Linear Logistic Restricted Latent Class Model for Polytomous Items With Fuzzy Skill Maps

This article introduces a class of restricted latent class model in statistics to handle the diagnosis problem of fuzzy knowledge structure, where the classification of the latent equivalence classes are based on the extent of proficiency in skills. The model includes skill magnitude and latent response probabilities, which consist of linear logistic constraints of the original parameters. Expectation-maximization algorithm is given for parameter estimation of the proposed fuzzy skill model. We also establish the identifiability results of the parametric model, which guarantee the validity of the parameter estimation. A simulation study was conducted to assess the recovery of model parameters. Additionally, the proposed model is illustrated through the use of real-world data to demonstrate its practical application. Finally, topics for further research are discussed.