A finite mixture model for biclustering longitudinal trajectories: an application to Italian crime data.

Motivated by the analysis of data entailing the number of crime events that the Italian enforcement authorities (Polizia, Arma dei Carabinieri, Guardia di Finanza) reported to justice from 2012 to 2019, a biclustering approach is developed based on a finite mixture model. The data at hand represent a particular type of three- way data, where the modes correspond to Italian provinces (rows), crime-types (columns), and years (layers). A finite mixture of generalized linear models is built up to obtain a clustering of provinces. Further, within each cluster, we use a flexible and parsimonious parameterization of the linear predictor to obtain a partition of columns, such that each partition collects crime-types sharing a similar evolution over time. The aim is to identify geographical areas in the country that share common longitudinal trajectories for specific subsets of crime-types. Model parameter estimates are derived via a maximum likelihood approach based on the use of an extended EM-type algorithm. This is based on three separate steps: an expectation (E-), a classification (C-), and a maximization (M-) step. The efficacy of the proposal is also evaluated via a large-scale simulation study, based on varying sample sizes, number of partitions, ad model specifications.