발표자 : 이세리
#install.packages("psych")
#install.packages("ltm")library(psych)
library(ltm)## Loading required package: MASS
## Loading required package: msm
## Loading required package: polycor
## Loading required package: mvtnorm
## Loading required package: sfsmisc
##
## Attaching package: 'polycor'
##
## The following object is masked from 'package:psych':
##
## polyserial
##
##
## Attaching package: 'ltm'
##
## The following object is masked from 'package:psych':
##
## factor.scores
data(bock)
class(lsat6)## [1] "matrix"
str(lsat6)## int [1:1000, 1:5] 0 0 0 0 0 0 0 0 0 0 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr [1:5] "Q1" "Q2" "Q3" "Q4" ...
head(lsat6)## Q1 Q2 Q3 Q4 Q5
## [1,] 0 0 0 0 0
## [2,] 0 0 0 0 0
## [3,] 0 0 0 0 0
## [4,] 0 0 0 0 1
## [5,] 0 0 0 0 1
## [6,] 0 0 0 0 1
summary(lsat6)## Q1 Q2 Q3 Q4
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:1.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:1.000
## Median :1.000 Median :1.000 Median :1.000 Median :1.000
## Mean :0.924 Mean :0.709 Mean :0.553 Mean :0.763
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.000 Max. :1.000 Max. :1.000 Max. :1.000
## Q5
## Min. :0.00
## 1st Qu.:1.00
## Median :1.00
## Mean :0.87
## 3rd Qu.:1.00
## Max. :1.00
lsat6[0:10,]## Q1 Q2 Q3 Q4 Q5
## [1,] 0 0 0 0 0
## [2,] 0 0 0 0 0
## [3,] 0 0 0 0 0
## [4,] 0 0 0 0 1
## [5,] 0 0 0 0 1
## [6,] 0 0 0 0 1
## [7,] 0 0 0 0 1
## [8,] 0 0 0 0 1
## [9,] 0 0 0 0 1
## [10,] 0 0 0 1 0
ord <- order(colMeans(lsat6), decreasing=TRUE)
ord## [1] 1 5 4 2 3
lsat6.sorted <- lsat6[, ord]
lsat6.sorted[0:10,]## Q1 Q5 Q4 Q2 Q3
## [1,] 0 0 0 0 0
## [2,] 0 0 0 0 0
## [3,] 0 0 0 0 0
## [4,] 0 1 0 0 0
## [5,] 0 1 0 0 0
## [6,] 0 1 0 0 0
## [7,] 0 1 0 0 0
## [8,] 0 1 0 0 0
## [9,] 0 1 0 0 0
## [10,] 0 0 1 0 0
describe(lsat6.sorted)## vars n mean sd median trimmed mad min max range skew kurtosis
## Q1 1 1000 0.92 0.27 1 1.00 0 0 1 1 -3.20 8.22
## Q5 2 1000 0.87 0.34 1 0.96 0 0 1 1 -2.20 2.83
## Q4 3 1000 0.76 0.43 1 0.83 0 0 1 1 -1.24 -0.48
## Q2 4 1000 0.71 0.45 1 0.76 0 0 1 1 -0.92 -1.16
## Q3 5 1000 0.55 0.50 1 0.57 0 0 1 1 -0.21 -1.96
## se
## Q1 0.01
## Q5 0.01
## Q4 0.01
## Q2 0.01
## Q3 0.02
Tau <- round(-qnorm(colMeans(lsat6.sorted)),2) #tau : estimates of threshold
#round : rounds the values in its first argument to the specified number of decimal places
#qnorm : quantile function with mean=0, sd=1
Tau## Q1 Q5 Q4 Q2 Q3
## -1.43 -1.13 -0.72 -0.55 -0.13
rasch(lsat6.sorted, constraint=cbind(ncol(lsat6.sorted)+1, 1.702))##
## Call:
## rasch(data = lsat6.sorted, constraint = cbind(ncol(lsat6.sorted) +
## 1, 1.702))
##
## Coefficients:
## Dffclt.Q1 Dffclt.Q5 Dffclt.Q4 Dffclt.Q2 Dffclt.Q3 Dscrmn
## -1.927 -1.507 -0.960 -0.742 -0.195 1.702
##
## Log.Lik: -2541
# constraint : The first column represents the item (p+1 - 문항변별력 discrimination parameter)
# the second column the value at which the corresponding parameter should be fixed