IRT.jackknife function

Jackknifing an Item Response Model

This function performs a Jackknife procedure for estimating standard errors for an item response model. The replication design must be defined by IRT.repDesign. Model fit is also assessed via Jackknife.

Statistical inference for derived parameters is performed by IRT.derivedParameters with a fitted object of class IRT.jackknife and a list with defining formulas.

IRT.jackknife(object,repDesign, ... )

IRT.derivedParameters(jkobject, derived.parameters )

## S3 method for class 'gdina'
IRT.jackknife(object, repDesign, ...)

## S3 method for class 'IRT.jackknife'
coef(object, bias.corr=FALSE, ...)

## S3 method for class 'IRT.jackknife'
vcov(object, ...)

Arguments

• object: Objects for which S3 method IRT.jackknife is defined.
• repDesign: Replication design generated by IRT.repDesign.
• jkobject: Object of class IRT.jackknife.
• derived.parameters: List with defined derived parameters (see Example 2, Model 2).
• bias.corr: Optional logical indicating whether a bias correction should be employed.
• ...: Further arguments to be passed.

Returns

List with following entries - jpartable: Parameter table with Jackknife estimates

• parsM: Matrix with replicated statistics

• vcov: Variance covariance matrix of parameters

Examples

## Not run:

library(BIFIEsurvey)

#############################################################################
# EXAMPLE 1: Multiple group DINA model with TIMSS data | Cluster sample
#############################################################################

data(data.timss11.G4.AUT.part, package="CDM")

dat <- data.timss11.G4.AUT.part$data
q.matrix <- data.timss11.G4.AUT.part$q.matrix2
# extract items
items <- paste(q.matrix$item)

# generate replicate design
rdes <- CDM::IRT.repDesign( data=dat,  wgt="TOTWGT", jktype="JK_TIMSS",
                   jkzone="JKCZONE", jkrep="JKCREP" )

#--- Model 1: fit multiple group GDINA model
mod1 <- CDM::gdina( dat[,items], q.matrix=q.matrix[,-1],
            weights=dat$TOTWGT, group=dat$female +1  )
# jackknife Model 1
jmod1 <- CDM::IRT.jackknife( object=mod1, repDesign=rdes )
summary(jmod1)
coef(jmod1)
vcov(jmod1)

#############################################################################
# EXAMPLE 2: DINA model | Simple random sampling
#############################################################################

data(sim.dina, package="CDM")
data(sim.qmatrix, package="CDM")
dat <- sim.dina
q.matrix <- sim.qmatrix

# generate replicate design with 50 jackknife zones (50 random groups)
rdes <- CDM::IRT.repDesign( data=dat,  jktype="JK_RANDOM", ngr=50 )

#--- Model 1: DINA model
mod1 <- CDM::gdina( dat, q.matrix=q.matrix, rule="DINA")
summary(mod1)
# jackknife DINA model
jmod1 <- CDM::IRT.jackknife( object=mod1, repDesign=rdes )
summary(jmod1)

#--- Model 2: DINO model
mod2 <- CDM::gdina( dat, q.matrix=q.matrix, rule="DINO")
summary(mod2)
# jackknife DINA model
jmod2 <- CDM::IRT.jackknife( object=mod2, repDesign=rdes )
summary(jmod2)
IRT.compareModels( mod1, mod2 )

# statistical inference for derived parameters
derived.parameters <- list( "skill1"=~ 0 + I(prob_skillV1_lev1_group1),
    "skilldiff12"=~ 0 + I( prob_skillV2_lev1_group1 - prob_skillV1_lev1_group1 ),
    "skilldiff13"=~ 0 + I( prob_skillV3_lev1_group1 - prob_skillV1_lev1_group1 )
                    )
jmod2a <- CDM::IRT.derivedParameters( jmod2, derived.parameters=derived.parameters )
summary(jmod2a)
coef(jmod2a)
## End(Not run)