Latent Ignorability and Item Selection for Nursing Home Case-Mix Evaluation

In the social, behavioral, and health sciences it is often of interest to identify latent or unobserved groups in the population with the group membership of the individuals depending on a set of observed variables. In particular, we focus on the field of nursing home assessment in which the response variables typically come from the administration of questionnaires made of categorical items. These types of data may suffer from missing values and the use of lengthy questionnaires may be problematic as a large number of items could have a negative impact on the responses. In such a context, we introduce an extended version of the Latent Class (LC) model aimed at dealing with missing values, by assuming a form of latent ignorability. Moreover, we propose an item selection algorithm, based on the LC model, for finding the smallest subset of items providing an amount of information close to that of the initial set. The proposed approach is illustrated through an application to a dataset collected within an Italian project on the quality-of-life of nursing home patients.