Person Parameter Estimation of the Rasch Copula Model (Braeken, 2011)

Ability estimates as maximum likelihood estimates (MLE) are provided by the Rasch copula model.

Usage

person.parameter.rasch.copula(raschcopula.object, numdiff.parm=0.001,
    conv.parm=0.001, maxiter=20, stepwidth=1,
    print.summary=TRUE, ...)

Arguments

raschcopula.object

Object which is generated by the rasch.copula2 function.

numdiff.parm

Parameter \(h\) for numerical differentiation

conv.parm

Convergence criterion

maxiter

Maximum number of iterations

stepwidth

Maximal increment in iterations

print.summary

Print summary?

...

Further arguments to be passed

Value

A list with following entries

person

Estimated person parameters

se.inflat

Inflation of individual standard errors due to local dependence

theta.table

Ability estimates for each unique response pattern

pattern.in.data

Item response pattern

summary.theta.table

Summary statistics of person parameter estimates

See also

See rasch.copula2 for estimating Rasch copula models.

Examples

#############################################################################
# EXAMPLE 1: Reading Data
#############################################################################

data(data.read)
dat <- data.read

# define item cluster
itemcluster <- rep( 1:3, each=4 )
mod1 <- sirt::rasch.copula2( dat, itemcluster=itemcluster )
summary(mod1)

# person parameter estimation under the Rasch copula model
pmod1 <- sirt::person.parameter.rasch.copula(raschcopula.object=mod1 )
## Mean percentage standard error inflation
##   missing.pattern Mperc.seinflat
## 1               1           6.35

if (FALSE) {
#############################################################################
# EXAMPLE 2: 12 items nested within 3 item clusters (testlets)
#   Cluster 1 -> Items 1-4; Cluster 2 -> Items 6-9;  Cluster 3 -> Items 10-12
#############################################################################

set.seed(967)
I <- 12                             # number of items
n <- 450                            # number of persons
b <- seq(-2,2, len=I)               # item difficulties
b <- sample(b)                      # sample item difficulties
theta <- stats::rnorm( n, sd=1 ) # person abilities
# itemcluster
itemcluster <- rep(0,I)
itemcluster[ 1:4 ] <- 1
itemcluster[ 6:9 ] <- 2
itemcluster[ 10:12 ] <- 3
# residual correlations
rho <- c( .35, .25, .30 )

# simulate data
dat <- sirt::sim.rasch.dep( theta, b, itemcluster, rho )
colnames(dat) <- paste("I", seq(1,ncol(dat)), sep="")

# estimate Rasch copula model
mod1 <- sirt::rasch.copula2( dat, itemcluster=itemcluster )
summary(mod1)

# person parameter estimation under the Rasch copula model
pmod1 <- sirt::person.parameter.rasch.copula(raschcopula.object=mod1 )
  ## Mean percentage standard error inflation
  ##   missing.pattern Mperc.seinflat
  ## 1               1          10.48
}