Extending finite Mixtures of Latent Trait Analyzers for clustering complex data

Complex data have become increasingly common in several fields involving high dimensional data sets and heterogeneous data types, as well as data with complex dependence structures. This clearly highlights the need for sophisticated analytical approaches that allow us to effectively extract information from such data. Finite mixture models represent an extensively used and flexible approach to analyze a wide variety of complex data structures. Here, we focus on the Mixture of Latent Trait Analyzers (MLTA). This can be conceived as a model-based clustering approach obtained from the combination of latent class and latent trait analysis. It proved to be a practical compromise between restrictiveness of model assumptions and interpretability of model parameters; further, its estimation is fast and straightforward to implement. The original specification of the MLTA model is tailored for the analysis of multivariate categorical (binary) data. We extend the model to deal with different data structures and illustrate its applicability in a wide variety of scientific settings, either from a clustering or a biclustering perspective. In the former case, we aim at the identification of homogeneous clusters of units; in the latter case, a simultaneous clustering of units and variables is obtained. The dissertation focuses on different data structures and modeling extensions. The proposals are supported by theoretical results and illustrated using simulation studies and real-world data.