Item Responce Theory
Rで項目反応理論 http://cogpsy.educ.kyoto-u.ac.jp/personal/Kusumi/datasem17/nishihata2.pdf
1 項目反応理論
data<-read.csv("gaku1.csv")
head(data)| X | V1 | V2 | V3 | V4 | V5 | V6 | V7 | V8 | V9 | V10 | V11 | V12 | V13 | V14 | V15 | V16 | V17 | V18 | V19 | V20 | V21 | V22 | V23 | V24 | V25 | V26 | V27 | V28 | V29 | V30 | V31 | V32 | V33 | V34 | V35 | V36 | V37 | V38 | V39 | V40 | V41 | V42 | V43 | V44 | V45 | V46 | V47 | V48 | V49 | V50 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 |
| 2 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |
| 3 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 |
| 4 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
| 5 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
| 6 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
data2 <- subset(data,select=c("V2","V6","V7","V8","V11","V12","V14","V15","V16","V17","V18","V19","V20","V21","V22","V23","V24","V25","V26","V29","V30","V32","V33","V34","V35","V38","V40","V44","V46","V49"))
data3 <- subset(data,select=c("V2","V6","V7"))
head(data3)| V2 | V6 | V7 |
|---|---|---|
| 1 | 1 | 1 |
| 0 | 1 | 1 |
| 0 | 0 | 1 |
| 1 | 1 | 1 |
| 1 | 1 | 1 |
| 0 | 0 | 1 |
1.1 1母数モデル
ans1<-rasch(data3)
ans1$coef[1:3,1:2]## beta.i beta
## V2 1.1109080 0.74338
## V6 0.9659537 0.74338
## V7 1.9877085 0.74338ans1##
## Call:
## rasch(data = data3)
##
## Coefficients:
## Dffclt.V2 Dffclt.V6 Dffclt.V7 Dscrmn
## -1.494 -1.299 -2.674 0.743
##
## Log.Lik: -359.169par(mfrow = c(1, 3))
plot(ans1, type = "ICC")#項目特性曲線
plot(ans1, type = "IIC")#項目情報曲線
plot(ans1, type = "IIC", items = 0)#テスト情報曲線
1.2 2母数モデル
ans2 <- ltm(data3 ~ z1)
ans2$coef[1:3,1:2]## (Intercept) z1
## V2 1.0699909 0.5880481
## V6 0.9300407 0.5867876
## V7 2.3083251 1.2900666ans2##
## Call:
## ltm(formula = data3 ~ z1)
##
## Coefficients:
## Dffclt Dscrmn
## V2 -1.820 0.588
## V6 -1.585 0.587
## V7 -1.789 1.290
##
## Log.Lik: -358.96par(mfrow = c(1, 3))
plot(ans2, type = "ICC")#項目特性曲線
plot(ans2, type = "IIC")#項目情報曲線
plot(ans2, type = "IIC", items = 0)#テスト情報曲線