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Subpopulation invariance of patterns in covariance matrices
Author(s) -
Ellis Jules L.
Publication year - 1993
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1993.tb01014.x
Subject(s) - mathematics , covariance , invariance principle , basis (linear algebra) , set (abstract data type) , sign (mathematics) , population , covariance matrix , law of total covariance , general covariance , statistics , covariance function , covariance intersection , computer science , mathematical analysis , philosophy , linguistics , geometry , demography , sociology , programming language
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.