PROBABILITY MATRIX DECOMPOSITION MODELS

In this paper, we consider a class of models for two-way matrices with binary entries of 0 and 1. First, we consider Boolean matrix decompos ition, conceptualize it as a latent response model (LRM) and, by makin g use of this conceptualization, generalize it to a larger class of ma trix decomposition models. Second, probability matrix decomposition (P MD) models are introduced as a probabilistic version of this larger cl ass of deterministic matrix decomposition models. Third, an algorithm for the computation of the maximum likelihood (ML) and the maximum a p osteriori (MAP) estimates of the parameters of PMD models is presented . This algorithm is an EM-algorithm, and is a special case of a more g eneral algorithm that can be used for the whole class of LRMs. And fou rth, as an example, a PMD model is applied to data on decision making in psychiatric diagnosis.