[R] how to get residuals in factanal

[Prof Brian Ripley]

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
>
> --- 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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>
>
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-- 
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