An application of set theoretic latent trait model

The set theoretic latent trait model (STLTM) proposed by Shiina (1990) is applied to Bergan's (1988) math-items data. The MSTLTM, a marginalized version of STLTM, which can be considered as a latent class model in which response probabilities are reparametrized by a set function of subject set structure and item set structure, is proposed. In applying the model, it is argued that: 1) in some situation the MSTLTM and the latent class model are equivalent, but the former utilizes a convenient graphical representation for items and subjects which will be helpful for explorative model construction, and 2) a major advantage of the STLTM lies in that it permits a statistical comparison among models by assuming various developmental paths.