Generalizations of the solution-error response-error model

In the last decade, several attempts have been made to relate item response theory (IRT) models to latent class analysis (LCA) models. One of these attempts is the solution-error response-error (SERS) model, an LCA model in which the structure of the latent class probabilities is explained by a one-dimensional loglinear Rasch model. In this paper, the SERE model is generalized to models for polytomously scored latent states that may be explained by a multidimensional latent space. In this generalized SERE model a distinction is made between some well-defined latent states in which the subject has a certain amount of knowledge of the answer. The probability that the subject is in a certain state is assumed to be governed by the multidimensional polytomous latent trait model. The relationship between the latent states and the observed answers is described by conditional probabilities. Two appendixes present items from a clinical pathology test and a proof of the collapsed generalized SERE model. Five tables and four figures illustrate the discussion.