Estimating multiple classification latent class models

This paper presents a new class of models for persons-by-items data. The es sential new feature of this class is the representation of the persons: eve ry person is represented by its membership to multiple latent classes, each of which belongs to one latent classification. The models can be considere d as a formalization of the hypothesis that the responses come about in a p rocess that involves the application of a number of mental operations. Two algorithms for maximum likelihood (ML) and maximum a posteriori (MAP) estim ation are described. They both make use of the tractability of the complete data likelihood to maximize the observed data likelihood. Properties of th e MAP estimators (i.e., uniqueness and goodness-of-recovery) and the existe nce of asymptotic standard errors were examined in a simulation study. Then , one of these models is applied to the responses to a set of fraction addi tion problems. Finally, the models are compared to some related models in t he literature.