Second-order item response theory models have been used for assessments consisting of several domains, such as content areas. We extend the second-order model to a third-order model for assessments that include subdomains nested in domains. Using a graphical model framework, it is shown how the model does not suffer from the curse of…

The reporting methods used in large scale assessments such as the National Assessment of Educational Progress (NAEP) rely on a "latent regression model." The first component of the model consists of a "p"-scale IRT measurement model that defines the response probabilities on a set of cognitive items in "p" scales…