[R] how to get residuals in factanal

[Yijun Zhao]

p.s. I tried to use both "regression" and "Bartlett" way to get the scores. In both 
cases, the scores are uncorrelated, but the errors are NOT uncorrelated to the scores,
and are also NOT uncorrelated among themselves. 

What am I missing? factanal() are supposed to give independent errors vectors, so at
least should be uncorrelated among themselves. 

Thank you in advance for the help.

Yijun

--- Yijun Zhao <yijun2011 at yahoo.com> wrote:

> 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.
> 
> Yijun
> 
> --- 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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