Chi-square techniques for testing goodness-of-fit in item response theory are shown to give incorrect results. A new measure, CB, based on cumulants is proposed which avoids the arbitrary nature of interval creation found in chi-square techniques. The distribution of CB is estimated using Monte Carlo techniques and critical values for testing goodness-of-fit are given.
Neel, John H.
"A New Goodness-of-Fit Test for Item Response Theory,"
Journal of Modern Applied Statistical Methods: Vol. 3
, Article 26.
Available at: http://digitalcommons.wayne.edu/jmasm/vol3/iss2/26