Latent Partially Ordered Classification Models and Normal Mixtures

Latent partially ordered sets (posets) can be employed in modeling cognitive functioning, such as in the analysis of neuropsychological (NP) and educational test data. Posets are cognitively diagnostic in the sense that classification states in these models are associated with detailed profiles of cognitive functioning. These profiles allow for deeper insight into how functioning can be affected by neurological conditions or by interventions that impact cognition or learning. Responses to NP measures or test items are used as a basis for classification. A natural and useful extension for response models that can be employed in cognitively diagnostic modeling is the implementation of nonparametric density estimation methods. For instance, an issue with NP assessment data is that complex response distributions can arise, such as for populations that are in part comprised of cognitively impaired subjects. To model such complexity, a Dirichlet process prior approach to Bayesian nonparametric density estimation for latent poset models is described. These methods are demonstrated with an analysis of NP data from a study of schizophrenia.