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, weights=NULL, conv=1e-04, maxiter=3000, progress=TRUE,
        b.init=NULL, zerosum=FALSE, power=1, direct_optim=TRUE)
# S3 method for rasch.pairwise
summary(object, digits=3, file=NULL, ...)

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

Arguments

dat: An \(N \times I\) data frame of dichotomous item responses
weights: Optional vector of sampling weights
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.
power: Power used for computing pairwise response probabilities like in row averaging approach
direct_optim: Logical indicating whether least squares criterion funcion should be minimized with stats::nlminb
object: Object of class rasch.pairwise
digits: Number of digits after decimal for rounding
file: Optional file name for summary output
...: Further arguments to be passed

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.

Examples

Run this code

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

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

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

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

if (FALSE) {
#** obtain standard errors by bootstrap
mod2$item$b   # extract item difficulties

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