Cara Cepat Transformasi dari Total Skore menjadi Logits
Heru Wiryanto
December 21, 2016
“Cara Cepat Transformasi dari Total Skore ke format Logit”
Apakah mungkin kita melakukan konversi Logit dari total skore seperti yang dilakukan oleh perhitungan rumus rasch model?. Bruce Thompson Menginformasikan kepada kita bahwa Fan (1998) dan MacDonald dan Paunonen (2002) mendukung persepsi bahwa korelasi antara skor mentah dengan hasil perhitungan Rasch Model selalu berkisar di nilai 0,97 ± 0,02, yaitu, dan hubungan yang terbentuk Efektif linier. Malec et al. (2000) melaporkan korelasi 0,98 untuk Ulasan data klinis mereka. Merujuk kepada hal tesebur maka hal ini bisa berlaku juga untuk data Anda dan mengijinkan Anda dapat mengkonversi skor mentah menjadi logits!
Rumus perhitungan bisa dilihat di : http://www.rasch.org/rmt/rmt162e.htm
Menarik data
Data Test dari bentuk csv
ctt.data <- read.csv("/home/heru/Desktop/test5.csv", header = TRUE, sep=",")
str(ctt.data)## 'data.frame': 49 obs. of 10 variables:
## $ A11: int 1 0 0 0 0 0 0 0 0 0 ...
## $ A12: int 1 1 1 1 1 1 1 1 1 1 ...
## $ A13: int 1 1 1 1 1 1 1 1 1 1 ...
## $ A14: int 1 1 1 1 1 1 1 1 1 1 ...
## $ A15: int 1 1 1 1 1 1 1 1 1 1 ...
## $ A16: int 1 0 0 0 0 0 0 0 0 0 ...
## $ A17: int 1 1 1 1 1 1 1 1 1 1 ...
## $ A18: int 0 1 1 1 1 1 1 1 1 1 ...
## $ A19: int 1 1 1 1 1 1 1 1 1 1 ...
## $ A20: int 1 1 1 1 1 1 1 1 1 1 ...# Ini Jawaban terhadap 10 Item
TKD<-ctt.data
responses <- as.matrix(ctt.data)
dimnames(responses) <- NULL
(N <- dim(responses)[2]) # Jumlah Item Test## [1] 10(K <- dim(responses)[1]) # Jumlah Peserta Test## [1] 49Menghitung Reliabilitas (dalam hal ini menggunakan Alpha Cornbach)
Menggunakan fungsi alpha cornbach maka dihasilkan sebesar
#Reliability
# Alpha Cornbachs
cronbachs.alpha <-
function(X){
X <- data.matrix(X)
n <- ncol(X) # Number of items
k <- nrow(X) # Number of examinees
# Cronbachs alpha
alpha <- (n/(n - 1))*(1 - sum(apply(X, 2, var))/var(rowSums(X)))
return(list("Crombach's alpha" = alpha,
"Number of items" = n,
"Number of examinees" = k))
}
dump("cronbachs.alpha", file = "responses")
# compute cronbachs alpha
a<-cronbachs.alpha(responses)
mat1<-matrix(a)
r<-mat1[1,1]
r1<-as.numeric(r)
print(r1)## [1] -0.8271355Melakukan transformasi ke bentuk Logit
Dengan menggunakan rumus :
Bn = (Rn - (Maximum score + Minimum score)/2 ) / S^2(1-R)
dimana - Bn = skore logit
Rn = raw score (total skore)
Maximum score = nilai maksimum dari total skore
Minimum score = nilai minimum dari total skore
S = standard deviasi dari total skore
R = Reliabilitas Total Skore
| A11 | A12 | A13 | A14 | A15 | A16 | A17 | A18 | A19 | A20 | score | Logit |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 9 | 1.958 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 9 | 1.958 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 7 | -0.653 |
| 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 7 | -0.653 |
| 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 8 | 0.653 |
| 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 8 | 0.653 |
| 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 7 | -0.653 |
| 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 6 | -1.958 |
| 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 9 | 1.958 |
## [1] 1Referensi :
Fan, X. (1998) Item Response Theory and classical test theory (CTT): An empirical comparison of their item/person statistics. Educational and Psychological Measurement, 58, 357-381.
MacDonald, P., & Paunonen, S.V. (2002) A Monte Carlo comparison of item and person statistics based on item response theory versus classical test theory. Educational and Psychological Measurement, 62.
Malec J. F., Moessner, A. M., Kragness, M., and Lezak, M.D. (2000) Refining a measure of brain injury sequelae to predict postacute rehabilitation outcome: rating scale analysis of the Mayo-Portland Adaptability Inventory (MPAI). Journal of Head Trauma Rehabilitation, 15 (1), 670-682.
Immediate raw score to logit conversion. Linacre, JM. … 16:2 p.877