R help - Sep 2013 - Question about R2 in pls package

Hi,

I have questions about R2 used in pls (or multivariate analysis).

Is R2 same with the square of the PCC (Pearson Correlation Coefficient)?

I found the following description from wiki (Coefficient of determination)

------------------------
Similarly, in linear least squares regression with an estimated intercept
term, R2 equals the square of the Pearson correlation coefficient between
the observed and modeled (predicted) data values of the dependent variable.
-------------------------

If so, Q2 (R2 of cross validation) should range between 0 and 1.
But it doesn't. I got negative values of Q2 when running my dataset.
Of course, from the definition of Q2, Q2 can be negative when my model is
not at all predictive.

My question is what the relationship between R2 and pcc^2 is.

Euna

	[[alternative HTML version deleted]]

On Sep 4, 2013, at 10:39 PM, Euna Jeong wrote:
> Hi,
>
> I have questions about R2 used in pls (or multivariate analysis).
>
> Is R2 same with the square of the PCC (Pearson Correlation  
> Coefficient)?
>
> I found the following description from wiki (Coefficient of  
> determination)
>
> ------------------------
> Similarly, in linear least squares regression with an estimated  
> intercept
> term, R2 equals the square of the Pearson correlation coefficient  
> between
> the observed and modeled (predicted) data values of the dependent  
> variable.
> -------------------------
>
> If so, Q2 (R2 of cross validation) should range between 0 and 1.
> But it doesn't. I got negative values of Q2 when running my dataset.
> Of course, from the definition of Q2, Q2 can be negative when my  
> model is
> not at all predictive.
>
> My question is what the relationship between R2 and pcc^2 is.
>
"Adjusted R-squareds" can become negative when the adjustment for the
added number of predictors overwhelms the increased model fit on the  
scale of adjustment.

Do a search of the archives for negative r-squared. Here's just one of  
many:

http://r-project.markmail.org/search/?q=list%3Aorg.r-project.r-help%20%20negative%20r-squared#query
:list%3Aorg.r-project.r-help%20%20negative%20r-squared+page:1+mid:rhiqm5bcm4maxnef+state:results

-- 

David Winsemius, MD
Alameda, CA, USA

Euna Jeong <eajeong at gmail.com> writes:
> I have questions about R2 used in pls (or multivariate analysis).
>
> Is R2 same with the square of the PCC (Pearson Correlation Coefficient)?
If you read the manual for R2 in the pls package, it will tell you how
R2 is calculated there, and that for _training_ data it is indeed
PCC^2, but _not_ for cross-validation or test data.

IMHO, R^2 only has a meaningful interpretation for training data.  For
test data or cross-validation, I prefer MSEP or RMSEP.

-- 
Regards,
Bj?rn-Helge Mevik