  In this note, we investigate the non-identifiability of the multivariate
unified skew-normal distribution under permutation of its latent variables. We
show that the non-identifiability issue also holds with other parametrizations
and extends to the family of unified skew-elliptical distributions and more
generally to selection distibutions. We provide several suggestions to make the
unified skew-normal model identifiable and describe various sub-models that are
identifiable.
