Nonparametric Estimation of Item Response Functions

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

dat: Original data frame
thetagrid: Vector of theta values at which the item response functions are evaluated
theta: Used theta values as person parameter estimates
estimate: Estimated item response functions
...

References

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

Examples

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

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