[R] factanal question

William Revelle lists at revelle.net
Mon Dec 1 16:25:49 CET 2008

Don and John,
   factor.residuals in the psych package does what you want (and 
basically what  John wrote).


At 9:30 AM -0500 12/1/08, John Fox wrote:
>Dear Don,
>All long as you leave the factors unrotated or do an orthogonal rotation (as
>is the default), you can compute reproduced correlations among the variables
>from the factor loadings, and thus residual correlations given the loadings
>and the original correlation matrix, both of which are accessible in the
>object returned by factanal(); the following isn't carefully tested, but
>should work:
>repRes <- function(F, round=3){
>   A <- loadings(F)
>   R <- F$correlation
>   RR <- A %*% t(A)
>   ResR <- R - RR
>   list(reproduced.correlations=round(RR, round),
>     residual.correlations=round(ResR, round))
>   }
>Here F is an object returned by factanal(). The diagonal elements of the
>reproduced correlations are the communalities, and of the residual
>correlations, the uniquenesses.
>To do this from an oblique rotation would require the factor-correlation
>matrix, which, as has been pointed out previously, factanal() oddly doesn't
>provide. In this case, that's not a real impediment, since reproduced and
>residual correlations are invariant with respect to rotation of the factors.
>I hope this helps,
>  John
>John Fox, Professor
>Department of Sociology
>McMaster University
>Hamilton, Ontario, Canada
>web: socserv.mcmaster.ca/jfox
>>  -----Original Message-----
>>  From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
>>  Behalf Of Don McNeil
>>  Sent: November-30-08 11:39 PM
>>  To: r-help at r-project.org
>>  Subject: [R] factanal question
>>  Dear R users:
>>  I'm wondering if it's possible to get the residual correlation matrix when
>>  using factanal.
>>  Since factanal assumes that the errors are normally distributed and
>>  independent (provided the factor model fits the data) this would be
>>  Of course you would need to submit the data to the function to get the
>>  residuals (not just their correlation matrix), but it should be possible
>>  get the residual correlation matrix if only the data correlation matrix is
>>  provided.
>>  Don McNeil
>>  ______________________________________________
>>  R-help at r-project.org mailing list
>>  https://stat.ethz.ch/mailman/listinfo/r-help
>>  PLEASE do read the posting guide
>>  and provide commented, minimal, self-contained, reproducible code.
>R-help at r-project.org mailing list
>PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>and provide commented, minimal, self-contained, reproducible code.

William Revelle		http://personality-project.org/revelle.html
Professor			http://personality-project.org/personality.html
Department of Psychology             http://www.wcas.northwestern.edu/psych/
Northwestern University	http://www.northwestern.edu/
Attend  ISSID/ARP:2009               http://issid.org/issid.2009/

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