```Date: Tue, 20 Sep 2005 09:30:41 +0000 Reply-To: "Luis O." Sender: "SPSSX(r) Discussion" From: "Luis O." Subject: Re: PCA and Rotation In-Reply-To: Content-Type: text/plain; format=flowed Hi Paul and Hector, Thank you very much for your explanations and clarifications. I sincerely appreciate your help. I want to ask one more question to Hector. In your explanations, you seem to be saying that in BOTH cases (i.e. PCA and principal axes method) we can rotate the principal components in order to "put one factor closer to one set of observed variables, and far from others, and the opposite for another factor". Is this a correct procedure in terms of PCA? I am asking this question, because this is precisely the doubt I have. Some of my stat friends contend that in PCA we should not rotate principal components, because it is a data reduction method (as Paul explains), and produces a best linear combination of the variance. They even say that if we rotate the principal components, they are no longer "principal" components. In short, their point is that PCA and FA are two different procedures, and the rotation should be applied ONLY in the case of FA. I would sincerely appreciate your further clarifications. Luis >From: Hector Maletta >Reply-To: Hector Maletta >To: SPSSX-L@LISTSERV.UGA.EDU >Subject: Re: PCA and Rotation >Date: Mon, 19 Sep 2005 20:54:50 -0300 > >Some clarification: >PCA is designed to maximize the first underlying factor, maximizing its >contribution, and (besides) when it extracts all possible factors (number >of >factor equal to the number of variables) it accounts for the entire >variance >of the variables. Other methods of extraction do not maximize the first, >and >besides they try to explain only the COMMON variance, leaving aside a >portion of variance that is regarded as unique to each observed variable. >Historically, PCA was used first to identify a single factor underlying a >set of related measures, supposedly measuring all the same trait >(intelligence, as it was), while Principal Axes was used based on the >theory >that instead of a single Intelligence factor there were underlying >"intelligences" for varios "faculties of the mind" such as linguistic, >graphic or mathematical ability. >In BOTH cases, the position of the coordinate system on which the >underlying >factors are measured is essentially arbitrary. By rotation, the analyst may >be able to put one factor closer to one set of observed variables, and far >from others, and the opposite for another factor. This make happen by >chance >in the initial extraction, but ordinarily doesn't, so rotation is used in >order to get that nice characteristic of a factor linked to sets of >interrelated variables. For instance, using the same IQ example, by >rotation >one may get one factor strongly associated with several linguistic tests, >and only weakly related to other tests, while another factor is strongly >related to mathematical tests and weakly to other tests, so one intuitively >calls the first factor "linguistic" and the second "mathematical". >These different factors may be independe from each other, or correlated. It >is perfectly possible that being good in language implies being good also >in >math, and so at least to some degree, some correlation between linguistic >and math factors is only to be expected. >Initial patterns of extraction ordinarily extract factors that are >orthogonal or uncorrelated to each other, because each successive factor is >extracted on the unexplained residuals left by the preceding ones, but >rotation can position the factor axes in ways that imply they are >correlated >to each other. >Rotation preserving the independence of factors is called orthogonal >rotation. Rotation allowing them to be correlated to each other is called >oblique rotation. >So in Paul Swank responde there is a (probably involuntary) confusion at >the >end: oblique rotation yields correlated factors (though it does not FORCE >them to be correlated) while orthogonal rotation methods FORCE rotated >factors to be uncorrelated to each other. > >Hector > > > > -----Original Message----- > > From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] > > On Behalf Of Swank, Paul R > > Sent: Monday, September 19, 2005 8:26 PM > > To: SPSSX-L@LISTSERV.UGA.EDU > > Subject: Re: PCA and Rotation > > > > Principal components is a data reduction procedure, not a way > > to identify interpretable factors. To do the latter, use > > principal axes analysis or some other factor algorithm that > > targets common factors. It makes sense to rotate these since > > you are intreseted in inpretable factors. However, I suggest > > an oblique rotation to ensure that the factors are no > > correlated before forcing them to be. > > > > > > Paul R. Swank, Ph.D. > > Professor, Developmental Pediatrics > > Director of Research, Center for Improving the Readiness of > > Children for Learning and Education (C.I.R.C.L.E.) Medical > > School UT Health Science Center at Houston > > > > -----Original Message----- > > From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] > > On Behalf Of Luis O. > > Sent: Monday, September 19, 2005 5:14 PM > > To: SPSSX-L@LISTSERV.UGA.EDU > > Subject: PCA and Rotation > > > > Dear List Members, > > > > I am new in the list and want to ask a very basic question > > regarding the principal component analysis. I was doing some > > analysis by using principal component method and VArimax > > rotation. However, one of my friends told me that the stat > > book says that we should not rotate principal components. > > That is, the principal component analysis should not rotate > > the soluations, because, by theory, it produces a unique > > soluation. On the other hand, when I read some SPSS manuals, > > they usually tell you to use the principal component method > > with some rotation method. Which is correct? > > > > Luis O. Benavent > > Benavnet Talps Research > > Gandía, Spain > > > > __________ Información de NOD32 1.1222 (20050919) __________ > > > > Este mensaje ha sido analizado con NOD32 Antivirus System > > http://www.nod32.com > > > > ```

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