```Date: Tue, 20 Sep 2005 14:52:30 +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 Hector, thank you for your clear explanations. Your comments bring me to the ultimate question: when we use SPSS's "Factor Analysis" with the "Principal Component" method and VARIMAX rotation. are we conducting FA or PCA? I realized that some researchers are arguing that SPSS's "Factor Analysis" with the default function of "Principal component" is causing a great confusion in distinguishing between FA and PCA. Because of this, my stat friends recommend not to choose principal componet method in FA. Furthermore, their explanations are accidentally similar to what Paul suggests: the use of oblique rotation. Luis >From: "Hector Maletta" >To: "'Luis O.'" >Subject: RE: PCA and Rotation >Date: Tue, 20 Sep 2005 08:26:07 -0300 > >Luis, >I do not think your friends are right. Historically rotation arose with >principal axes, but nothing hinders rotation for principal components. Both >PCA and PA are methods of data reduction. They represent or summarize n >variables through kthinking that if you apply PCA to identify one dominant factor underlying >all your varibles, and explaining by itself a large portion of total >variance, it is pointless to rotate it. But PCA is not restricted to that >situation, and often two or more factors are needed to explain a large part >of variance. Those factors may be rotated to make the structure more clear, >i.e. to associate each factor more closely with some group of variables >that >have a common meaning (e.g. various linguistic tests associated mainly with >one factor or component). > >By the way, factor and component are the same. The vocabulary just reflects >how they were used by their introductors in the past, nearly 100 years ago. > >Hector > > > > -----Original Message----- > > From: Luis O. [mailto:soka28806@hotmail.com] > > Sent: Tuesday, September 20, 2005 5:43 AM > > To: hmaletta@fibertel.com.ar > > Subject: Re: PCA and Rotation > > > > Paul and Hector, thank you very much for your quick reply. I > > sincerely appreciaed your explanations. > > > > I want to ask one more question to Hector. Based on your > > explanations, you seem to be saying that in BOTH cases (PCA > > and Principal Axes), we can rotate the principal components > > (although you switched the word to "factor" in the later > > paragraphs) 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 correct? I am asking this question, > > because this is precisely the doubt I had. Some of my stat > > friends say that in PCA the rotation should not be used, > > because it is a data reduction procedure (as Paul explains), > > and provides a best linear combination of the variance. > > Furthermore, they are making a point in that if we rotate the > > principal components in PCA, they are no longer "principal" > > components. > > > > I would appreciate your further clarification. > > > > 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 > > > > > > > > > > > > > > > > __________ Información de NOD32 1.1224 (20050920) __________ > > > > Este mensaje ha sido analizado con NOD32 Antivirus System > > http://www.nod32.com > > > > > ```

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