A universal model is defined as a set of behavioural laws that hold for almost every subject of a given population. Universal models satisfy the principle of subpopulation invariance: If the model holds in a population, then the model and its predictions hold in every non-negligible subpopulation. On basis of this principle it is shown that only one universal model, namely congenerity, can explain the ratio pattern of observed-score covariance matrices. Similar results are obtained for the sign and order pattern of covariance matrices. More specifically, the necessary and sufficient conditions of these models can be formulated by the principle. Factor analysis representations can satisfy the principle, but do not necessarily do so. Multidimensional scaling distance representations, on the other hand, in general will violate the principle and are therefore not reducible to a universal model.