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…

The partial credit model with a varying slope parameter is developed and called the generalized partial credit model (GPCM). Analysis results for simulated data by this and other polytomous item-response models demonstrate that the rating formulation of the GPCM is adaptable to the analysis of polytomous item responses. (SLD)

The extent to which properties of the ability scale and the form of the latent trait distribution influence the estimated item parameters of item response theory (IRT) was investigated using real and simulated data. Simulated data included 5,000 ability values randomly drawn from the standard normal distribution. Real data included the results for…

National Assessment of Educational Progress reading data were scaled using a unidimensional item response theory model. Bock's full-information factor analysis and Rosenbaum's test of unidimensionality were applied. Conclusions about unidimensionality for balanced incomplete block spiralled data were the same as for complete data. (Author/GDC)

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…