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In R the princomp()and the factanal() are somewhat similar. At least their output looks pretty similar. I learned that this is not surprising since the print function of princomp comes from factanal. I understand that SS loadings do not make much sense for princomp as it is bounded to 1 anyway. Moreover, as Joris stated on nabble, the proportion of variance is only printed because of the common print function, but does not contain valuable information when princomp is used.

What I do not understand is rather not an R question but more a multivariate stats question what is the conceptual difference between these PCA and Factor Analysis functions as they are used in R? This question relates particularly to the scores (let's assume "regression" scores for FA) respectively the difference between scores in both concepts? What should I rather use when I want to use to resulting scores in a regression model (for example in order to circumvent multicollinearity)? I also understand that PCA has a fixed number of components while FA has fewer factors than variables.

richiemorrisroe's answer in the thread suggested by Rob Hyndman might go into that direction.

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    $\begingroup$ See stats.stackexchange.com/questions/1576/… $\endgroup$ – Rob Hyndman Jun 15 '11 at 23:05
  • $\begingroup$ first of all thanks for the pointer. Maybe I should restate the question and narrow it down to the difference between scores. $\endgroup$ – hans0l0 Jun 16 '11 at 8:06
  • $\begingroup$ A couple of comments: (1) the No. components retained for interpreting a PCA rarely go beyond 5, in applied settings; (2) can you provide a link to the discussion about PCA SS loadings -- in my understanding, the % of var. explained (whether it be PCA or FA-based, without rotation) come into play when deciding about the number of components to retained; (3) as you said you're also interested in a regression framework where PCA might be used to circumvent multicollinearity, it would be interesting to know more about your goal because in this case PLS regression or PCR might do the job. $\endgroup$ – chl Jun 16 '11 at 9:19
  • $\begingroup$ here's the link to Joris' answer on nabble: r.789695.n4.nabble.com/… $\endgroup$ – hans0l0 Jun 16 '11 at 9:40
  • $\begingroup$ my.princomp - my.fractanal :) ;) $\endgroup$ – John Jun 16 '11 at 12:00

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