Q3 | R Documentation |
Q_3
Statistic (Yen, 1984)
This function estimates the Q_3
statistic according to Yen (1984).
The statistic Q_3
is calculated for every item pair (i,j)
which is the correlation between item residuals after fitting the Rasch model.
Q3(dat, theta, b, progress=TRUE)
dat |
An |
theta |
Vector of length |
b |
Vector of length |
progress |
Should iteration progress be displayed? |
A list with following entries
q3.matrix |
An |
q3.long |
Just the |
expected |
An |
residual |
An |
Q3.stat |
Vector with descriptive statistics of |
Yen, W. M. (1984). Effects of local item dependence on the fit and equating performance of the three-parameter logistic model. Applied Psychological Measurement, 8, 125-145.
For the estimation of the average Q_3
statistic within testlets see
Q3.testlet
.
For modeling testlet effects see mcmc.3pno.testlet
.
For handling local dependencies in IRT models see
rasch.copula2
, rasch.pml3
or
rasch.pairwise.itemcluster
.
#############################################################################
# EXAMPLE 1: data.read. The 12 items are arranged in 4 testlets
#############################################################################
data(data.read)
# estimate the Rasch model
mod <- sirt::rasch.mml2( data.read)
# estmate WLEs
mod.wle <- sirt::wle.rasch( dat=data.read, b=mod$item$b )
# calculate Yen's Q3 statistic
mod.q3 <- sirt::Q3( dat=data.read, theta=mod.wle$theta, b=mod$item$b )
## Yen's Q3 Statistic based on an estimated theta score
## *** 12 Items | 66 item pairs
## *** Q3 Descriptives
## M SD Min 10% 25% 50% 75% 90% Max
## -0.085 0.110 -0.261 -0.194 -0.152 -0.107 -0.051 0.041 0.412
# plot Q3 statistics
I <- ncol(data.read)
image( 1:I, 1:I, mod.q3$q3.matrix, col=gray( 1 - (0:32)/32),
xlab="Item", ylab="Item")
abline(v=c(5,9)) # borders for testlets
abline(h=c(5,9))
## Not run:
# obtain Q3 statistic from modelfit.sirt function which is based on the
# posterior distribution of theta and not on observed values
fitmod <- sirt::modelfit.sirt( mod )
# extract Q3 statistic
q3stat <- fitmod$itempairs$Q3
## > summary(q3stat)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.21760 -0.11590 -0.07280 -0.05545 -0.01220 0.44710
## > sd(q3stat)
## [1] 0.1101451
## End(Not run)
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