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1 . (22) * * (22)

2 .2 ( ) ( ) (?? ).3 *2 ( ) *2 2

3 ( ) *3 n N n < N N ( n N ) N ( ) ICC(Item Characteristic Curve, ) ( ) 2 *4 x ( ) f (x) = 2π e.5x2 Φ( f (x)) = f (x) f (x)dx *3 ( ) *4 Excel 3 3 A = 3. A2 = 2.95 A3 = 2.9 A2 = +3. NORMSDIST B = NormDist(A) k C k C k 3

4 Excel 2 f (x) f (x)dx + exp(.7 f (x)) () (exp) a, b, c 4

5 p j (x) = c j + c j + exp(.7a j (x b j )) (2) j a, b, c a =., b =., c =. a. a =. a = a=. a= a =. a =

6 .45.4 a=. a= a =. a = 2. /4 a a (= ) a.3 2. b b ( 6) b b b c c ( ) c a, b, c a, b 2 (a ) 3 6

7 b=. b=. b= b =.,., c=. c=.3 c= c =.,.3, ICC ICC ( +2., +3.) 96% ICC 7

8 5 7 (pass, ) P i j P j = P i j /N Q Q2 Q ICC 2.3 ICC ( ) θ θ i x% ( 8

9 ) i j i u i = [ ] a j, b j, c j θ i *5 f (u i θ i, a, b, c) = n f (u i j θ i, a j, b j, c j ) (3) j= f (u θ, a, b, c) = N i= n f (u i j θ i, a j, b j, c j ) (4) j= U θ i, a j, b j, c j U ( )?? IRT BILOG-MG 25 Easy Estimation( 2.4 IRT 2 52 ICC ( 9 5) F2 C B ICC D3 E *6 2 *7 G2 C3 G2 *5?? *6 *7 EasyEstimation 9

10 A B C D E F G A A2 A3 A B B2 B3 9 A ICC B ICC C C2 C D D2 C ICC 2 D ICC C3 N zwi z yi *8 6 G2 C3 ICC x = *8 w y

11 E E2 E F F2 3 E ICC 4 F ICC G G2 G3 5 G ICC C3 G2 6 G2 C3 ICC B w w F2 ICC 7 θ i

12 2 IRT itemid a j b j A A A A B B B C C C D D err err E.5 54 err err E E F F G G G ( ) (= ) IRT i θ i ˆθ i θ i ˆθ i e = θ i ˆθ i IRT IRT = 2

13 B F2 7 F2 B ICC θ i n n n /I(θ) I(θ) 3 I(θ i ) =.7 2 n a 2 j (p j(θ i ) c j ) 2 q j (θ i ) j= p j (θ i )( c j ) 2 2 I(θ i ) =.7 2 n a 2 j p j(θ i )q j (θ i ) j= I(θ i ) =.7 2 a 2 n p j (θ i )q j (θ i ) j= p j (θ) θ j q j (θ) q j (θ) = p j (θ) IRT θ I(θ) I(θ) θ = Max θ = 3

14 (Test Characteristic Curve) ˆθ θ /I(θ) θ i (= ) n E[y i θ i ] = w j p j (θ i ) w j j ( ) θ i j= TCC(x) "TCCsanpu.txt"

15 9 ˆθ i N TCC IRT 3 IRT / IRT 3. IRT ( ) 2 a j b j j c b jc 2 p jc (θ) = + exp(.7(θ b jc )) j θ c u j c (Boundary Charactaristic Curve) θ u j = c p(u j = c θ) p(u j = c θ) = p jc (θ) p jc+ (θ) (5) c =,, 2, 3 b jc b j =, b j2 =.5, b j3 =.2 p(u j = θ) = p j (θ) p j (θ) j u j =,, 2, 3 5

16 p j = *9, 2, 3 p(u j = θ) = 2 + exp(.7(θ b j )) θ θ p(u j = 3 θ) = p j3 (θ) p j4 (θ) p j4 3 4 p j4 = p(u j = 3 θ) = + exp(.7(θ b j3 )) 2 θ p(u j = θ) = + exp(.7(θ b j )) + exp(.7(θ b j2 )) *9 6

17 p(u j = 2 θ) = 22 + exp(.7(θ b j2 )) + exp(.7(θ b j3 )) c= c= (c = ) (c = 2) ICC b jc ( ) θ ( ) τ τ =. 7

18 23 θ τ 2 =.2 j z j θ z j = α j θ + e k IRT α j τ jc ( j c ) a j = α j / α 2 j b jc = τ jc/α j f θ f = θ u j c 5 SEM LISREL Mplus IRT 8

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