• Advanced Question - Direct Oblimin Rotation

    From vinitavader@gmail.com@21:1/5 to Daniel Soper on Sat May 9 14:30:31 2020
    On Wednesday, October 6, 2004 at 12:25:00 PM UTC-7, Daniel Soper wrote:
    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

    Hello Dan,

    I am dealing with the exact same problem that you mentioned here and trying to understand why the R and SPSS outputs do not match. Could you please share your suggestions on this. I am unable to access the spss support website mentioned above.

    -Vinita

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Rich Ulrich@21:1/5 to vinitavader@gmail.com on Sun May 10 13:14:17 2020
    On Sat, 9 May 2020 14:30:31 -0700 (PDT), vinitavader@gmail.com wrote:

    On Wednesday, October 6, 2004 at 12:25:00 PM UTC-7, Daniel Soper wrote:
    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

    Hello Dan,

    I am dealing with the exact same problem that you mentioned here and trying to understand why the R and SPSS outputs do not match. Could you please share your suggestions on this. I am unable to access the spss support website mentioned above.


    I found the original thread, and the original answers.

    SPSS was bought by IBM since Bruce gave 2004's support URL,
    which no longer exists.

    Looking for the SPSS algorithms manual, I found ftp://public.dhe.ibm.com/software/analytics/spss/documentation/statistics/24.0/en/client/Manuals/

    - which includes a listing for the algorithms manual.

    Notice, the manual has an FTP prefix, not http (where you
    see the Link translated, probably at the bottom of your screen.)
    I clicked on the manual multiple times in Firefox without having
    it open, before I noticed FTP and realized that "FTP" isn't going
    to open. FTP is an old file-transfer protocol which I haven't
    used in years. But clicking the link in Firefox did download the
    pdf file every time I had clicked.

    Anyway, I discovered multiple versions of the manual now
    exist in my DOWNLOADs directory. The one that is 61 MB
    is version 24. Earlier clicking around had gotten me a
    larger document which is version 25. The section you want
    will not have changed, I expect.

    Hope this helps. - BTW, the fact that I did not find a more
    common, HTTP, on-line file does not prove that one does
    not exist.

    --
    Rich Ulrich

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)