Mixture item response theory (IRT) models have been suggested as an efficient method of detecting the different response patterns derived from latent classes when developing a test. In testing situations, multiple latent traits measured by a battery of tests can exhibit a higher-order structure, and mixtures of latent classes may occur on…

Scratch, a visual programming language, was used in many studies in computer science education. Most of them reported positive results by integrating Scratch into K-12 computer courses. However, the object-oriented concept, one of the important computational thinking skills, is not represented well in Scratch. Alice, another visual programming…

In the social sciences, latent traits often have a hierarchical structure, and data can be sampled from multiple levels. Both hierarchical latent traits and multilevel data can occur simultaneously. In this study, we developed a general class of item response theory models to accommodate both hierarchical latent traits and multilevel data. The…