Last data update: 2014.03.03
R: Converts a theta Score into a True Score tau ( theta)
IRT.truescore R Documentation
Converts a θ Score into a True Score τ ( θ)
Description
Converts a θ score into an unweighted true score
τ ( θ) = ∑_i ∑_h h P_i ( θ ) .
In addition, a weighted true score
τ ( θ) = ∑_i ∑_h q_{ih} P_i ( θ )
can also be computed by specifying item-category weights
q_{ih} in the matrix Q
.
Usage
IRT.truescore(object, iIndex = NULL, theta = NULL, Q = NULL)
Arguments
object
Object for which the
CDM::IRT.irfprob
S3 method is defined
iIndex
Optional vector with item indices
theta
Optional vector with θ values
Q
Optional weighting matrix
Value
Data frame containing θ values and corresponding
true scores τ( θ ) .
See Also
See also sirt::truescore.irt
for a conversion function for generalized partial credit models.
Examples
#############################################################################
# EXAMPLE 1: True score conversion for a test with polytomous items
#############################################################################
data(data.Students, package="CDM")
dat <- data.Students[ , paste0("mj",1:4) ]
# fit partial credit model
mod1 <- tam.mml( dat ,control=list(maxiter=20) )
summary(mod1)
# true score conversion
tmod1 <- IRT.truescore( mod1 )
round( tmod1 , 4 )
# true score conversion with user-defined theta grid
tmod1b <- IRT.truescore( mod1 , theta=seq( -8,8, len=33 ) )
# plot results
plot( tmod1$theta , tmod1$truescore , type="l" ,
xlab=expression(theta) , ylab=expression(tau( theta ) ) )
points( tmod1b$theta , tmod1b$truescore , pch=16 , col="brown" )
## Not run:
#############################################################################
# EXAMPLE 2: True scores with different category weightings
#############################################################################
data(data.timssAusTwn.scored)
dat <- data.timssAusTwn.scored
# extract item response data
dat <- dat[ , grep("M03" , colnames(dat) ) ]
# select items with do have maximum score of 2 (polytomous items)
ind <- which( apply( dat , 2, max , na.rm=TRUE ) == 2 )
I <- ncol(dat)
# define Q-matrix with scoring variant
Q <- matrix( 1 , nrow=I , ncol=1 )
Q[ ind , 1 ] <- .5 # score of 0.5 for polyomous items
# estimate model
mod1 <- tam.mml( dat , Q=Q , irtmodel="PCM2" , control=list( nodes=seq(-10,10,len=61) ) )
summary(mod1)
# true score with scoring (0,1,2) which is the default of the function
tmod1 <- IRT.truescore(mod1)
# true score with user specified weighting matrix
Q <- mod1$B[,,1]
tmod2 <- IRT.truescore(mod1, Q=Q)
## End(Not run)
Results