rasch.jml.jackknife1: Jackknifing the IRT Model Estimated by Joint Maximum...

In sirt: Supplementary Item Response Theory Models

Jackknifing the IRT Model Estimated by Joint Maximum Likelihood (JML)

Description

Jackknife estimation is an alternative to other ad hoc proposed methods for bias correction (Hahn & Newey, 2004).

Usage

rasch.jml.jackknife1(jmlobj)

Arguments

jmlobj

Output of rasch.jml

Details

Note that items are used for jackknifing (Hahn & Newey, 2004). By default, all I items in the data frame are used as jackknife units.

Value

A list with following entries

item

A data frame with item parameters b.JML: Item difficulty from JML estimation b.JMLcorr: Item difficulty from JML estimation by applying the correction factor (I-1)/I b.jack: Item difficulty from Jackknife estimation b.jackse: Standard error of Jackknife estimation for item difficulties. Note that this parameter refer to the standard error with respect to item sampling b.JMLse: Standard error for item difficulties obtained from JML estimation

jack.itemdiff

A matrix containing all item difficulties obtained by Jackknife

References

Hahn, J., & Newey, W. (2004). Jackknife and analytical bias reduction for nonlinear panel models. Econometrica, 72, 1295-1319.

See Also

For JML estimation rasch.jml.

For analytical bias correction methods see rasch.jml.biascorr.

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Simulated data from the Rasch model
#############################################################################
set.seed(7655)
N <- 5000    # number of persons
I <- 11      # number of items
b <- seq( -2, 2, length=I )
dat <- sirt::sim.raschtype( rnorm( N ), b )
colnames(dat) <- paste( "I", 1:I, sep="")

# estimate the Rasch model with JML
mod <- sirt::rasch.jml(dat)
summary(mod)

# re-estimate the Rasch model using Jackknife
mod2 <- sirt::rasch.jml.jackknife1( mod )
  ##
  ##   Joint Maximum Likelihood Estimation
  ##   Jackknife Estimation
  ##   11 Jackknife Units are used
  ##   |--------------------PROGRESS--------------------|
  ##   |------------------------------------------------|
  ##
  ##          N     p  b.JML b.JMLcorr b.jack b.jackse b.JMLse
  ##   I1  4929 0.853 -2.345    -2.131 -2.078    0.079   0.045
  ##   I2  4929 0.786 -1.749    -1.590 -1.541    0.075   0.039
  ##   I3  4929 0.723 -1.298    -1.180 -1.144    0.065   0.036
  ##   I4  4929 0.657 -0.887    -0.806 -0.782    0.059   0.035
  ##   I5  4929 0.576 -0.420    -0.382 -0.367    0.055   0.033
  ##   I6  4929 0.492  0.041     0.038  0.043    0.054   0.033
  ##   I7  4929 0.409  0.502     0.457  0.447    0.056   0.034
  ##   I8  4929 0.333  0.939     0.854  0.842    0.058   0.035
  ##   I9  4929 0.264  1.383     1.257  1.229    0.065   0.037
  ##   I10 4929 0.210  1.778     1.617  1.578    0.071   0.040
  ##   I11 4929 0.154  2.266     2.060  2.011    0.077   0.044
#-> Item parameters obtained by jackknife seem to be acceptable.

## End(Not run)

sirt documentation built on May 29, 2024, 8:43 a.m.