Abstract
A general framework for obtaining all possible factor analytic solutions, orthogonal and oblique, for a given common factor space is developed in detail. Interestingly, and seemingly paradoxically, any one of these solutions may be obtained by orthogonal transformations of selected matrices; thus an oblique solution may be determined by orthogonal transformations. Within the possible oblique solutions, two distinct categories of solutions emerge, a special case of the simpler of which apparently provides a definitive solution to the problem of independent, but correlated, clusters. Possible further specializations of the general approach to specific problems are discussed.
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References
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Horst, P. A non-graphical method for transforming an arbitrary factor matrix into a simple structure factor matrix.Psychometrika, 1941,6, 79–99.
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Harris, C.W., Kaiser, H.F. Oblique factor analytic solutions by orthogonal transformations. Psychometrika 29, 347–362 (1964). https://doi.org/10.1007/BF02289601
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DOI: https://doi.org/10.1007/BF02289601