sirt (version 1.5-0)

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
• 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 <- 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 )