Daniel Soper

2004-10-06 19:25:00 UTC

Greetings everyone...

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

answer.

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!

-Dan

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

answer.

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!

-Dan