Modeling mortality rates through hierarchical clustering for three-way data

Modeling mortality rates is crucial in longevity risk analysis to accurately estimate life expectancies. However, standard models are often inadequate to handle mortality data because they fail to account for its complex structure. Mortality rates typically span multiple dimensions, such as age, year, and country, forming a three-way structure. Three-way data can be studied by ad-hoc models that summarize them by seeking a low-dimensional configuration through components. Rather than summarizing such data by means of component-based methods, clustering techniques can offer a more effective approach. Within the framework of longevity risk analysis, this consists of identifying clusters of countries with similar mortality patterns. Specifically, a novel hierarchical clustering model for three-way data is proposed and applied to mortality data. Unlike the non-hierarchical approach, this model provides deeper insight into the data by illustrating the progressive merging of clusters.