Add to ORKGFactor analysis is a well-known model for describing the covariance structure among a set of manifest variables through a limited number of unobserved factors. When the observed variables are collected at various occasions on the same statistical units, the data have a three-way structure and standard factor analysis may fail to discover the interrelations among the variables. To overcome these limitations, three-way models can be adopted. Among them, the so-called Parallel Factor (Parafac) model can be applied. In this article, the structural version of such a model, i.e. as a reparameterization of the covariance matrix, is studied by discussing under what conditions factor uniqueness is preserved