sirt (version 1.9-0)

rasch.pairwise: Pairwise Estimation Method of the Rasch Model

Description

This function estimates the Rasch model with a minimum chi square estimation method (cited in Fischer, 2007, p. 544) which is a pairwise conditional likelihood estimation approach.

Usage

rasch.pairwise(dat, conv = 1e-04, maxiter = 3000, progress = TRUE, 
        b.init = NULL, zerosum = FALSE)

## S3 method for class 'rasch.pairwise':
summary(object,...)

Arguments

dat

An $N \times I$ data frame of dichotomous item responses

conv

Convergence criterion

maxiter

Maximum number of iterations

progress

Display iteration progress?

b.init

An optional vector of length $I$ of item difficulties

zerosum

Optional logical indicating whether item difficulties should be centered in each iteration. The default is that no centering is conducted.

object

Object of class rasch.pairwise

...

Further arguments to be passed

Value

• An object of class rasch.pairwise with following entries
• b
  Item difficulties
• eps
  Exponentiated item difficulties, i.e. eps=exp(-b)
• iter
  Number of iterations
• conv
  Convergence criterion
• dat
  Original data frame
• freq.ij
  Frequency table of all item pairs
• item
  Summary table of item parameters

References

Fischer, G. H. (2007). Rasch models. In C. R. Rao and S. Sinharay (Eds.), Handbook of Statistics, Vol. 26 (pp. 515-585). Amsterdam: Elsevier.

See Also

See summary.rasch.pairwise for a summary. A slightly different implementation of this conditional pairwise method is implemented in rasch.pairwise.itemcluster. Pairwise marginal likelihood estimation (also labeled as pseudolikelihood estimation) can be conducted with rasch.pml3.

Examples

#############################################################################
# EXAMPLE 1: Reading data set | pairwise estimation Rasch model
#############################################################################

data(data.read)

#*** Model 1: no constraint on item difficulties
mod1 <- rasch.pairwise( data.read )
summary(mod1)

#*** Model 2: sum constraint on item difficulties
mod2 <- rasch.pairwise( data.read , zerosum=TRUE)
summary(mod2)

mod2$item$b   # extract item difficulties

# Bootstrap for item difficulties
boot_pw <- function(data, indices ){   
        dd <- data[ indices , ] # bootstrap of indices
        mod <- rasch.pairwise( dd , zerosum=TRUE , progress=FALSE)
        mod$item$b   
    }
set.seed(986)
library(boot)
dat <- data.read
bmod2 <- boot::boot( dat , boot_pw , R =999 ) 
bmod2
summary(bmod2)
# quantiles for bootstrap sample (and confidence interval)
apply( bmod2$t , 2 , quantile, c(.025 ,.5 , .975) )