Factor Analysis for Multivariate Compositional Data and an Economic Application

This paper aims to address the lack of appropriate methods for analysing multivariate compositional data by introducing FAMCoDa, a factor analysis model tailored for such data, along with a two-step estimation method.First, we outline the mathematical framework of FAMCoDa and the procedures for estimating factor loadings and scores, validating its effectiveness through simulation experiments.We then apply FAMCoDa to analyse the industrial consumption structure data of 41 countries.The results reveal that FAMCoDa efficiently manages multivariate compositional data, identifying correlations between variables.Our contributions are threefold: (1) presenting a novel factor analysis model for multivariate compositional data, focusing on inter-variable correlations, unlike existing models; (2) devising a two-step estimation process, starting with multivariate CoDa PCA for initial loadings and refining them through variance rotation, followed by ilr transformation and OLS regression for factor scores; (3) ensuring the compositional structure of the extracted factors remains consistent with the original variables.This work has significant implications for economic applications.