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)

Arguments

jmlobj

Output of rasch.jml

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} Hahn, J., & Newey, W. (2004). Jackknife and analytical bias reduction for nonlinear panel models. Econometrica, 72, 1295-1319. [object Object],[object Object] For JML estimation rasch.jml. For analytical bias correction methods see rasch.jml.biascorr. ############################################################################# # SIMULATED 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 <- sim.raschtype( rnorm( N ) , b ) colnames(dat) <- paste( "I" , 1:I , sep="") # estimate the Rasch model with JML mod <- rasch.jml( dat ) summary(mod) # re-estimate the Rasch model using Jackknife mod2 <- 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.Joint maximum likelihood (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.