Thurstonian Thresholds and Wright Map for Item Response Models

The function IRT.threshold computes Thurstonian thresholds for item response models. It is only based on fitted models for which the IRT.irfprob does exist.

The function IRT.WrightMap creates a Wright map and works as a wrapper to the WrightMap::wrightMap function in the WrightMap package. Wright maps operate on objects of class IRT.threshold.

IRT.threshold(object, prob.lvl=.5, type="category")

# S3 method for IRT.threshold
print(x, ...)

IRT.WrightMap(object, ...)

# S3 method for IRT.threshold
IRT.WrightMap(object, label.items=NULL, ...)

Arguments

object	Object of fitted models for which IRT.irfprob exists.
prob.lvl	Requested probability level of thresholds.
type	Type of thresholds to be calculated. The default is category-wise calculation. If only one threshold per item should be calculated, then choose type="item". If an item possesses a maximum score of \(K_i\), then a threshold is defined as a value which produces an expected value of \(K_i /2\) (see Ali, Chang & Anderson, 2015).
x	Object of class IRT.threshold
label.items	Vector of item labels
...	Further arguments to be passed.

Value

Function IRT.threshold:
Matrix with Thurstonian thresholds

Function IRT.WrightMap:
A Wright map generated by the WrightMap package.

References

Ali, U. S., Chang, H.-H., & Anderson, C. J. (2015). Location indices for ordinal polytomous items based on item response theory (Research Report No. RR-15-20). Princeton, NJ: Educational Testing Service. doi: 10.1002/ets2.12065

See also

See the WrightMap::wrightMap function in the WrightMap package.

Examples

if (FALSE) {
#############################################################################
# EXAMPLE 1: Fitted unidimensional model with gdm
#############################################################################

data(data.Students)
dat <- data.Students

# select part of the dataset
resp <- dat[, paste0("sc",1:4) ]
resp[ paste(resp[,1])==3,1] <-  2
psych::describe(resp)

# Model 1: Partial credit model in gdm
theta.k <- seq( -5, 5, len=21 )   # discretized ability
mod1 <- CDM::gdm( dat=resp, irtmodel="1PL", theta.k=theta.k, skillspace="normal",
              centered.latent=TRUE)

# compute thresholds
thresh1 <- TAM::IRT.threshold(mod1)
print(thresh1)
IRT.WrightMap(thresh1)

#############################################################################
# EXAMPLE 2: Fitted mutidimensional model with gdm
#############################################################################

data( data.fraction2 )
dat <- data.fraction2$data
Qmatrix <- data.fraction2$q.matrix3

# Model 1: 3-dimensional Rasch Model (normal distribution)
theta.k <- seq( -4, 4, len=11 )   # discretized ability
mod1 <- CDM::gdm( dat, irtmodel="1PL", theta.k=theta.k, Qmatrix=Qmatrix,
              centered.latent=TRUE, maxiter=10 )
summary(mod1)

# compute thresholds
thresh1 <- TAM::IRT.threshold(mod1)
print(thresh1)

#############################################################################
# EXAMPLE 3: Item-wise thresholds
#############################################################################

data(data.timssAusTwn.scored)
dat <- data.timssAusTwn.scored
dat <- dat[, grep("M03", colnames(dat) ) ]
summary(dat)

# fit partial credit model
mod <- TAM::tam.mml( dat )
# compute thresholds with tam.threshold function
t1mod <- TAM::tam.threshold( mod )
t1mod
# compute thresholds with IRT.threshold function
t2mod <- TAM::IRT.threshold( mod )
t2mod
# compute item-wise thresholds
t3mod <- TAM::IRT.threshold( mod, type="item")
t3mod
}