Modelling missingness with a Rasch-type model

In this paper we focus on a model-based approach to the treatment of missing data due to examinees' nonresponse, in the context of Item Response Theory (IRT). With model-based approach we mean that item nonresponses are to be included in the analysis - indeed we assume that nonresponses are caused by a specific latent trait, summarizing the response propensity of the examinee. Then, the idea is to postulate the existence of two latent traits: one for response propensity and the other for ability/proficiency. Different models have been proposed in the literature. In this paper, a new class of multidimensional IRT models, called Rasch-Rasch models, is introduced. The Rasch-Rasch model belongs to the wider class of Rasch models - and, as a member of the exponential family, it can be viewed as a generalized linear mixed model. Real and artificial datasets are used to illustrate the characteristics of this new model.