A Partial Mastery, Higher-Order Latent Structural Model for Polytomous Attributes in Cognitive Diagnostic Assessments

The latent attribute space in cognitive diagnosis models (CDMs) is often assumed to be unstructured or saturated. In recent years, the number of latent attributes in real tests has often been found to be large, and polytomous latent attributes have been advocated. Therefore, it is preferable to adopt substantive theories to connect seemingly unrelated latent attributes, to replace the unstructured or saturated latent structural models (LSMs) with structured or parsimonious ones, with simplified parameter estimation. In the present study, we developed a partial mastery, higher-order LSM for polytomous attributes, which was built upon the framework of adjacent-category logit models to account for a higher-order latent structure of multiple polytomous attributes. The proposed model can be incorporated into many existing CDMs. We conducted simulations to evaluate the psychometric properties of the proposed model and obtained good parameter recovery. We then provided an empirical example to demonstrate the applications and the advantages of the proposed model.