sirt (version 3.12-66)

rasch.jml.jackknife1: 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)

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

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.

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

#############################################################################
# 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.