person.parameter.rasch.copula: Person Parameter Estimation of the Rasch Copula Model...

In sirt: Supplementary Item Response Theory Models

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

Description

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

## Not run: 
#############################################################################
# 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

## End(Not run)

sirt documentation built on May 29, 2024, 8:43 a.m.