[R-sig-Geo] Principal Component Analysis - Selecting components? + right choice?

[Edzer Pebesma]

Principle components don't search for directions that best explain your 
dependent variable, but rather try to capture variability and/or 
correlation in the predictors. Methods that look for subspaces that best 
predict the dependent are for instance are partial least squares and 
ridge regression. Using them, you could with the same amount of degrees 
of freedom look at completely different directions.

In addition to Ashton's remark: a variety of principle components that 
tries to pick up spatial correlated patterns in addition to maximum 
variability/correlation between variables is MNF (minimum nois fraction) 
factors, also called min/max autocorrelation factors; see the papers by 
Green, Switzer and others. I'm not aware of implementations of them in 
R, but would be interested to hear.

Best regards,
--
Edzer

Ashton Shortridge wrote:
> Hi Corrado,
>
>   
>> I run the PCA using prcomp, quite successfully. Now I need to use a
>> criteria to select the right number of PC. (that is: is it 1,2,3,4?)
>>
>> What criteria would you suggest?
>>     
>
> that's an interesting and probably controversy-generating question. It's 
> probably not an R-sig-geo question, either. I am not a PCA person, but the 
> rule of thumb I am aware of is to plot the variability each 
> component 'explains' and look for a clear breakpoint. I would think about any 
> multivariate analysis text would have a better explanation than I can give, 
> though.
>
> As for something more rigorous, I think a lot of people are reluctant to use 
> PCA as a modeling approach not so much because it's hard to choose a 
> threshold for selecting components, but because the interpretation of the 
> meaning of each component is pretty subjective. If you want an explanatory 
> model, be careful about using PCA. You would be better served by deciding, 
> based perhaps on expert knowledge about the variables, which ones to use in 
> the model and which ones not to.
>
> To try to make this a bit more spatial, and therefore more relevant to the 
> list, I will also warn you that your various climate variables are almost 
> certainly spatially autocorrelated - that is, neighboring and nearby 
> observations in the grid are not independent. That has serious implications 
> for standard multivariate analysis techniques and diagnostics.
>
> Yours,
>
> Ashton
>
> On Thursday 11 December 2008 06:46:37 am Corrado wrote:
>   
>> Dear R gurus,
>>
>> I have some climatic data for a region of the world. They are monthly
>> averages 1950 -2000 of precipitation (12 months), minimum temperature (12
>> months), maximum temperature (12 months). I have scaled them to 2 km x 2km
>> cells, and I have around 75,000 cells.
>>
>> I need to feed them into a statistical model as co-variates, to use them to
>> predict a response variable.
>>
>> The climatic data are obviously correlated: precipitation for January is
>> correlated to precipitation for February and so on .... even precipitation
>> and temperature are heavily correlated. I did some correlation analysis and
>> they are all strongly correlated.
>>
>> I though of running PCA on them, in order to reduce the number of
>> co-variates I feed into the model.
>>
>> I run the PCA using prcomp, quite successfully. Now I need to use a
>> criteria to select the right number of PC. (that is: is it 1,2,3,4?)
>>
>> What criteria would you suggest?
>>
>> At the moment, I am using a criteria based on threshold, but that is highly
>> subjective, even if there are some rules of thumb (Jolliffe,Principal
>> Component Analysis, II Edition, Springer Verlag,2002).
>>
>> Could you suggest something more rigorous?
>>
>> By the way, do you think I would have been better off by using something
>> different from PCA?
>>
>> Best,
>>     
>
>
>
>   

-- 
Edzer Pebesma
Institute for Geoinformatics (ifgi), University of Münster
Weseler Straße 253, 48151 Münster, Germany. Phone: +49 251
8333081, Fax: +49 251 8339763 http://ifgi.uni-muenster.de/
http://www.springer.com/978-0-387-78170-9 e.pebesma at wwu.de