In an empirical comparison, the new method of factor rotation called
Trasid has been shown to yield solutions with more optimal simple
structure than Harris-Kaiser II-, Promax-, and Oblimin-rotations with
regard to the hyperplane count. Especially the number of factors with
significant simple structure according to Bargmann (1955) is nearly
double those in the Trasid-solutions compared to the Harris-Kaiser II-,
Promax-, and Oblimin-solutions. Some empirical comparisons with new
methods of oblique factor rotation as PPFP-, Simplimax-, and Promaj
yield lower hyperplane counts for these methods. For the Hyball-rotation
only one comparison was possible for Harman's 24 tests, which yields the
same number of absolute loadings 
0.10.
Further comparisons are necessary.
When the number of absolute loadings 0.10 without divison by h is
maximised with priority, the hyperplane count is even higher in the
Trasid-solution than in the Hyball-solution. But it could be shown
that maximising of absolute loadings 0.10 without division by h does
not maximise the number of factors with significant simple structure
according to Bargmann (1955). It could be demonstrated in an example,
that simple structure should not be maximised only with regard to the
number of absolute loadings 0.10, if an influence of variables with
low communality on the solution is to be avoided. Oblimin-rotation may
also be influenced by variables with low communality. This point is
important because variables with low communality are often variables
with low reliability. Maximising hyperplane counts or maximising simple
structure in general may be problematic, if the simple structure is
maximised on the basis of the variables with the lowest reliability in a
data set. Additional studies on the influence of variables with low
communalities on rotation with different methods of factor rotation are
necessary. There may be different ways to deal with this problem, but
Trasid-rotation is at least one way to avoid the difficulties with
variables of low communality and possibly low reliability.
It should be noted, that direct maximisation of the hyperplane count may have some correspondence with the treatment of factor loadings in confirmatory factor analysis: non-significant loadings and loadings which are expected to be non-significant are generally fixed as zero-elements in the factor matrix. This means that in the context of confirmatory factor analysis, the factor matrix is rarely forced to correspond to a complex criterion of analytical factor rotation as for example the Varimax- or Oblimin-criterion. In most cases of confirmatory factor analysis, only significant and non-significant loadings are differentiated. Thus, a method of factor rotation like Trasid, which focusses only on main loadings and on maximisation of zero-elements instead of maximising a complex analytical criterion is closer to the treatment of the loadings in confirmatory factor analysis. So, results of confirmatory and exploratory factor analysis can more easily be compared, if Trasid-rotation is used for rotation in the exploratory context. Even in the case, that one wants to identify the maximum of zero-elements in exploratory factor analysis via oblique rotation before fixing them to zero in confirmatory factor analysis, Trasid-rotation may be recommended. The above-mentioned problem of maximising zero-elements in factor matrices, which may be due to unreliability of the variables, is also important in the case of confirmatory factor analysis, but this issue cannot be dealt with here.
More generally, the following can be concluded: if an oblique simple structure is intended, and if one wants to maximise the hyperplane count of a solution, the Trasid-rotation can be recommended. In addition, Trasid-rotation helps to avoid the influence of variables with low communality on factor rotation. A programme for PC (DOS) enabling Trasid-rotation with up to 20 factors is available on request from the author.