Principal Components - SAS vs SPSS

[ilikesas]

Hi,

I am doing a Principal Component Analysis on a data and compare the results with results that were obtained previously with SPSS.

I am using Proc Factor to perform a Varimax Rotation to obtain 7 Principal Components. I noticed that the results that I get with SAS are slightly different from the SPSS results:

1) In the Factor Loadings (called Rotated Factor Pattern) I noticed that the loadings for the 4th and 6th factor that I obtained in SAS have the opposite sign of the loadings that are obtained with SPSS (although the absolute value is the same).

2) The Principal Components of the 4th and 6th factor from SAS have the opposite sign of those from SPSS, and the Absolute value is slightly different for all Principal Components for all 7 factors.

So I guess that the algorithm that SAS uses is different from SPSS. If this is the case I will use the results obtained by SAS, but I just want to make sure that such thing can happen.

Thanks! 

[Reeza]

Eigenvectors are not necessarily unique. 

http://stats.stackexchange.com/questions/30348/is-it-acceptable-to-reverse-a-sign-of-a-principal-com...

[Rick_SAS · Accepted solution]

 Yes, if u is an eigenvector of a matrix A, then -u is also an eigenvector. Many times I  have seen different software come up with solutions like you describe. Neither answer is wrong; they are both correct and the results are equivalent.

[ilikesas]

Hi Rick,

I ran a regression in SAS and found out that all the coefficients are the same as those of the SPSS regression, except that the signs for Factors 4 and 6 are opposite. So since I have 2 opposites (first in the loadings and than in the coefficients) the interpretation of the end result is the same!