sirt (version 1.9-0)

person.parameter.rasch.copula: 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 code{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 <- rasch.copula2( dat , itemcluster = itemcluster )
summary(mod1)

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

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

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

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