Item selection by an extended Latent Class model: An application to nursing homes evaluation

The evaluation of nursing homes and the assessment of the quality of the health care provided to their patients are usually based on the administration of questionnaires made of a large number of polytomous items. In applications involving data collected by questionnaires of this type, the Latent Class (LC) model represents a useful tool for classifying subjects in homogenous groups. In this paper, we propose an algorithm for item selection, which is based on the LC model. The proposed algorithm is aimed at finding the smallest subset of items which provides an amount of information close to that of the initial set. The method sequentially eliminates the items that do not significantly change the classification of the subjects in the sample with respect to the classification based on the full set of items. The LC model, and then the item selection algorithm, may be also used with missing responses that are dealt with assuming a form of latent ignorability. The potentialities of the proposed approach are illustrated through an application to a nursing home dataset collected within the ULISSE project, which concerns the quality-of-life of elderly patients hosted in Italian nursing homes. The dataset presents several issues, such as missing responses and a very large number of items included in the questionnaire.