Transformation-matrix-Search
and -Identification (Trasid): A new method for oblique rotation to simple structure

André Beauducel

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Abstract

In the first instance current oblique rotational procedures and their disadvantages are treated. New developments in this area will then be discussed. Finally, the Transformation-matrix-Search and -Identification (Trasid) is presented as a new method of factor rotation. An orthogonal prerotation (e.g. Varimax) is followed by two rotational steps: (1) rotation in order to orient the factors to the main loadings, (2) rotation in order to maximise the number of variables in the hyperplane. The number of loadings, divided by the squareroot of communality, with absolute values 0.10 and simultaneously, but with lower priority, the number of absolute loadings 0.10, without division by the squareroot of communality, is maximised. Simultaneously, but with the lowest priority an index for the mean proximity of the loadings to the hyperplane is maximised. An empirical comparison of Trasid-rotation with Promax-, Oblimin- and Harris-Kaiser-rotation demonstrates the equality of the new procedure concerning the orientation of the factors on the main loadings with superiority concerning the number of variables in the hyperplane. In addition, Trasid-rotation is shown as clearly superior for the Bargmann-Test. Then, the influence of variables with extremly low communality on the solutions is shown for the case of maximising the number of loadings with absolute values 0.10 without division by the squareroot of communality. This is an argument in favor of the use of an algorithm, maximising the number of loadings 0.10 divided by the squareroot of communality with the highest priority. A computer programme for Trasid-rotation with up to 20 factors is available.

 
• Introduction
• Trasid-Rotation
  • Rotation for orientation of the factors on main loadings
  • Maximising the hyperplane count (with and without division by the square root of the communality)
  • Empirical comparison between Trasid and other methods of oblique rotation
  • Maximising the number of absolute loadings 0.10 only
• Discussion
• References
• Acknowledgments
• Author's Address