[R] PCA for Binary data

[Prof Brian Ripley]

On Tue, 12 Jun 2007, Spencer Graves wrote:

>      The problem with applying prcomp to binary data is that it's not
> clear what problem you are solving.
>
>      The standard principal components and factor analysis models
> assume that the observations are linear combinations of unobserved
> "common" factors (shared variability), normally distributed, plus normal
> noise, independent between observations and variables.  Those
> assumptions are clearly violated for binary data.
>
>      RSiteSearch("PCA for binary data") produced references to 'ade4'
> and 'FactoMineR'.  Have you considered these?  I have not used them, but
> FactoMineR included functions for 'Multiple Factor Analysis for Mixed
> [quantitative and qualitative] Data'

AFAIK, that is not using 'factor analysis' in the same sense as e.g. 
factanal().

Continuous underlying variables with binary manifest variables is part of 
latent variable analysis.  Package 'ltm' covers a variety of such models.

But to begin to give advice we would need to know the scientific problem 
for which Ranga Chandra Gudivada is looking for a tool. Simon Blomberg 
mentioned ordination, but that is only one of several classes of uses of 
PCA (which finds a linear subspace that both has maximal variance within 
and is least-squares fitting to the data).

>
>      Hope this helps.
>      Spencer Graves
>
> Josh Gilbert wrote:
>> I don't understand, what's wrong with using prcomp in this situation?
>>
>> On Sunday 10 June 2007 12:50 pm, Ranga Chandra Gudivada wrote:
>>
>>> Hi,
>>>
>>>     I was wondering whether there is any package implementing Principal
>>> Component Analysis for Binary data
>>>
>>>                                               Thanks chandra
>>>
>>>
>>> ---------------------------------
>>>
>>>
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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)
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