[R-SIG-Finance] Coefficients, Principal Component Regression. pcr

[Matthieu Stigler]

Dear Karla

I have really limited knowledge in pls and pcr models, but I believe one 
still can have inference in those models, since you are doing a 
regression among different factors.

I don't know exactly to what you are applying your models, but another 
framework very similar to PLS/PCR is Structural Equation Modelling, 
which allows to make different regressions among latent variables (and 
nest factor models, maybe even pcr).

If this is useful for you, you might have a look at the openMx R 
project, which has just done an important release (see annoucement 
below) and seems to be very impressive.

Hope this helps

Matthieu

Dear R users,

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For the OpenMx team.


Le 18. 10. 10 01:13, Sarbo a écrit :
> Karla,
>
> The mathematics you've outlined are not quite correct. In multiple
> linear regression you are attempting to find the hyperplane that most
> closely approximates the data set that you are dealing with. In PCA, you
> are performing a change of coordinates so that your data are arranged in
> a different Cartesian space. This means that all of your data can now be
> represented as linear combinations of the eigenvectors calculated from
> your correlation (or covariance) matrix. There is no "approximation"
> going on, hence no t-values or F-statistics to calculate goodness of
> fit. You can, however, figure out the explanatory power of each new
> variable pretty easily.
>
> The significance of each of the basis vectors in your eigenspace is
> represented by the absolute magnitude of each eigenvalue. You can figure
> out how much of your data are represented by each eigenvector by
> plotting the cumulative variance explained by the eigenvectors. The
> function "princomp", which is part of the base R distribution these days
> unless I'm very much mistaken, will help you do this using the "plot"
> method.
>
> On Thu, 2010-10-14 at 08:20 -0600, karla hernandez villafuerte wrote:
>
>    
>> Dear Members:
>>
>> I am trying to applied a Principal Component Regression using the pls package and the next formula:
>>
>> PCA<-pcr(Beta~XCT+XCLa+XCLb+XCLc+XCLd+XCLe+XCLf+XCLg+XCLh,
>> data=mydata,ncomp=15,validation="LOO",method="svdpc", model=TRUE, y=TRUE, x=TRUE)
>>
>> where XCT is a matrix of cuantitatives variables and each one of  XCL are cualitatives variables.
>>
>> I can estimate the coefficient matrix using:
>>
>> coef(PCA,comps=5)
>>
>> As far I understand, the PCR perform a multilple regression analysis of the response variable against the reduced set of principal components, using OLS. The results coefficients are transformed into a new set of coefficients (those in coef(PCA,comps=5)) that correspond to a mathematic transformation of the original ones.
>>
>> My question is: Can I see the t values for the final coefficents estimated in coef(PCA,comps=5) or can I have the results of the OLS equation?. In other case which is the best way to analyse the significance of the variables?
>>
>> Thanks!!
>>
>> Karla Hernndez Villafuerte
>>
>>    		 	   		
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