ᩘ⌮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߹ߣ߼ࠄࠇࠆ‫(ޕ‬1)⥄ାᐲࠍ⵬ഥᖱႎߣ
ߒߡขࠅ౉ࠇࠆߎߣߦࠃߞߡ‫ޔ‬⢻ജ୯(ǰ㧕ߩផቯ♖ᐲࠍ㜞߼
ࠆߣหᤨߦ‫ⵍޔ‬ᬌ⠪ߦߟ޿ߡߩᣂߒ޿ઃട⊛ߥᖱႎࠍᓧࠆ‫ޕ‬
(2)೽ᰴ⊛ߥലᨐߣߒߡ‫ޔ‬ฃᬌᆫ൓ߦ⦟޿ᓇ㗀ࠍਈ߃ࠆߎߣࠍ
ᦼᓙߔࠆ‫ޕ‬
⛔⸘⊛ߦߪ‫ޔ‬ẜ࿷ᄌᢙࠍዉ౉ߒߚࡌࠗ࠭㓏ጀࡕ࠺࡞ߢ޽ࠆ
(Shigemasu, Yoshimura, Ohmori, 2000)‫࠭ࠗࡌޕ‬㓏ጀࡕ࠺࡞ߪ‫ޔ‬
ታ〣⊛ߥ࠺࡯࠲ಽᨆߩߚ߼ߩࡕ࠺࡞ߣߒߡ‫ߡ߼ࠊ߈ޔ‬ታ↪⊛
ߢ޽ࠆ‫ޕ‬
ᣇ ᴺ
⸥ภߩ⚫੺
ࠕ࡞ࠧ࡝࠭ࡓ㧔ࠡࡉࠬࠨࡦࡊ࡝ࡦࠣ㧕
Step 1 : ୘ੱࡄ࡜ࡔ࡯࠲(θ i , γ i , δ i )ߣ
㗄⋡ࡄ࡜ࡔ࡯࠲( β j )ߩೋᦼ୯⸳ቯ
Step 2 : ẜ࿷ᄌᢙ(ui , vi ) ߩ⊒↢
( ᷹ⷰ୯ߩ᧦ઙߦว߁߽ߩߩߺᱷߔ)
Step 3 : ࡄ࡜ࡔ࡯࠲(θ i , γ i , δ i )ߩ੐ᓟಽᏓ߆ࠄߩrandom draw
Step 4 : ࡄ࡜ࡔ࡯࠲( β j )ߩ ੐ᓟಽᏓ߆ࠄߩrandom draw
Step 5 : ࡄ࡜ࡔ࡯࠲ⴕ೉Ρߩ੐ᓟಽᏓ߆ࠄߩrandom draw
ߎߩࠕ࡞ࠧ࡝࠭ࡓࠍㆡ↪ߔࠆ㓙ߦ‫ޔ‬ታ㓙ߩ࠺࡯࠲ߦࠃߞߡ೙
⚂߇↢ߓࠆ‫ࠍࠄࠇߘޕ‬೉᜼ߔࠆ‫ޕ‬
ᱜ╵ ( x ij = 1)ߩߣ߈ Ÿ uθ ij > v ij
ᱜ╵߆ߟ⥄ା޽ࠅ ( y ij = 1)ߩߣ߈
ࡕ࠺࡞
P ( xij = 1) = P(u θ ij > vij ) ≡ π ij (θ i )
Ÿ 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
Ÿ 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࠹ࠬ࠻ߢ޽ࠆ‫ᧄޕ‬ႎ
๔ߢឭ᩺ߔࠆࡕ࠺࡞߇‫⏕ޔ‬ାᐲᖱႎࠍട๧ߔࠆߎߣߦࠃߞߡ‫ޔ‬
ታ⾰⊛ߥᖱႎࠍᓧߡ޿ࠆߣߔࠇ߫‫⵬ޔ‬ഥᖱႎࠍ⚵ߺ౉ࠇߚᧄ
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 ߢ޽ߞߚ‫ޕ‬
⠨ ኤ
⋧㑐ଥᢙߪ‫ޔ‬ឭ᩺ߔࠆࡕ࠺࡞ࠍㆡ↪ߒߚ߶߁߇㜞ߊ಴ߚ߇‫ޔ‬
ᦼᓙ߶ߤߢߪߥ޿‫ޕ‬઒ߦ‫ޔ‬ฃᬌᘒᐲߦኻߔࠆࠃ޿ᓇ㗀߇޽ࠆ
ߎߣࠍᢵ㈨ߒߚߣߒߡ߽‫ࠍ࡞࠺ࡕߩߎߦ․ޔ‬ផᅑߔࠆℂ↱ߦ
ߪߥࠄߥ޿ᓸᒙߥᏅߢ޽ࠆ‫߼ࠄ߈޽ࠍ࡞࠺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
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