[R] how to get residuals in factanal

[Yijun Zhao]

1. ?factanal says:

======================================
The factor analysis model is

x = Lambda f + e
...
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.
===============================================

so if I do x - Lambda * f, I should get those independent e's. What am I missing?


2. Could you also please tell me what's the difference btw 'residuals' and 'errors'. I
guess (x - lambda * f) are called 'errors'. So what is the definition of 'residuals'?

Thank you.

Yijun


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

> On Sun, 6 Jan 2008, Yijun Zhao wrote:
> 
> > 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.
> 
> Supposed by whom?  You are confusing 'error' and 'residual': the residuals 
> from a regression are not uncorrelated.
> 
> >
> > Thank you in advance for the help.
> >
> > Yijun
> >

> >
> >> 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
> >>>
> >>
> >>
> >>
> >>
> >> ____________________________________________________________________________________
> >> Never miss a thing.  Make Yahoo your home page.

> >>
> >
> >
> >
> >     
> ____________________________________________________________________________________
> > Looking for last minute shopping deals?


> >
> 
> -- 
> 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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