rasch.pairwise: Pairwise Estimation Method of the Rasch Model

In alexanderrobitzsch/sirt: Supplementary Item Response Theory Models

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 class 'rasch.pairwise'
summary(object, digits=3, file=NULL, ...)

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

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)
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)

## Not run: 
#** 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) )

## End(Not run)

alexanderrobitzsch/sirt documentation built on Dec. 1, 2024, 2:18 a.m.