ ᅡ ᆸ ᄋᄀ ᆫᄅ ᅪ ᆫᄉ ᅧ ᅵᄀ ᆫᄋ ᅡ ᅦᄃ ᅢᄒ ᅡᄋ ᅧᄉ ᅥᄂ ᆫᄑ ᅳ ᅩᄋ ᅡᄉ ᆼᄇ ᅩ ᆫᄑ ᅮ ᅩᄅ ᆯᄀ ᅳ ᅡᄌ ᆼ ᅥ ᅡᄋ ᄒ ᅧ LTMMᄋ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᆫᄇ ᅡ ᆫᄉ ᅮ ᆨᄋ ᅥ ᆯᄌ ᅳ ᆫᄒ ᅵ ᆼᄒ ᅢ ᅡᄋ ᆻᄃ ᅧ ᅡ. LTMᄋ ᅦᄉ ᅥᄋ ᅪᄆ ᅡᄎ ᆫᄀ ᅡ ᅡᄌ ᅵᄅ ᅩᄌ ᆨᄃ ᅥ ᆼᅡ ᅡ ᆫ ᄒᄌ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄋ ᅴᄀ ᅢᄉ ᅮᄅ ᆯᄀ ᅳ ᆯᅥ ᅧ ᆼ ᄌᄒ ᅡ ᅵᄋ ᄀ ᅱᄒ ᅢᄆ ᆫᄌ ᅥ ᅥ 2ᄀ ᅢᄇ ᅮᄐ ᅥ 8ᄀ ᅢᄁ ᅡᄌ ᅵᄌ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄅ ᆯᄀ ᅳ ᅡᄌ ᅵᄂ ᆫᄆ ᅳ ᅩᄒ ᆼᄋ ᅧ ᅦᄃ ᅢᄒ ᅡᄋ ᅧ AIC, BIC, CAICᄅ ᆯ Table 4.5ᄋ ᅳ ᅦᄂ ᅡ ᅡᄂ ᄐ ᅢᅥ ᆻ ᄋᄃ ᅡ. ᄀ ᅨᄉ ᆫᄃ ᅡ ᆫ AIC, BIC, CAICᄅ ᅬ ᆯᄇ ᅳ ᅩᄋ ᆻᄋ ᅡ ᆯᄄ ᅳ ᅢ, AICᄂ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄋ ᅴᄉ ᅮᄀ ᅡ 8ᄀ ᅢᄋ ᆯᄄ ᅵ ᅢᄀ ᅡᄌ ᆼᄂ ᅡ ᆽᄋ ᅡ ᆻᄀ ᅡ ᅩ BIC, CAICᄂ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄋ ᅴᄉ ᅮᄀ ᅡ 7ᄀ ᅢᄋ ᆯᄄ ᅵ ᅢᄀ ᅡᄀ ᅡᄌ ᆼᄂ ᅡ ᆽᄋ ᅡ ᆻᄀ ᅡ ᅩᄇ ᆫᄉ ᅮ ᆨᄋ ᅥ ᅦᄂ ᆫᄌ ᅳ ᆷᄌ ᅡ ᅢᄉ ᆼᄐ ᅡ ᅢᄀ ᅡ 7ᄀ ᅢᄋ ᆫ LTMMᄋ ᅵ ᆯᄉ ᅳ ᅡᄋ ᆼᄒ ᅭ ᅡᄋ ᆻᄃ ᅧ ᅡ. LTMMᄌ ᆨᄒ ᅥ ᆸᄀ ᅡ ᆯᄀ ᅧ ᅪᄂ ᆫ Table 4.6, 4.7, 4.8ᄋ ᅳ ᅦᄌ ᆼᄅ ᅥ ᅵᄒ ᅡᄋ ᆻᄀ ᅧ ᅩᄌ ᆨᄒ ᅥ ᆸᄀ ᅡ ᆯᄀ ᅧ ᅪᄅ ᆯᄇ ᅳ ᅡᄐ ᆼᄋ ᅡ ᅳᄅ ᅩᄀ ᆨᄆ ᅡ ᅩᄉ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄀ ᅥ ᆹᄋ ᅡ ᅦᄄ ᅡᄅ ᆫ ᅳ ᆨᅡ ᅡ ᄀ ᆼ 새 ᄐᄃ ᆯᄋ ᅳ ᅴᄐ ᆨᄌ ᅳ ᆼᄋ ᅵ ᆯ 4.2ᄌ ᅳ ᆯᄋ ᅥ ᅦᄉ ᅥᄋ ᅪᄀ ᇀᄋ ᅡ ᅵ Table 4.9ᄋ ᅦᄂ ᅡᄐ ᅡᄂ ᅢᄋ ᆻᄃ ᅥ ᅡ. Table 4.5 AIC, BIC, and CAIC for different number of latent status in LTMM. AIC BIC CAIC. 2 93465 93645 93678. Number of latent status 3 4 5 6 91512 90807 90055 89695 91817 91259 90676 90507 91873 91342 90790 90656. 7 89202 90226 90414. 8 89018 90277 90508. Table 4.6 Estimated item-response probabilities in LTMM Status prevalence at time 1 well done Korean medium poor well done Math medium poor well done English medium poor Interest level did well in class did not well Achievement did well level of homework did not well Understanding did well level in class did not well Actively asking did well questions did not well. Status 1 0.216 0.707 0.218 0.075 0.646 0.184 0.169 0.752 0.154 0.094 0.502 0.498 0.690 0.310 0.688 0.312 0.747 0.253. Status 2 0.414 0.886 0.102 0.013 0.849 0.128 0.023 0.885 0.091 0.024 0.939 0.061 0.957 0.043 0.999 0.001 0.958 0.042. Status 3 0.031 0.077 0.166 0.757 0.018 0.049 0.933 0.026 0.057 0.918 0.260 0.740 0.190 0.810 0.081 0.919 0.419 0.581. Status 4 0.020 0.085 0.214 0.701 0.121 0.143 0.736 0.093 0.119 0.788 0.695 0.305 0.689 0.311 0.668 0.332 0.853 0.147. Status 5 0.119 0.140 0.777 0.083 0.125 0.661 0.214 0.174 0.623 0.203 0.423 0.577 0.369 0.631 0.372 0.628 0.544 0.456. Status 6 0.065 0.416 0.456 0.128 0.118 0.362 0.526 0.170 0.360 0.470 0.779 0.221 0.826 0.174 0.834 0.166 0.890 0.110. Status 7 0.134 0.190 0.761 0.048 0.213 0.640 0.147 0.268 0.603 0.129 0.902 0.098 0.879 0.121 0.913 0.037 0.939 0.061. Table 4.7 Estimated poisson mean parameters Private institute hours School homework hours Private institute homework hours Other study hours. Status 1 1.691 0.362 0.547 0.491. Status 2 1.696 0.512 0.755 1.001. Status 3 0.349 0.181 0.051 0.222. Status 4 1.490 0.449 0.464 0.519. Status 5 1.171 0.350 0.278 0.372. Status 6 0.094 0.683 0.000 0.999. Status 7 1.726 0.588 0.666 0.748. ᄀᄉ ᆨ ᅡ ᆼᄐ ᅡ ᅢᄋ ᅴᄌ ᆯᄆ ᅵ ᆫᄒ ᅮ ᆼᄆ ᅡ ᆨᄋ ᅩ ᅴᄋ ᆼᄃ ᅳ ᆸᄇ ᅡ ᅵᄋ ᆯᄆ ᅲ ᆾᄒ ᅵ ᆨᅥ ᅡ ᆸ ᄋᄀ ᆫᄅ ᅪ ᆫᄉ ᅧ ᅵᄀ ᆫᄋ ᅡ ᅴᄑ ᆼᄀ ᅧ ᆫᄋ ᅲ ᆯᄒ ᅳ ᆨᄋ ᅪ ᆫᄒ ᅵ ᆫᄀ ᅡ ᆯᄀ ᅧ ᅪ, ᄉ ᆼᄐ ᅡ ᅢ 1, 2ᄂ ᆫᄒ ᅳ ᆨᄋ ᅡ ᆸᅥ ᅥ ᆼ ᄉᄎ ᅱᄃ ᅩ ᅦᄉ ᄋ ᅥ “ᄌ ᆯᄒ ᅡ ᆻᄃ ᅢ ᅡ”ᄅ ᅩᄋ ᆼᄃ ᅳ ᆸᅡ ᅡ ᆫ ᄒᄇ ᅵᄋ ᆯᄋ ᅲ ᅵᄂ ᇁᄀ ᅩ ᅦᄂ ᅡᄐ ᅡᄂ ᆫᄀ ᅡ ᆺᄋ ᅥ ᅳᄅ ᅩᄇ ᅩᄋ ᅡᄒ ᆨᅥ ᅡ ᆸ 어 ᆼ ᄉᄎ ᅱᄃ ᅩᄀ ᅡᄂ ᇁᄋ ᅩ ᆫᄌ ᅳ ᆸᄃ ᅵ ᆫᄋ ᅡ ᅳᄅ ᅩᄑ ᆫᅡ ᅡ ᆫ 다 ᆯ ᄒᄉ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᅡᄌ ᄒ ᅵᄆ ᆫᅡ ᅡ ᆼ ᄉᄐ ᅢ 1ᄋ ᆫᄉ ᅳ ᆼᄐ ᅡ ᅢ 2ᄋ ᅦᄇ ᅵᄒ ᅢᄒ ᆨᄀ ᅡ ᅭᄉ ᆼᄒ ᅢ ᆯᄌ ᅪ ᆨᄀ ᅥ ᆨᄉ ᅳ ᆼᄋ ᅥ ᆫᄄ ᅳ ᆯᄋ ᅥ ᅥᄌ ᅧ “ᄀ ᅳᄅ ᆫᄑ ᅥ ᆫᄋ ᅧ ᅵᄃ ᅡ”ᄅ ᅡᄀ ᅩᄋ ᆼᄃ ᅳ ᆸᅡ ᅡ ᆫ ᄒᄇ ᅵᄋ ᆯᄋ ᅲ ᅵᄃ ᅥᄂ ᇁᄋ ᅩ ᆻᄃ ᅡ ᅡ. ᆼᄐ ᅡ ᄉ ᅢ 5ᄋ ᅪ 7ᄋ ᆫᄇ ᅳ ᅩᄐ ᆼᄉ ᅩ ᅮᄌ ᆫᄋ ᅮ ᅴᄒ ᆨᄋ ᅡ ᆸᅥ ᅥ ᆼ ᄉᄎ ᅱᄃ ᅩᄅ ᆯᄂ ᅳ ᅡᄐ ᅡᄂ ᆻᄌ ᅢ ᅵᄆ ᆫᄉ ᅡ ᆼᄐ ᅡ ᅢ 5ᄂ ᆫᄉ ᅳ ᆼᄐ ᅡ ᅢ 7ᄋ ᅦᄇ ᅵᄒ ᅢᄒ ᆨᄀ ᅡ ᅭᄉ ᆼᄒ ᅢ ᆯᄋ ᅪ ᅦᄃ ᅢᄒ ᆫᄌ ᅡ ᆨᄀ ᅥ ᆨᄉ ᅳ ᆼᄋ ᅥ ᅵ.
(11) Latent transition model for mixed variable with applications to youth’s study habits and academic achievement659. Table 4.8 Estimated transition probabilities in LTMM Status 1 Status 2 Status 3 Transition Status 4 probability Status 5 from time 1 to 2 Status 6 Status 7 Status 1 Status 2 Status 3 Transition Status 4 probability Status 5 from time 2 to 3 Status 6 Status 7 Status prevalence at time 1 Status prevalence at time 2 Status prevalence at time 3. Status 1 0.396 0.110 0.000 0.000 0.026 0.019 0.033 0.672 0.090 0.000 0.045 0.255 0.000 0.061 0.216 0.140 0.156. Status 2 0.008 0.535 0.000 0.000 0.000 0.000 0.067 0.105 0.782 0.000 0.018 0.000 0.000 0.160 0.414 0.232 0.231. Status 3 0.028 0.014 0.694 0.134 0.343 0.220 0.000 0.000 0.006 0.700 0.162 0.138 0.078 0.015 0.031 0.091 0.112. Status 4 0.188 0.019 0.118 0.820 0.185 0.115 0.359 0.025 0.000 0.067 0.471 0.170 0.033 0.112 0.020 0.146 0.119. Status 5 0.203 0.000 0.000 0.000 0.227 0.013 0.117 0.097 0.000 0.079 0.084 0.356 0.032 0.044 0.119 0.089 0.077. Status 6 0.057 0.083 0.154 0.046 0.024 0.633 0.040 0.044 0.010 0.154 0.000 0.018 0.811 0.056 0.065 0.101 0.188. Status 7 0.115 0.239 0.034 0.000 0.196 0.000 0.383 0.056 0.111 0.000 0.220 0.063 0.046 0.553 0.134 0.200 0.187. Table 4.9 Interpretation of each latent status from LTMM. Status Status Status Status Status Status Status. 1 2 3 4 5 6 7. Academic achievement High High Low Low Medium Medium Medium. Positiveness in school Medium High Low Medium Medium High High. Study hours in school Medium High Low Medium Medium High High. Study hours in private institute High High Low Medium Medium Low High. ᄂᄋ ᆽ ᅡ ᆫᄌ ᅳ ᆸᄃ ᅵ ᆫᄋ ᅡ ᅵᄅ ᅡᄀ ᅩᄇ ᆯᄉ ᅩ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᄉ ᆼᄐ ᅡ ᅢ 3, 4ᄂ ᆫᄒ ᅳ ᆨᅥ ᅡ ᆸ 어 ᆼ ᄉᄎ ᅱᄃ ᅩᄀ ᅡᄂ ᆽᄋ ᅡ ᆫᄒ ᅳ ᆨᅢ ᅡ ᆼ ᄉᄃ ᆯᄋ ᅳ ᅵᄌ ᅵᄆ ᆫᄉ ᅡ ᆼᄐ ᅡ ᅢ 4ᄋ ᅦᄉ ᆨᄒ ᅩ ᅡᄂ ᆫᄌ ᅳ ᆸᄃ ᅵ ᆫᄋ ᅡ ᆫᄉ ᅳ ᆼ ᅡ ᅢ 3ᄋ ᄐ ᅦᄇ ᅵᄒ ᅢᄇ ᅵᄀ ᅭᄌ ᆨᄒ ᅥ ᆨᄀ ᅡ ᅭᄉ ᆼᄒ ᅢ ᆯᄋ ᅪ ᅦᄌ ᆨᄀ ᅥ ᆨᄌ ᅳ ᆨᆫ ᅥ ᄋ ᅵᄌ ᆸᄃ ᅵ ᆫᄋ ᅡ ᅵᄅ ᅡᄀ ᅩᄒ ᅢᄉ ᆨᄒ ᅥ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᄉ ᆼᄐ ᅡ ᅢ 6ᄋ ᆫᄒ ᅳ ᆨᄀ ᅡ ᅭᄉ ᆼᄒ ᅢ ᆯᄌ ᅪ ᆨᄀ ᅥ ᆨᄉ ᅳ ᆼᄋ ᅥ ᆫᄋ ᅳ ᆻ ᅵ ᅳᄂ ᄋ ᅡᄇ ᅩᄐ ᆼᄋ ᅩ ᅵᄒ ᅡᄋ ᅴᄒ ᆨᅥ ᅡ ᆸ 어 ᆼ ᄉᄎ ᅱᄃ ᅩᄅ ᆯᄀ ᅳ ᆽᄂ ᅡ ᆫᄌ ᅳ ᆸᄃ ᅵ ᆫᄋ ᅡ ᅳᄅ ᅩᄒ ᅢᄉ ᆨᄒ ᅥ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᄒ ᆨᄀ ᅡ ᅭᄉ ᆼᄒ ᅢ ᆯᄌ ᅪ ᆨᄀ ᅥ ᆨᄉ ᅳ ᆼᄋ ᅥ ᅦᄃ ᅢᄒ ᆫᄋ ᅡ ᅵᄅ ᅥᄒ ᆫᄒ ᅡ ᅢᄉ ᆨᄋ ᅥ ᆫ ᅳ Table 4.7ᄋ ᅦᄉ ᅥ “ᄒ ᆨᄀ ᅡ ᅭᄉ ᆨᄌ ᅮ ᅦᄉ ᅵᄀ ᆫ”ᄋ ᅡ ᅴᅣ ᆼ ᄋᄋ ᆯᄀ ᅳ ᅩᄅ ᅧᄒ ᆻᄋ ᅢ ᆯᄄ ᅳ ᅢᄃ ᅩᄋ ᆯᄎ ᅵ ᅵᄃ ᆫᄀ ᅬ ᆼᄒ ᅧ ᆼᄋ ᅣ ᆯᄂ ᅳ ᅡᄐ ᅡᄂ ᆷᄋ ᅢ ᆯᄋ ᅳ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᄄ ᅩᄒ ᆫ Table ᅡ 4.7ᄋ ᆫᄒ ᅳ ᆨᄀ ᅡ ᅭᄋ ᅵᄋ ᅬᄋ ᅴᄀ ᆼᄇ ᅩ ᅮᄆ ᆾᄒ ᅵ ᆯᄃ ᅪ ᆼᄋ ᅩ ᅦᄃ ᅢᄒ ᆫᄌ ᅡ ᆼᄇ ᅥ ᅩᄃ ᅩᄌ ᅦᄀ ᆼᄒ ᅩ ᅢᄌ ᅮᄀ ᅩᄋ ᆻᄂ ᅵ ᆫᄃ ᅳ ᅦ, ᄋ ᅵᄅ ᆯᄇ ᅳ ᅡᄐ ᆼᄋ ᅡ ᅳᄅ ᅩᄇ ᅩᄆ ᆫᄉ ᅧ ᆼᄐ ᅡ ᅢ 1, 2, 7ᄋ ᆫ ᅳ ᅩᄃ ᄆ ᅮᄒ ᆨᄋ ᅡ ᆫᄋ ᅯ ᅵᄋ ᆼᄉ ᅭ ᅵᄀ ᆫᄋ ᅡ ᅵᄆ ᆭᄋ ᅡ ᆫᄌ ᅳ ᆸᄃ ᅵ ᆫ, ᄉ ᅡ ᆼᄐ ᅡ ᅢ 3ᄀ ᅪ 6ᄋ ᆫᄒ ᅳ ᆨᄋ ᅡ ᆫᄋ ᅯ ᅵᄋ ᆼᄉ ᅭ ᅵᄀ ᆫᄋ ᅡ ᅵᄌ ᆨᄋ ᅥ ᆫᄌ ᅳ ᆸᄃ ᅵ ᆫ, ᄉ ᅡ ᆼᄐ ᅡ ᅢ 4, 5ᄂ ᆫᄒ ᅳ ᆨᄋ ᅡ ᆫᄋ ᅯ ᅵᄋ ᆼᄉ ᅭ ᅵᄀ ᆫ ᅡ ᅵᄌ ᄋ ᆼᄀ ᅮ ᆫᄌ ᅡ ᆼᄃ ᅥ ᅩᄋ ᆫᄌ ᅵ ᆸᄃ ᅵ ᆫᄋ ᅡ ᅳᄅ ᅩᄇ ᆯᄉ ᅩ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᆨᅡ ᅡ ᄀ ᆼ ᄉᄐ ᅢᄋ ᅴᄌ ᆫᄋ ᅥ ᅵᄒ ᆨᄅ ᅪ ᆯᅳ ᅲ ᆯ ᄋᄒ ᆨᄋ ᅪ ᆫᄒ ᅵ ᅡᄆ ᆫ LTMᄀ ᅧ ᅪᄆ ᅡᄎ ᆫᄀ ᅡ ᅡᄌ ᅵᄅ ᅩᄀ ᆨᅡ ᅡ ᆼ ᄉᄐ ᅢᄋ ᅦᄆ ᅥᄆ ᆯᄅ ᅮ ᅧᄂ ᆫᄒ ᅳ ᆨᄅ ᅪ ᆯᄋ ᅲ ᅵᄂ ᇁᄀ ᅩ ᅦᄂ ᅡᄐ ᅡᄂ ᆻᄌ ᅡ ᅵᄆ ᆫᅡ ᅡ ᆼ ᄉ ᅢ 5ᄂ ᄐ ᆫᄉ ᅳ ᆼᄐ ᅡ ᅢ 3ᄋ ᅳᄅ ᅩᄇ ᅡᄁ ᅱᄅ ᅧᄂ ᆫᄒ ᅳ ᆨᄅ ᅪ ᆯᄋ ᅲ ᅵᄀ ᅡᄌ ᆼᄂ ᅡ ᇁᄋ ᅩ ᆻᄀ ᅡ ᅩᄉ ᆼᄐ ᅡ ᅢ 1ᄋ ᆫᄉ ᅳ ᆼᄐ ᅡ ᅢ 4, 5, 7ᄅ ᅩᄇ ᅡᄁ ᅱᄂ ᆫᄒ ᅳ ᆨᄅ ᅪ ᆯᄋ ᅲ ᅵᄋ ᅥᄂ ᅳᄌ ᆼᄃ ᅥ ᅩᄂ ᇁ ᅩ ᅦᄂ ᄀ ᅡᅪ ᆻ ᄋᄃ ᅡ. ᄃ ᅮᄇ ᆫᄍ ᅥ ᅢᄉ ᅵᄌ ᆷᄋ ᅥ ᅦᄉ ᅥᄉ ᅦᄇ ᆫᄍ ᅥ ᅢᄉ ᅵᄌ ᆷᄋ ᅥ ᅳᄅ ᅩᄀ ᆯᄄ ᅡ ᅢᄋ ᅦᄂ ᆫᄆ ᅳ ᅡᄎ ᆫᄀ ᅡ ᅡᄌ ᅵᄅ ᅩᄀ ᆨᅡ ᅡ ᆼ ᄉᄐ ᅢᄋ ᅦᄂ ᆷᄋ ᅡ ᅡᄋ ᆻᄂ ᅵ ᆫᄒ ᅳ ᆨᄅ ᅪ ᆯᄋ ᅲ ᅵᄂ ᇁᄋ ᅩ ᆫ ᅳ ᅡᄋ ᄀ ᆫᅦ ᅮ ᄃᄉ ᆼᄐ ᅡ ᅢ 4ᄂ ᆫᄉ ᅳ ᆼᄐ ᅡ ᅢ 3, ᄉ ᆼᄐ ᅡ ᅢ 7ᄅ ᅩᄇ ᅡᄁ ᅱᄂ ᆫᄒ ᅳ ᆨᄅ ᅪ ᆯᄋ ᅲ ᅵᄂ ᇁᄀ ᅩ ᅦᄂ ᅡᄐ ᅡᄂ ᆻᄀ ᅡ ᅩ, ᄉ ᆼᄐ ᅡ ᅢ 5ᄂ ᆫᄉ ᅳ ᆼᄐ ᅡ ᅢ 1, ᄉ ᆼᄐ ᅡ ᅢ 3, ᄉ ᆼᄐ ᅡ ᅢ 4ᄅ ᅩᄇ ᅡ ᅱᄅ ᄁ ᅧᄂ ᆫᄒ ᅳ ᆨᄅ ᅪ ᆯᄋ ᅲ ᅵᄂ ᇁᄀ ᅩ ᅦᄂ ᅡᄐ ᅡᄂ ᆻᄃ ᅡ ᅡ. ᄀ ᆨᄉ ᅡ ᆼᄐ ᅡ ᅢᄋ ᅴᄌ ᆫᄌ ᅩ ᅢᄇ ᅵᄋ ᆯᄋ ᅲ ᆯᄒ ᅳ ᆨᄋ ᅪ ᆫᄒ ᅵ ᅡᄆ ᆫᄉ ᅧ ᆼᄐ ᅡ ᅢ 1ᄋ ᆫᄉ ᅳ ᅵᄀ ᆫᄋ ᅡ ᅵᄇ ᆫᄒ ᅧ ᅪᅡ ᆯ ᄒᄄ ᅢᄆ ᅡᄃ ᅡᄀ ᆷᄉ ᅡ ᅩᄒ ᅡ ᅡᄀ ᄃ ᅡᄌ ᆼᄀ ᅳ ᅡᄒ ᅡᄂ ᆫᄆ ᅳ ᅩᄉ ᆸᅳ ᅳ ᆯ ᄋᄇ ᅩᄋ ᆻᄀ ᅧ ᅩᄉ ᆼᄐ ᅡ ᅢ 2, ᄉ ᆼᄐ ᅡ ᅢ 5ᄂ ᆫᄉ ᅳ ᅵᄀ ᆫᄋ ᅡ ᅵᄇ ᆫᄒ ᅧ ᅪᅡ ᆯ ᄒᄄ ᅢᄆ ᅡᄃ ᅡᄀ ᆷᄉ ᅡ ᅩᄒ ᅡᄂ ᆫᄆ ᅳ ᅩᄉ ᆸᅳ ᅳ ᆯ ᄋᄇ ᅩᄋ ᆻᄃ ᅧ ᅡ. ᄉ ᆼᄐ ᅡ ᅢ 3, ᆼᄐ ᅡ ᄉ ᅢ 6ᄋ ᆫᄉ ᅳ ᅵᄀ ᆫᄋ ᅡ ᅵᄇ ᆫᄒ ᅧ ᅪᅡ ᆯ ᄒᄄ ᅢᄆ ᅡᄃ ᅡᄌ ᆼᄀ ᅳ ᅡᄒ ᅡᄂ ᆫᄆ ᅳ ᅩᄉ ᆸᅳ ᅳ ᆯ ᄋᄇ ᅩᄋ ᆻᄀ ᅧ ᅩ, ᄉ ᆼᄐ ᅡ ᅢ 4, ᄉ ᆼᄐ ᅡ ᅢ 7ᄋ ᆫᄌ ᅳ ᆼᄀ ᅳ ᅡᄒ ᅡᄃ ᅡᄀ ᅡᄀ ᆷᄉ ᅡ ᅩᄒ ᅡᄂ ᆫᄆ ᅳ ᅩᄉ ᆸᅳ ᅳ ᆯ ᄋ ᅩᄋ ᄇ ᆻᅡ ᅧ ᄃ. ᆫᄉ ᅮ ᄇ ᆨᅧ ᅥ ᆯ ᄀᄀ ᅪᄅ ᆯᄇ ᅳ ᅡᄐ ᆼᄋ ᅡ ᅳᄅ ᅩᄂ ᆫᄋ ᅮ ᅧᄀ ᅧᄇ ᆯᄌ ᅩ ᆷᄋ ᅥ ᆫ, ᄎ ᅳ ᅩᄃ ᆼᄒ ᅳ ᆨᄀ ᅡ ᅭ 6ᄒ ᆨᅧ ᅡ ᆫ ᄂᄄ ᅢᄋ ᅦᄂ ᆫᄀ ᅳ ᆼᄇ ᅩ ᅮᄅ ᆯᄌ ᅳ ᆯᄒ ᅡ ᅡᄂ ᆫᄒ ᅳ ᆨᅢ ᅡ ᆼ ᄉᄃ ᆯᄋ ᅳ ᅵᄂ ᇁᄋ ᅩ ᆫᄇ ᅳ ᅵᄋ ᆯᄋ ᅲ ᆯᄎ ᅳ ᅡ ᅵᄒ ᄌ ᅡᅵ ᄌᄆ ᆫᄌ ᅡ ᆼᄒ ᅮ ᆨᄀ ᅡ ᅭᄋ ᅦᄋ ᆸᄒ ᅵ ᆨᄒ ᅡ ᆫᄋ ᅡ ᅵᄒ ᅮᄋ ᆫᄌ ᅵ ᆼᄒ ᅮ ᆨᄀ ᅡ ᅭ 1ᄒ ᆨᅧ ᅡ ᆫ ᄂᄄ ᅢᄋ ᅦᄂ ᆫᄀ ᅳ ᆼᄇ ᅩ ᅮᄅ ᆯᄌ ᅳ ᆯᄒ ᅡ ᅡᄂ ᆫᄒ ᅳ ᆨᅢ ᅡ ᆼ ᄉᄃ ᆯᄋ ᅳ ᅵᄀ ᆼᄇ ᅩ ᅮᄅ ᆯᄇ ᅳ ᅩᄐ ᆼᄉ ᅩ ᅮᄌ ᆫᄋ ᅮ ᅳᄅ ᅩ ᅡᄀ ᄒ ᅥᅡ ᄂᄆ ᆺᄒ ᅩ ᅡᄂ ᆫᄉ ᅳ ᆼᄐ ᅡ ᅢᄅ ᅩᄇ ᅡᄁ ᅱᄂ ᆫᄀ ᅳ ᆼᄒ ᅧ ᆼᄋ ᅣ ᆯᄇ ᅳ ᅩᄋ ᆷᄋ ᅵ ᆯᄋ ᅳ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᄋ ᅵᄂ ᆫᄎ ᅳ ᅩᄃ ᆼᄒ ᅳ ᆨᄀ ᅡ ᅭᄄ ᅢᄋ ᅦᄂ ᆫᄉ ᅳ ᆼᄃ ᅡ ᅢᄑ ᆼᄀ ᅧ ᅡᄅ ᆯᄉ ᅳ ᆯᄉ ᅵ ᅵᄒ ᅡᄌ ᅵᄋ ᆭ ᅡ.
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