Planning for preparedness, in terms of multi-hazard disasters, involves testing the relevant abilities to mitigate damage and build resilience, through the assessment of deterministic disaster scenarios. Among risk-prone assets, open spaces (OSs) play a significant role in the characterization of the built environment (BE) and represent the relevant urban portion on which to develop multi-risk scenarios. The aim of this paper is to elaborate ideal scenarios—namely, Built Environment Typologies (BETs)—for simulation-based risk assessment actions, considering the safety and resilience of BEs in emergency conditions. The investigation is conducted through the GIS data collection of the common characteristics of OSs (i.e., squares), identified through five parameters considered significant in the scientific literature. These data were processed through a non-hierarchical cluster analysis. The results of the cluster analysis identified five groups of OSs, characterized by specific morphological, functional, and physical characteristics. Combining the outcomes of the cluster analysis with a critical analysis, nine final BETs were identified. The resulting BETs were linked to characteristic risk combinations, according to the analysed parameters. Thus, the multi-risk scenarios identified through the statistical analysis lay the basis for future risk assessments of BEs, based on the peculiar characteristics of Italian towns.

The problem of multivariate regression modelling in the presence of heterogeneous data is dealt to address the relevant issue of the influence of such heterogeneity in assessing the linear relations between responses and explanatory variables. In spite of its popularity, clusterwise regression is not designed to identify the linear relationships within ‘homogeneous’ clusters exhibiting internal cohesion and external separation. A within-clusterwise regression is introduced to achieve this aim and, since the possible presence of a linear relation ‘between’ clusters should be also taken into account, a general regression model is introduced to account for both the between-cluster and the within-cluster regression variation. Some decompositions of the variance of the responses accounted for are also given, the least-squares estimation of the parameters is derived, together with an appropriate coordinate descent algorithms and the performance of the proposed methodology is evaluated in different datasets.