Dynamic analysis of equitable and sustainable well-being: a multivariate parsimonious hidden Markov model for clustering longitudinal Italian NUTS3 data.

Motivated by the analysis of well-being equitable and sustainable indicators across Italian NUTS3 areas from 2004 to 2019, we introduce a family of parsimonious hidden Markov models for clustering multivariate longitudinal data. This approach offers an alternative to existing model-based clustering methods by capturing both temporal dynamics and latent heterogeneity among territorial units. Given the multivariate dimensionality of the data, we adopt a factor model representation to reparameterize the covariance structure, reducing the number of parameters and enhancing interpretability. Parameter estimation is carried out using an Alternating Expectation Conditional Maximization (AECM) algorithm. Our results reveal a substantial degree of heterogeneity, identifying 15 clusters across NUTS3 areas. Despite this, Italian well-being patterns show a remarkable degree of temporal stability. To further simplify interpretation and support policy analysis, we apply cluster merging techniques (discussed in the Appendix C), which group the original clusters into four broader macro-clusters, each characterized by distinct well-being profiles across subsets of indicators.