To find population proficiency distributions, a two-level hierarchical linear model may be applied to large-scale survey assessments such as the National Assessment of Educational Progress (NAEP). The model and parameter estimation are developed and a simulation was carried out to evaluate parameter recovery. Subsequently, both a hierarchical and…

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…

More than a dozen statistical models have been developed for the purpose of cognitive diagnosis. These models are supposed to extract a much finer level of information from item responses than traditional unidimensional item response models. In this paper, a general diagnostic model (GDM) was used to analyze a set of simulated sparse data and real…