Abstract
In the present paper, a latent structure analysis for studying the systematic learning process of acquiring several skills is developed. The learning structure considered in this paper means not only the linear hierarchical learning structure but also the branching hierarchical learning structure. The acquisition of each skill is assessed on the basis of the response to the related binary item (Success or Failure), Further, it is assumed that each subject responds to each item stochastically, that is, we admit both guessing errors and forgetting errors. With regards to the model, the hypothesized structure is incorporated into the model itself within the framework of the latent class model. An algorithm for maximum likelihood estimation of the latent parameters (MLE algorithm) is constructed according to the EM algorithm. A numerical example is also presented to demonstrate the estimation procedure.
