Methodological and Operating Questions of the Three Way Lee-Carter Model

The three-way model has been proposed as a development of the original Lee- Carter (LC) model when a three-mode data structure is available. The three-way LC model allows enriching the basic LC model by introducing several tools of exploratory data analysis. Such exploratory tools allow giving a new perspective to the demographic analysis supporting the analytical results with a geometrical interpretation and a graphical representation. From a methodological point of view, there are several issues to deal with when focusing on such kind of data. Specially, in presence of the three-way data structure, several choices on data pre-treatment could affect the whole data modelling. The first step of a three-way mortality data investigation consists in exploring the different source of variations and highlighting the significant ones. We will consider the three-way LC model investigated through a three-way analysis of variance with fixed effects, where each cell is given by the mortality rate in a given year of a specific age-group for a country. Firstly, we consider the variability attached to each of the three ways main effects: age, years and countries. Then, we consider the variability induced by the interactions between each pair of the three ways. Finally, the three-way interaction could give information on which country have a specific trend (along years) in each age-group. This kind of analysis is useful to assess the source of variation in the raw mortality data, before to extract rank-one components by the LC-model.