Multilevel item response models for hierarchal latent traits

In the human sciences, sampled data may have a multilevel structure. For example, repeated measures are nested within persons; and students are nested within schools. In addition to a multilevel structure in sampled data, the latent traits of interest may have a hierarchal structure. For instance, a language proficiency test may measure four kinds of proficiency: listing, speaking, reading and writing. Not only the “overall” language proficiency but also the four “domain” proficiencies are of great interest and should be reported. Likewise, a test of quality of life may contain multiple domains, such as physical, mental, social, and environmental, so that not only the overall quality of life measure but also the four domain quality of life measures are of interest. It is likely that not only sampled data have a multilevel structure but also latent traits have a hierarchical structure. Existing IRT models can accommodate either multilevel structure in sampled data or hierarchical structure in latent traits. In this study, we developed a series of item response models that can accommodate both multilevel structure and hierarchical structure simultaneously, and conducted a series of simulations to evaluate parameter recovery. It was found that the parameters of the new models can be recovered very well by using WinBUGS. Two empirical examples of the Civic Education Study were analyzed for demonstration of the new model.