2004-10-06 19:25:00 UTC
I have a rather advanced SPSS question related to rotations in a factor
analysis, and I sincerely hope that one of the gurus out there will know the
Here's a little background on the problem:
SPSS has an implementation of the direct oblimin rotation strategy that can
be used when an oblique set of rotated factors is desired. The purpose of
direct oblimin rotation is to minimize the covariance of the squared
loadings in distinct columns. The loss function for direct oblimin rotation
as defined by McDonald (1985, p.86) contains a parameter known as "gamma"
that can be set to a value between zero and one. As gamma increases from
zero to one, the factors become less and less correlated. Unfortunately,
SPSS does not seem to directly adhere to the definitional formula for direct
oblimin rotation. Rather than providing the ability to adjust the gamma
parameter, SPSS instead provides access to a parameter known as "delta",
which is not a part of the definitional formula. The delta parameter seems
to operate in the opposite direction of the formally defined gamma
parameter, in that high values of delta yield higher correlations among
factors. According to the SPSS manual, the highest correlations among
factors are achieved when delta is left at its default value of zero,
however the maximum value of delta (which actually yields the highest
correlations) seems to be 0.80. As delta decreases into the negative range,
the factors become more and more orthogonal.
Given all of the background information listed above, here's my question:
Mathematically, what is this"delta" parameter that SPSS provides, and how
does it relate to the definitional formula? Does it have a basis in
literature, or did the good people at SPSS invent it? If anyone has any
information on this topic, please reply to this post. I've scoured the web
for a solution, and have found absolutely nothing.
Thank you in advance for your help!