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Despite the popularity of sparse factor models, little attention has beengiven to formally address identifiability of these models beyond standardrotation-based identification such as the positive lower triangular constraint.To fill this gap, we provide a counting rule on the number of nonzero factorloadings that is sufficient for achieving uniqueness of the variancedecomposition in the factor representation. Furthermore, we introduce thegeneralised lower triangular representation to resolve rotational invarianceand show that within this model class the unknown number of common factors canbe recovered in an overfitting sparse factor model. By combining point-massmixture priors with a highly efficient and customised MCMC scheme, we obtainposterior summaries regarding the number of common factors as well as thefactor loadings via postprocessing. Our methodology is illustrated for monthlyexchange rates of 22 currencies with respect to the euro over a period of eightyears and for monthly log returns of 73 firms from the NYSE100 over a period of20 years.

Sparse Bayesian Factor Analysis when the Number of Factors is Unknown