[R-sig-Geo] negative r-squares

[Jason Gasper]

Hello Pinar,

I don't know for sure what your calculation is, but R2 values can range 
from -inf to 1 if an adjusted R2 is being used. In other words, one 
possibility is that your adjusting for degrees of freedom using some 
variation of the following (n-1/n-k)(1-R2) where the adjusted R2 is 
equivalent to simple regression when k=1.  So when the estimated R2 less 
than or equal to 0 that means the model forecast is inferior to the mean 
(really poor fit). Another way of looking at a negative R2 is that the 
fit is worse than a horizontal line, so the sum-of-squares from the 
model is larger than the sum-of-squares from a horizontal line. Again, 
poor fit.

Cheers-Jason


Pinar Aslantas Bostan wrote:
> Hi all,
>
> I am working about comparison of kriging and regression methods. I 
> have one dependent (PREC) and seven independent variables. I created 
> 10 different test and train datasets. I am using train datasets for 
> building the models and test datasets for calculating error (RMSE) and 
> r-squares. When I obtained prediction values for grid, then I use 
> overlay() to get predictions for test dataset. For example:
>
> # regression kriging
> # dem is the grid (I want to get predictions for each pixel of dem) 
> and dem$rk.pred1 contains regression kriging predictions
>> test1$rk.predicted = dem$rk.pred1[overlay(dem, test1)]
>
> # calculating r-square values based on test values
>> ss <-(test1$PREC-mean(test1$PREC))*(test1$PREC-mean(test1$PREC))
>> sst1<-sum(ss)
>> e <-(test1$PREC-test1$rk.predicted)*(test1$PREC-test1$rk.predicted)
>> sse.rk<-sum(e)
>> rk1.r.square<-1-(sse.rk/sst1)
>
> My problem is that, for some datasets the methods can be resulted with 
> negative r-squares. Here I gave an example about regression kriging 
> but also same problem may occur for linear regression. I checked the 
> dependent and independent variables and there is no problem with them. 
> Are there anyone who knows another function instead of overlay() for 
> the same purpose? (I thougt that maybe the problem is because of 
> overlay function) or do you have any idea about reason of negative 
> r-square values?
>
> Best regards,
> Pinar
>
>
> ******************************************************************************** 
>
> Pinar Aslantas Bostan
> Research Assistant
> Department of Geodetic and
> Geographic Information Technologies (GGIT)
> Middle East Technical University
> 06531 Ankara/TURKEY
> aslantas at metu.edu.tr
>
> _______________________________________________
> R-sig-Geo mailing list
> R-sig-Geo at stat.math.ethz.ch
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo

-- 
Jason Gasper
National Marine Fisheries Service
Alaska Region, Sustainable Fisheries Division
709 W. 9th St. Juneau, Alaska 99801 
Juneau, Alaska 99801

Phone  907-586-7237
Fax 907-586-7249