It is a well-known problem in testing the fit of models to multinomial data that the full underlying contingency table will inevitably be sparse for tests of reasonable length and for realistic sample sizes. Under such conditions, full-information test statistics such as Pearson's X[superscript 2] and the likelihood ratio statistic G[superscript…

Despite the growing popularity of diagnostic classification models (e.g., Rupp, Templin, & Henson, 2010) in educational and psychological measurement, methods for testing their absolute goodness-of-fit to real data remain relatively underdeveloped. For tests of reasonable length and for realistic sample size, full-information test statistics…

In this article some results are presented relating to the dimensionality of instruments containing polytomously scored as well as dichotomously scored items, concentrating on the 1992 National Assessment of Educational Progress' (NAEP) mathematics and reading assessment data and several simulated datasets. The maximum likelihood factor analytic…