ᩘ⌮䞉⤫ィ㻌 㻞㻭㻹㻝㻟㻢 ᪥ᚰ➨ 㻣㻞 ᅇ䠄㻞㻜㻜㻤䠅㻌 ഥᖱႎࠍ↪ߚ㗄⋡ᔕℂ⺰ ٤❥▚↵㧝ጟ↰⻞㧝 㧔 ᧲੩ᄢቇᄢቇ㒮✚วᢥൻ⎇ⓥ⑼㧕 Key words: 㗄⋡ᔕℂ⺰ޔഥᖱႎ࠭ࠗࡌޔផ⺰ 㧝 ⋡ ⊛ ᧄႎ๔ߩ⋡⊛ߪੑߟߦ߹ߣࠄࠇࠆ(ޕ1)⥄ାᐲࠍഥᖱႎߣ ߒߡขࠅࠇࠆߎߣߦࠃߞߡޔ⢻ജ୯(ǰ㧕ߩផቯ♖ᐲࠍ㜞 ࠆߣหᤨߦⵍޔᬌ⠪ߦߟߡߩᣂߒઃട⊛ߥᖱႎࠍᓧࠆޕ (2)ᰴ⊛ߥലᨐߣߒߡޔฃᬌᆫߦ⦟ᓇ㗀ࠍਈ߃ࠆߎߣࠍ ᦼᓙߔࠆޕ ⛔⸘⊛ߦߪޔẜᄌᢙࠍዉߒߚࡌࠗ࠭㓏ጀࡕ࠺࡞ߢࠆ (Shigemasu, Yoshimura, Ohmori, 2000)࠭ࠗࡌޕ㓏ጀࡕ࠺࡞ߪޔ ታ〣⊛ߥ࠺࠲ಽᨆߩߚߩࡕ࠺࡞ߣߒߡߡࠊ߈ޔታ↪⊛ ߢࠆޕ ᣇ ᴺ ⸥ภߩ⚫ ࠕ࡞ࠧ࠭ࡓ㧔ࠡࡉࠬࠨࡦࡊࡦࠣ㧕 Step 1 : ੱࡄࡔ࠲(θ i , γ i , δ i )ߣ 㗄⋡ࡄࡔ࠲( β j )ߩೋᦼ୯⸳ቯ Step 2 : ẜᄌᢙ(ui , vi ) ߩ⊒↢ ( ᷹ⷰ୯ߩ᧦ઙߦว߁߽ߩߩߺᱷߔ) Step 3 : ࡄࡔ࠲(θ i , γ i , δ i )ߩᓟಽᏓ߆ࠄߩrandom draw Step 4 : ࡄࡔ࠲( β j )ߩ ᓟಽᏓ߆ࠄߩrandom draw Step 5 : ࡄࡔ࠲ⴕΡߩᓟಽᏓ߆ࠄߩrandom draw ߎߩࠕ࡞ࠧ࠭ࡓࠍㆡ↪ߔࠆ㓙ߦޔታ㓙ߩ࠺࠲ߦࠃߞߡ ⚂߇↢ߓࠆࠍࠄࠇߘޕߔࠆޕ ᱜ╵ ( x ij = 1)ߩߣ߈ uθ ij > v ij ᱜ╵߆ߟ⥄ାࠅ ( y ij = 1)ߩߣ߈ ࡕ࠺࡞ P ( xij = 1) = P(u θ ij > vij ) ≡ π ij (θ i ) u γ ij > 0 vij ~ N ( β j ,1) P ( yij = 1 | xij = 1) = P (uγ ij > 0) ≡ π ij (γ i ), ⺋╵߆ߟ⥄ାߥߒ ( y ij = 0 )ߩߣ߈ u δ ij > 0 P ( yij = 0 | xij = 0) = P (uδ ij > 0) ≡ π ij (δ i ) ታ࠺࠲߳ߩㆡ↪ ᧄࡕ࠺࡞ࠍታ㓙ߩᔃℂቇߩ࠹ࠬ࠻ߦㆡ↪ߔࠆޔߪ࠻ࠬ࠹ߩߎޕ 10 ߩ 4 ᨑㆬᛯߩㇱಽߣޔ4 ߩ⺰ㅀᑼ࠹ࠬ࠻ߢࠆᧄޕႎ ๔ߢឭ᩺ߔࠆࡕ࠺࡞߇⏕ޔାᐲᖱႎࠍടߔࠆߎߣߦࠃߞߡޔ ታ⾰⊛ߥᖱႎࠍᓧߡࠆߣߔࠇ߫ޔഥᖱႎࠍ⚵ߺࠇߚᧄ ࡕ࠺࡞ߦࠃࠆ⌀ߩ୯ߩផቯ୯ߪ⺰ޔㅀᑼᬌᩏߩᚑ❣ߣࠃࠅ㜞 ⋧㑐ࠍ␜ߔߎߣ߇ᦼᓙߐࠇࠆޕ ೨ಽᏓ ⚿ ᨐ 70 ฬߩ࠺࠲ߦኻߒߡޔㅢᏱߩ㗄⋡ᔕℂ⺰ߦࠃࠆ⌀ߩቇ ജߩផቯ୯ߣᧄޔႎ๔ߢផቯ୯ࠍᓧߚ⺰ߩࠇߙࠇߘޕㅀᑼᬌ ᩏᓧὐߣߩ⋧㑐ଥᢙߪޔࠇߙࠇߘޔ0.30 ߣޔ0.33 ߢߞߚޕ ⠨ ኤ ⋧㑐ଥᢙߪޔឭ᩺ߔࠆࡕ࠺࡞ࠍㆡ↪ߒߚ߶߁߇㜞ߊߚ߇ޔ ᦼᓙ߶ߤߢߪߥޕߦޔฃᬌᘒᐲߦኻߔࠆࠃᓇ㗀߇ࠆ ߎߣࠍᢵ㈨ߒߚߣߒߡ߽ࠍ࡞࠺ࡕߩߎߦ․ޔផᅑߔࠆℂ↱ߦ ߪߥࠄߥᓸᒙߥᏅߢࠆࠄ߈ࠍ࡞࠺ࡕߩߎޔߒ߆ߒޕ ࠆߩ߽ᣧߔ߉ࠆߣ⠨߃ࠆߩߎޕᓟୃߩ࡞࠺ࡕޔᱜࠍ⠨߃ࠆߎ ߣߩ࡞࠺ࡕᧄޔㆡ↪߇ታ⾰⊛ߥᡷༀࠍ↢ߓࠆࠃ߁ߥ⁁ᴫࠍត ߔߎߣࠍ᧪ߩ⺖㗴ߦߔࠆޕ ዕᐲ p (data | parameters) = ∏∏ (π i ij (γ i )π ij (θ i )) xij yij ((1 −π ij (γ i ))π ij (θ i )) j ((1 − π ij (δ i ))(1 − π ij (θ i ))) (π ij (δ i )(1 − π ij (θ i ))) xij (1− yij ) (1− xij )(1− yij ) (1− xij ) yij ᒁ↪ᢥ₂ Kazuo Shigemasu., Yoshimura, O., Nakamura, T. Bayesian Hierarchical Analysis of Polychotomous Item Responses. Behaviormetrika, 27(1), 51-65. 2000. 㧔Shigemasu Kazuo, Okada Kensuke㧕 㸫452㸫
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