Item selection via Latent Class Based Clustering

Given a set of items used to measure a latent trait, we introduce a method for finding the smallest subset of these items which provides an amount of information close to that of the initial set. The method is based on the latent class (LC) model and proceeds by sequentially eliminating the items that do not significantly change the classification of the subjects in the sample with respect to that based on the full set of items. As usual, this classification is based on the posterior probabilities of belonging to each latent class. The approach is illustrated through an application concerning the evaluation of the quality-of-life of elderly people hosted in nursing homes, which is based on a dataset collected within the “Ulisse” project. For this dataset, we adopt an LC model for polytomous items, which also accounts for missing responses. To deal with multimodality of the model likelihood, we rely on a hierarchical clustering procedure to find sensible starting values for the EM algorithm used for parameter estimation.