Bayesian PCA

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Bayesian PCA

Lucy Asher
First of all I should say this email is more of a general statistics questions rather than being specific to using R but I'm hoping that this may be of general interest.

I have a dataset that I would really like to use PCA on and have been using the package pcaMethods to examine my data. The results using traditional PCA come out really nicely. The dataset is comprised of a set of questions on dog behaviour answered by their handlers. The questions fall into distinct components which may biological sense and the residuals are reasonable small. Now the problem. I don't have a big enough sample to run traditional PCA. I have about 40 dogs and 60 questions so which ever way you look at it not enough. There is past data available on some of the questions and the realtionships between them so I was wondering whether Bayesian PCA would be a useful alternative using past research to inform my priors. I wondered if anyone knew whether Bayesian PCA was better suited to smaller datasets than traditional (ML) PCA? If not I wondered if anyone knew of packages in R that could do dimension reduction on datasets with small sample sizes?

Many Thanks,

Lucy
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Re: Bayesian PCA

Christian Hennig
Dear Lucy,

not an R-related response at all, but if it's questionnaire data, I'd
probably try to do dimension reduction in a non-automated way by defining
a number of 10 or so meaningful scores that summarise your questions.
Dimension reduction is essentially about how to aggregate
the given information into low-dimensional measurements, which
according to my opinion should be rather driven by the research aim and
meaning of the variables than by the distribution of the data, if at all
possible.
You can then use PCA in order to examine the remaining dimensions

Christian

On Tue, 12 Apr 2011, Lucy Asher wrote:

> First of all I should say this email is more of a general statistics
> questions rather than being specific to using R but I'm hoping that this
> may be of general interest.
>
> I have a dataset that I would really like to use PCA on and have been
> using the package pcaMethods to examine my data. The results using
> traditional PCA come out really nicely. The dataset is comprised of a
> set of questions on dog behaviour answered by their handlers. The
> questions fall into distinct components which may biological sense and
> the residuals are reasonable small. Now the problem. I don't have a big
> enough sample to run traditional PCA. I have about 40 dogs and 60
> questions so which ever way you look at it not enough. There is past
> data available on some of the questions and the realtionships between
> them so I was wondering whether Bayesian PCA would be a useful
> alternative using past research to inform my priors. I wondered if
> anyone knew whether Bayesian PCA was better suited to smaller datasets
> than traditional (ML) PCA? If not I wondered if anyone knew of packages
> in R that could do dimension reduction on datasets with small sample
> sizes?
>
> Many Thanks,
>
> Lucy
> This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it.   Please do not use, copy or disclose the information contained in this message or in any attachment.  Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham.
>
> This message has been checked for viruses but the contents of an attachment
> may still contain software viruses which could damage your computer system:
> you are advised to perform your own checks. Email communications with the
> University of Nottingham may be monitored as permitted by UK legislation.
> [[alternative HTML version deleted]]
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

*** --- ***
Christian Hennig
University College London, Department of Statistical Science
Gower St., London WC1E 6BT, phone +44 207 679 1698
[hidden email], www.homepages.ucl.ac.uk/~ucakche

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Re: Bayesian PCA

William Revelle
Dear Lucy,
   You might consider some of the scale construction techniques
available in the psych package.  In particular, the iclust function
is meant for this very problem:  how to form reliable item composites.

Bill

At 4:38 PM +0100 4/12/11, Christian Hennig wrote:

>Dear Lucy,
>
>not an R-related response at all, but if it's questionnaire data,
>I'd probably try to do dimension reduction in a non-automated way by
>defining a number of 10 or so meaningful scores that summarise your
>questions.
>Dimension reduction is essentially about how to aggregate the given
>information into low-dimensional measurements, which according to my
>opinion should be rather driven by the research aim and meaning of
>the variables than by the distribution of the data, if at all
>possible.
>You can then use PCA in order to examine the remaining dimensions
>
>Christian
>
>On Tue, 12 Apr 2011, Lucy Asher wrote:
>
>>First of all I should say this email is more of a general
>>statistics questions rather than being specific to using R but I'm
>>hoping that this may be of general interest.
>>
>>I have a dataset that I would really like to use PCA on and have
>>been using the package pcaMethods to examine my data. The results
>>using traditional PCA come out really nicely. The dataset is
>>comprised of a set of questions on dog behaviour answered by their
>>handlers. The questions fall into distinct components which may
>>biological sense and the residuals are reasonable small. Now the
>>problem. I don't have a big enough sample to run traditional PCA. I
>>have about 40 dogs and 60 questions so which ever way you look at
>>it not enough. There is past data available on some of the
>>questions and the realtionships between them so I was wondering
>>whether Bayesian PCA would be a useful alternative using past
>>research to inform my priors. I wondered if anyone knew whether
>>Bayesian PCA was better suited to smaller datasets than traditional
>>(ML) PCA? If not I wondered if anyone knew of packages in R that
>>could do dimension reduction on datasets with small sample sizes?
>>
>>Many Thanks,
>>
>>Lucy
>>This message and any attachment are intended solely for the
>>addressee and may contain confidential information. If you have
>>received this message in error, please send it back to me, and
>>immediately delete it.   Please do not use, copy or disclose the
>>information contained in this message or in any attachment.  Any
>>views or opinions expressed by the author of this email do not
>>necessarily reflect the views of the University of Nottingham.
>>
>>This message has been checked for viruses but the contents of an attachment
>>may still contain software viruses which could damage your computer system:
>>you are advised to perform your own checks. Email communications with the
>>University of Nottingham may be monitored as permitted by UK legislation.
>> [[alternative HTML version deleted]]
>>
>>______________________________________________
>>[hidden email] mailing list
>>https://stat.ethz.ch/mailman/listinfo/r-help
>>PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>>and provide commented, minimal, self-contained, reproducible code.
>>
>
>*** --- ***
>Christian Hennig
>University College London, Department of Statistical Science
>Gower St., London WC1E 6BT, phone +44 207 679 1698
>[hidden email], www.homepages.ucl.ac.uk/~ucakche
>
>______________________________________________
>[hidden email] mailing list
>https://stat.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>and provide commented, minimal, self-contained, reproducible code.


--
William Revelle http://personality-project.org/revelle.html
Professor http://personality-project.org
Department of Psychology             http://www.wcas.northwestern.edu/psych/
Northwestern University http://www.northwestern.edu/
Use R for psychology                       http://personality-project.org/r
It is 6 minutes to midnight http://www.thebulletin.org

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