Dimensionality of the latent structure and item selection via latent class multidimensional IRT models

With reference to a questionnaire aimed at assessing the performance of Italian nursing homes on the basis of the health condition of their patients, we investigate two relevant issues: dimensionality of the latent structure and discriminating power of the items composing the questionnaire. The approach is based on a multidimensional Item Response Theory model, which assumes a two-parameter logistic parametrization for the response probabilities. This model represents the health status of a patient by latent variables having a discrete distribution and, therefore, it may be seen as a constrained version of the latent class model. On the basis of the adopted model, we implement a hierarchical clustering algorithm aimed at assessing the actual number of dimensions measured by the questionnaire. These dimensions correspond to disjoint groups of items. Once the number of dimensions is selected, we also study the discriminating power of every item, so that it is possible to select the subset of these items which is able to provide an amount of information close to that of the full set. We illustrate the proposed approach on the basis of the data collected on a sample of 1051 elderly people hosted in a sample of Italian nursing homes.