sirt: rasch.pairwise – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

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 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.

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)

sirt

Supplementary Item Response Theory Models

v3.10-118

GPL (>= 2)

Authors

Alexander Robitzsch [aut,cre] (<https://orcid.org/0000-0002-8226-3132>)

Initial release

2021-09-22 17:45:34