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LATENT STRUCTURE AND POSITIVE MANIFOLD
Author(s) -
Gibson W. A.
Publication year - 1962
Publication title -
british journal of statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0950-561X
DOI - 10.1111/j.2044-8317.1962.tb00096.x
Subject(s) - centring , factoring , mathematics , manifold (fluid mechanics) , rotation (mathematics) , zero (linguistics) , pure mathematics , latent class model , mathematical analysis , geometry , statistics , engineering , linguistics , mechanical engineering , philosophy , finance , economics
Analytic discrete class latent structure solutions must use third order joint positive frequencies and often cannot get all latent probabilities between zero and one inclusive. An early geometric approach gave a solution, permissible in that sense, but cumbersome because of complex rotational limits and centring criteria. The inclusion, after factoring, of a vector for each negative response makes the rotational limits those of a strictly positive orthogonal manifold, and the centring criteria those of a best‐fitting orthogonal reference frame. After factoring but before rotation it can be determined whether a permissible r ‐class solution exists. An empirical example is provided, and various rotational approaches are discussed.