np.dich: Nonparametric Estimation of Item Response Functions

Description

This function does nonparametric item response function estimation (Ramsay, 1991).

Usage

np.dich(dat, theta, thetagrid, progress = FALSE, bwscale = 1.1,
       method = "normal")

Arguments

dat

An $N \times I$ data frame of dichotomous item responses

theta

Estimated theta values, for example weighted likelihood estimates from wle.rasch

thetagrid

A vector of theta values where the nonparametric item response functions shall be evaluated.

progress

Display progress?

bwscale

The bandwidth parameter $h$ is calculated by the formula $h=$bwscale$\cdot N^{-1/5}$

method

The default normal performs kernel regression with untransformed item responses. The method binomial uses nonparametric logistic regression implemented in the sm library.

Value

A list with following entries
datOriginal data frame
thetagridVector of theta values at which the item response functions are evaluated
thetaUsed theta values as person parameter estimates
estimateEstimated item response functions
...

References

Ramsay, J. O. (1991). Kernel smoothing approaches to nonparametric item characteristic curve estimation. Psychometrika, 56, 611-630.

Examples

Run this code

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

# estimate Rasch model
mod <- rasch.mml2( dat )
# WLE estimation
wle1 <- wle.rasch( dat=dat , b =mod$item$b )$theta
# nonparametric function estimation
np1 <- np.dich( dat=dat, theta= wle1, thetagrid = seq(-2.5 , 2.5 , len=100 ) )
print( str(np1))
# plot nonparametric item response curves
plot( np1 , b = mod$item$b )