Bias Correction of Item Parameters for Joint Maximum Likelihood Estimation in the Rasch model

This function computes an analytical bias correction for the Rasch model according to the method of Arellano and Hahn (2007).

Usage

rasch.jml.biascorr(jmlobj,itemfac=NULL)

Arguments

jmlobj

An object which is the output of the rasch.jml function

itemfac

Number of items which are used for bias correction. By default it is the average number of item responses per person.

Value

A list with following entries

b.biascorr

Matrix of item difficulty estimates. The column b.analytcorr1 contains item difficulties by analytical bias correction of Method 1 in Arellano and Hahn (2007) whereas b.analytcorr2 corresponds to Method 2.

b.bias1

Estimated bias by Method 1

b.bias2

Estimated bias by Method 2

itemfac

Number of items which are used as the factor for bias correction

References

Arellano, M., & Hahn, J. (2007). Understanding bias in nonlinear panel models: Some recent developments. In R. Blundell, W. Newey & T. Persson (Eds.): Advances in Economics and Econometrics, Ninth World Congress, Cambridge University Press.

See also

See rasch.jml.jackknife1 for bias correction based on Jackknife.

See also the bife R package for analytical bias corrections.

Examples

#############################################################################
# EXAMPLE 1: Dataset Reading
#############################################################################
data(data.read)
dat <- data( data.read )

# estimate Rasch model
mod <- sirt::rasch.jml( data.read  )

# JML with analytical bias correction
res1 <- sirt::rasch.jml.biascorr( jmlobj=mod  )
print( res1$b.biascorr, digits=3 )
  ##        b.JML b.JMLcorr b.analytcorr1 b.analytcorr2
  ##   1  -2.0086   -1.8412        -1.908        -1.922
  ##   2  -1.1121   -1.0194        -1.078        -1.088
  ##   3  -0.0718   -0.0658        -0.150        -0.127
  ##   4   0.5457    0.5002         0.393         0.431
  ##   5  -0.9504   -0.8712        -0.937        -0.936
  ##  [...]