[R] how to get residuals in factanal

Yijun Zhao yijun2011 at yahoo.com
Sun Jan 6 20:04:01 CET 2008

The factanal was called with 'varimax' rotation. The factors scores are uncorrelated. But
the residuals I got by using

X - sum(loadings*factors-scores) is not uncorrelated to the factor scores. 

I thought the residuals should be independent to the factor scores as ?factanal says:

The factor analysis model is 

x = Lambda f + e

for a p¨Celement row-vector x, a p x k matrix of loadings, a k¨Celement vector of scores
and a p¨Celement vector of errors. None of the components other than x is observed, but
the major restriction is that the scores be uncorrelated and of unit variance, and that
the errors be independent with variances Phi, the uniquenesses. 

Thank you.


--- Prof Brian Ripley <ripley at stats.ox.ac.uk> wrote:

> On Sun, 6 Jan 2008, Yijun Zhao wrote:
> > In R factanal output, I can't find a function to give me residuals e.
> >
> > I mannually got it by using x -lamda1*f1 -lamda2*f2  - ... -lamdan*fn, but the e
> > I got are not uncorrelated with all the f's.
> >
> > What did I do wrong? Please help.
> What did you use for 'f'?  The factors ('scores') are latent quantities in 
> factor analysis, and there is more than one way to predict them.  Most 
> likely your assumption of uncorrelatedness is not correct for the 
> residuals and scores as you computed them.
> -- 
> Brian D. Ripley,                  ripley at stats.ox.ac.uk
> Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
> University of Oxford,             Tel:  +44 1865 272861 (self)
> 1 South Parks Road,                     +44 1865 272866 (PA)
> Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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