Abstract
Under mild assumptions, when appropriate elements of a factor loading matrix are specified to be zero, all orthogonally equivalent matrices differ at most by column sign changes. Here a variety of results are given for the more complex case when the specified values are not necessarily zero. A method is given for constructing reflections to preserve specified rows and columns. When the appropriatek(k − 1)/2 elements have been specified, sufficient conditions are stated for the existence of 2k orthogonally equivalent matrices.
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References
Dunn, J. E. A note on a sufficiency condition for uniqueness of a restricted factor matrix.Psychometrika, 1973,38, 141–143.
Jöreskog, K. G. A general approach to confirmatory maximum likelihood factor analysis.Psychometrika, 1969,34, 183–202.
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This research was supported in part by the National Institute of Health Grant RR-3.
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Jennrich, R.I. Rotational equivalence of factor loading matrices with specified values. Psychometrika 43, 421–426 (1978). https://doi.org/10.1007/BF02293650
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DOI: https://doi.org/10.1007/BF02293650