Comparing Categorical Data Arrays across Opportunities: Adapting STATIS to CBA with Plithogenic Fuzzy Soft Sets

Abstract

A method is proposed that adapts the STATIS methodology to correspondence analysis (CA), which allows analyzing data structures of two categorical variables on several occasions. On each occasion, a CA is applied and then a comparative analysis is performed between occasions in order to evaluate changes in the association between variables. The procedure allows: (1) Analyzing the variability of individual profiles on each occasion, projecting them onto spaces of optimal fit; (2) Comparing data structures between occasions, using a Hilbert -Schmidt distance, constructed as a direct function of the association between the variables that identify each occasion and inverse function of the association between the variables measured between occasions; (3) Representing individuals in a compromise space, using a score that captures the positions of their coordinates throughout the occasions; and (4) Performing the trajectory analysis of individuals throughout the occasions on the compromise space. The proposed method was applied in a nutritional assessment study of schoolchildren in 2017 and 2018, who were provided with food supplements. The results allowed us to identify trajectories of changes recorded in the children, facilitating the diagnosis of this problem. Additionally, an analysis based on plithogenic fuzzy soft sets was incorporated to model the uncertainty inherent in external factors, enriching the interpretation of nutritional trajectories.