sirt: rasch.jml – R documentation

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rasch.jml

Joint Maximum Likelihood (JML) Estimation of the Rasch Model

Description

This function estimates the Rasch model using joint maximum likelihood estimation (Lincare, 1994). The PROX algorithm (Lincare, 1994) is used for the generation of starting values of item parameters.

Usage

rasch.jml(dat, method="MLE", b.init=NULL, constraints=NULL, weights=NULL,
    center="persons", glob.conv=10^(-6), conv1=1e-05, conv2=0.001, progress=TRUE,
    bsteps=4, thetasteps=2, wle.adj=0, jmliter=100, prox=TRUE,
    proxiter=30, proxconv=0.01, dp=NULL, theta.init=NULL, calc.fit=TRUE,
    prior_sd=NULL)

## S3 method for class 'rasch.jml'
summary(object, digits=3, ...)

Arguments

`dat`	An N \times I data frame of dichotomous item responses where N indicates the number of persons and I the number of items
`method`	Method for estimating person parameters during JML iterations. `MLE` is maximum likelihood estimation (where person with perfect scores are deleted from analysis). `WLE` uses weighted likelihood estimation (Warm, 1989) for person parameter estimation. Default is `MLE`.
`b.init`	Initial values of item difficulties
`constraints`	Optional matrix or data.frame with two columns. First column is an integer of item indexes or item names (`colnames(dat)`) which shall be fixed during estimation. The second column is the corresponding item difficulty.
`weights`	Person sample weights. Default is `NULL`, i.e. all persons in the sample are equally weighted.
`center`	Character indicator whether persons (`"persons"`), items (`"items"`) should be centered or (`"none"`) should be conducted.
`glob.conv`	Global convergence criterion with respect to the log-likelihood function
`conv1`	Convergence criterion for estimation of item parameters
`conv2`	Convergence criterion for estimation of person parameters
`progress`	Display progress? Default is `TRUE`

`bsteps`	Number of steps for b parameter estimation
`thetasteps`	Number of steps for theta parameter estimation
`wle.adj`	Score adjustment for WLE estimation
`jmliter`	Number of maximal iterations during JML estimation
`prox`	Should the PROX algorithm (see `rasch.prox`) be used as initial estimations? Default is `TRUE`.
`proxiter`	Number of maximal PROX iterations
`proxconv`	Convergence criterion for PROX iterations
`dp`	Object created from data preparation function (`.data.prep`) which could be created in earlier JML runs. Default is `NULL`.
`theta.init`	Initial person parameter estimate
`calc.fit`	Should itemfit being calculated?
`prior_sd`	Optional value for standard deviation of prior distribution for ability values if penalized JML should be utilized
`object`	Object of class `rasch.jml`
`digits`	Number of digits used for rounding
`...`	Further arguments to be passed

Details

The estimation is known to have a bias in item parameters for a fixed (finite) number of items. In literature (Lincare, 1994), a simple bias correction formula is proposed and included in the value item$itemdiff.correction in this function. If I denotes the number of items, then the correction factor is \frac{I-1}{I}.

Value

A list with following entries

`item`	Estimated item parameters
`person`	Estimated person parameters
`method`	Person parameter estimation method
`dat`	Original data frame
`deviance`	Deviance
`data.proc`	Processed data frames excluding persons with extreme scores
`dp`	Value of data preparation (it is used in the function `rasch.jml.jackknife1`)

References

Linacre, J. M. (1994). Many-Facet Rasch Measurement. Chicago: MESA Press.

Warm, T. A. (1989). Weighted likelihood estimation of ability in the item response theory. Psychometrika, 54, 427-450.

Examples

#############################################################################
# EXAMPLE 1: Simulated data from the Rasch model
#############################################################################

set.seed(789)
N <- 500    # number of persons
I <- 11     # number of items
b <- seq( -2, 2, length=I )
dat <- sirt::sim.raschtype( stats::rnorm( N, mean=.5 ), b )
colnames(dat) <- paste( "I", 1:I, sep="")

# JML estimation of the Rasch model (centering persons)
mod1 <- sirt::rasch.jml( dat )
summary(mod1)

# JML estimation of the Rasch model (centering items)
mod1b <- sirt::rasch.jml( dat, center="items" )
summary(mod1b)

# MML estimation with rasch.mml2 function
mod2 <- sirt::rasch.mml2( dat )
summary(mod2)

# Pairwise method of Fischer
mod3 <- sirt::rasch.pairwise( dat )
summary(mod3)

# JML estimation in TAM
## Not run: 
library(TAM)
mod4 <- TAM::tam.jml( resp=dat )

#******
# item parameter constraints in JML estimation
# fix item difficulties: b[4]=-.76 and b[6]=.10
constraints <- matrix( cbind( 4, -.76,
                              6, .10 ),
                  ncol=2, byrow=TRUE )
mod6 <- sirt::rasch.jml( dat, constraints=constraints )
summary(mod6)
  # For constrained item parameters, it this not obvious
  # how to calculate a 'right correction' of item parameter bias

## 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