Special issue on Advances in latent variables: methods, models and applications

Starting from Spearman’s 1904 pioneering work on factor analysis, latent variable models have witnessed an ever increasing, even though sometimes controversial, diffusion in the statistical literature. They have been extended to deal with different kinds of data structures, and thereby helped to analyse more and more complex situations. Finally, they turned out to be both a powerful instrument for a better understanding of reality and a necessary tool to perform dimension reduction. With the development of refined latent variable models new computational algorithms have been designed that rendered the corresponding parameter estimation fast and reliable. New research lines have incorporated latent variables as a necessary building block. A class of latent variable models that has been deeply studied and widely applied is Latent Class Analysis, which aims at modelling and testing the existence of latent subgroups based on the association among a set of discrete observed variables. The key assumption is conditional independence of the observed variables given the latent classes. This strong assumption largely simplifies the model and prevents it to be affected by the curse of dimensionality, but as for any strong assumption, its violation may lead to poor model performances and to inconsistent results. Although widely used and explored the research area related to Latent Class Models still leaves space for advances and new solutions in terms of modelling strategies, ability to deal with complex data structures (e.g. multilevel or longitudinal) or with mixed type variables, and development of new methods to test model fit. This Special Issue of ADAC, entitled Latent Variables: Methods, Models and Applications has been designed to collect a range of innovative and high quality research papers on new challenges and recent developments in the field of latent variable models and their application to real problems. Topics of particular interest in the issue are related to multilevel latent class models, mixture models for mixed-type data in model-based clustering, latent class CUB models, latent class growth models, model selection, tests and item selection in Latent Class Models.