In component analysis, the components resulting
immediately from an analysis are often hard to interpret. Exploiting rotational
freedom of the components, however, one can rotate these components to simple structure
(for instance, by “varimax”) and thus considerably simplify the interpretation
of the components. This is well-known for principal components analysis, but it
also holds for various other models. I have developed varimax rotation
procedures for Multiple correspondence analysis and variants thereof (see
Kiers, 1991), and am currently working with Michel van de Velden on varimax
rotation for Correspondence Analysis.
In three-way analysis, the results of
Tucker3 analysis have rotational freedom in various directions: All component
matrices as well as the core array can be rotated. It is very important in
practical applications to have techniques for simplifying the component
matrices and the core, so as to simplify interpretation. After some first attempts
to rotate the core over all three directions simultaneously to a simple form
(see Kiers, 1992), rotation to optimal simple forms was proposed by Kiers
(1997, 1998), in the form of three-way generalizations of varimax and simplimax
rotation. A procedure which, additionally, aims at simplicity of the component
matrices for the three modes is provided in Kiers (1998).
The above involvement in simple
structure rotations led to some developments for simple structure rotation of
ordinary two-way components as well. Properties of existing simple structure
rotation techniques were described (Kiers & Ten Berge, 1994), and a new
procedure called SIMPLIMAX, leading to optimally simple loading matrices, was
developed (Kiers, 1994).