Hierarchical Graphical Models and Item Response Theory

The topic of this article is IRT modeling in the presence of nonignorable missing item responses. A Multilevel (or Hierarchical) Bayesian model is developed and represented by a Directed Acyclic Graph. In the context of Educational Assessment (PISA, TMISS, NEAP), it makes sense to believe that pattern of missingness depends on the ability that is measured and hence data are missing not at random. Three different Graphical Models, in a Hierarchical framework, are considered and compared: 1) a between-item-multidimensional model, taking into account missing data mechanism; 2) a unidimensional Rasch model, ignoring missing data process; 3) a unidimensional Rasch model for which omitted responses are treated as incorrect.