The method of factor rotation, which will be presented here, has some
paralleles with Maxplane by Cattell & Muerle (1960) and PPFP by Katz and
Rohlf (1974, 1975), who tried to maximise the hyperplane count. Two
precursors of this method are presented in Beauducel (1996). In contrast to
Cattell and Muerle (1960) and Katz and Rohlf (1974) the hyperplane count is
not maximised in the reference-vectors, but as for PPFP (Katz & Rohlf, 1975)
it is maximised directly in the factor pattern
.
In addition, an orientation of
the factor axes on the main loadings is realised before maximising the
hyperplane count. When the orientation on the main loadings is neglected,
the position of a factor may be more strongly determined by variables,
which do not load on the respective factor.
The new method is called Transformation-matrix-Search and Identification (Trasid). After orthogonal prerotation (e.g. Varimax), two steps are distinguished: (1) rotation in order to orient the factors on the respective main loadings, and (2) rotation in order to maximise the hyperplane count.
Trasid works in a rather heuristic way and it cannot be excluded that better working methods may exist. However, the empirical results are quite satisfactory and, with regard to hyperplane count, the method outperforms other methods which are based on more analytical criteria and procedures (see below). The results of Trasid-rotation depend on the prerotation method as in Promax-rotation and Casey's Method (Piaggio, 1972; Kaiser & Cerny, 1978). Different methods of prerotation for Trasid have been checked and on this basis the Varimax-prerotation is recommended (Equamax is not recommended).
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