Bayesian (non-)unique sparse factor modelling

Factor modelling extracts common information from a high-dimensional data set into few common components, where the latent factors usually explain a large share of data variation. Exploratory factor estimation induces sparsity into the loading matrix to associate units or series with those factors most strongly loading on them, eventually determining factor interpretation. The authors motivate geometrically under which circumstances it may be necessary to consider the existence of multiple sparse factor loading matrices with similar degrees of sparsity for a given data set. They propose two MCMC approaches for Bayesian inference and corresponding post-processing algorithms to uncover multiple sparse representations of the factor loading matrix. They investigate both approaches in a simulation study. Applying the methods to data on U.S. sectoral inflation and country-specific gross domestic product growth series, they retrieve multiple sparse factor representations for each data set. Both approaches prove useful to discriminate between pervasive and weaker factors.