Standard Error Estimation of WLE by Jackknifing
This function calculates standard errors of WLEs (Warm, 1989) for stratified item designs and item designs with testlets for the Rasch model.
wle.rasch.jackknife(dat, b, itemweights=1 + 0 * b, pid=NULL,
testlet=NULL, stratum=NULL, size.itempop=NULL)dat |
An N \times I data frame of item responses |
b |
Vector of item difficulties |
itemweights |
Weights for items, i.e. fixed item discriminations |
pid |
Person identifier |
testlet |
A vector of length I which defines which item belongs to which testlet. If some items does not belong to any testlet, then define separate testlet labels for these single items. |
stratum |
Item stratum |
size.itempop |
Number of items in an item stratum of the finite item population. |
The idea of Jackknife in item response models can be found in Wainer and Wright (1980).
A list with following entries:
wle |
Data frame with some estimated statistics. The column
|
wle.rel |
WLE reliability (Adams, 2005) |
Adams, R. J. (2005). Reliability as a measurement design effect. Studies in Educational Evaluation, 31(2-3), 162-172. doi: 10.1016/j.stueduc.2005.05.008
Gershunskaya, J., Jiang, J., & Lahiri, P. (2009). Resampling methods in surveys. In D. Pfeffermann and C.R. Rao (Eds.). Handbook of Statistics 29B; Sample Surveys: Inference and Analysis (pp. 121-151). Amsterdam: North Holland. doi: 10.1016/S0169-7161(09)00228-4
Wainer, H., & Wright, B. D. (1980). Robust estimation of ability in the Rasch model. Psychometrika, 45(3), 373-391. doi: 10.1007/BF02293910
Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54(3), 427-450. doi: 10.1007/BF02294627
#############################################################################
# EXAMPLE 1: Dataset Reading
#############################################################################
data(data.read)
dat <- data.read
# estimation of the Rasch model
res <- sirt::rasch.mml2( dat, parm.conv=.001)
# WLE estimation
wle1 <- sirt::wle.rasch(dat, b=res$item$thresh )
# simple jackknife WLE estimation
wle2 <- sirt::wle.rasch.jackknife(dat, b=res$item$thresh )
## WLE Reliability=0.651
# SE(WLE) for testlets A, B and C
wle3 <- sirt::wle.rasch.jackknife(dat, b=res$item$thresh,
testlet=substring( colnames(dat),1,1) )
## WLE Reliability=0.572
# SE(WLE) for item strata A,B, C
wle4 <- sirt::wle.rasch.jackknife(dat, b=res$item$thresh,
stratum=substring( colnames(dat),1,1) )
## WLE Reliability=0.683
# SE (WLE) for finite item strata
# A (10 items), B (7 items), C (4 items -> no sampling error)
# in every stratum 4 items were sampled
size.itempop <- c(10,7,4)
names(size.itempop) <- c("A","B","C")
wle5 <- sirt::wle.rasch.jackknife(dat, b=res$item$thresh,
stratum=substring( colnames(dat),1,1),
size.itempop=size.itempop )
## Stratum A (Mean) Correction Factor 0.6
## Stratum B (Mean) Correction Factor 0.42857
## Stratum C (Mean) Correction Factor 0
## WLE Reliability=0.876
# compare different estimated standard errors
a2 <- stats::aggregate( wle2$wle$wle.jackse, list( wle2$wle$wle), mean )
colnames(a2) <- c("wle", "se.simple")
a2$se.testlet <- stats::aggregate( wle3$wle$wle.jackse, list( wle3$wle$wle), mean )[,2]
a2$se.strata <- stats::aggregate( wle4$wle$wle.jackse, list( wle4$wle$wle), mean )[,2]
a2$se.finitepop.strata <- stats::aggregate( wle5$wle$wle.jackse,
list( wle5$wle$wle), mean )[,2]
round( a2, 3 )
## > round( a2, 3 )
## wle se.simple se.testlet se.strata se.finitepop.strata
## 1 -5.085 0.440 0.649 0.331 0.138
## 2 -3.114 0.865 1.519 0.632 0.379
## 3 -2.585 0.790 0.849 0.751 0.495
## 4 -2.133 0.715 1.177 0.546 0.319
## 5 -1.721 0.597 0.767 0.527 0.317
## 6 -1.330 0.633 0.623 0.617 0.377
## 7 -0.942 0.631 0.643 0.604 0.365
## 8 -0.541 0.655 0.678 0.617 0.384
## 9 -0.104 0.671 0.646 0.659 0.434
## 10 0.406 0.771 0.706 0.751 0.461
## 11 1.080 1.118 0.893 1.076 0.630
## 12 2.332 0.400 0.631 0.272 0.195Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.