If there were statistics that could be used to appropriately
test the fit of the data for each item to the Item Response
Theory (IRT) scales, decisions about the use of items within IRT
scales would be simple. Item fit statistics, such as those
provided by PARSCALE (Muraki and Bock 1997), provide a measure
of how closely the observed student item responses match what
the IRT models would predict. Most of the statistics of this
type that are available for use have distributions that are
unknown. Therefore, they cannot be used for final decisions
about the fit of the items to the IRT model. Because of the lack
of statistical tests for IRT model fit, the fit of the IRT
models to the observed data is visually examined within each
scale by comparing the empirical item response functions (IRFs)
with the theoretical curves. The primary means of accomplishing
this is to generate plots of empirical versus theoretical item
response curves. In practice, item fit statistics are used as a
way to identify items that need f