From: Patrick Burns <pburns_at_pburns.seanet.com>

Date: Thu, 20 Dec 2007 19:58:59 +0000

R-help_at_r-project.org 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. Received on Thu 20 Dec 2007 - 20:03:12 GMT

Date: Thu, 20 Dec 2007 19:58:59 +0000

What I see is the predictions being less extreme than the actual values -- predictions for large actual values are smaller than the actual, and predictions for small actual values are larger than the actual. That makes sense to me. The object is to maximize out-of-sample predictive power, not in-sample predictive power.

Or am I missing something in what you are saying?

Patrick Burns

patrick_at_burns-stat.com

+44 (0)20 8525 0696

http://www.burns-stat.com

(home of S Poetry and "A Guide for the Unwilling S User")

Joshua Knowles wrote:

>Hi all,

*>
**>I have observed that when using the randomForest package to do regression, the
**>predicted values of the dependent variable given by a trained forest are not
**>centred and have the wrong slope when plotted against the true values.
**>
**>This means that the R^2 value obtained by squaring the Pearson correlation are
**>better than those obtained by computing the coefficient of determination
**>directly. The R^2 value obtained by squaring the Pearson can, however, be
**>exactly reproduced by the coeff. of det. if the predicted values are first
**>linearly transformed (using lm() to find the required intercept and slope).
**>
**>Does anyone know why the randomForest behaves in this way - producing offset
**>predictions? Does anyone know a fix for the problem?
**>
**>(By the way, the feature is there even if the original dependent variable
**>values are initially transformed to have zero mean and unit variance.)
**>
**>As an example, here is some simple R code that uses the available swiss
**>dataset to show the effect I am observing.
**>
**>Thanks for any help.
**>
**>--
**>#### EXAMPLE OF RANDOM FOREST REGRESSION
**>
**>library(randomForest)
**>data(swiss)
**>swiss
**>
**>#Build the random forest to predict Infant Mortality
**>rf.rf<-randomForest(Infant.Mortality ~ ., data=swiss)
**>
**>#And predict the training set again
**>pred<-c(predict(rf.rf,swiss))
**>actual<-swiss$Infant.Mortality
**>
**>#Plotting predicted against actual values shows the effect (uncomment to see
**>this)
**>#plot(pred,actual)
**>#abline(0,1)
**>
**># calculate R^2 as pearson coefficient squared
**>R2one<-cor(pred,actual)^2
**>
**># calculate R^2 value as fraction of variance explained
**>residOpt<-(actual-pred)
**>residnone<-(actual-mean(actual))
**>R2two<-1-var(residOpt,na.rm=TRUE)/var(residnone, na.rm=TRUE)
**>
**># now fit a line through the predicted and true values and
**># use this to normalize the data before calculating R^2
**>
**>fit<-lm(actual ~ pred)
**>coef(fit)
**>pred2<-pred*coef(fit)[2]+coef(fit)[1]
**>residOpt<-(actual-pred2)
**>R2three<-1-var(residOpt,na.rm=TRUE)/var(residnone, na.rm=TRUE)
**>
**>cat("Pearson squared = ",R2one,"\n")
**>cat("Coeff of determination = ", R2two, "\n")
**>cat("Coeff of determination after linear fitting = ", R2three, "\n")
**>
**>## END
**>
**>
**>
**>
*

R-help_at_r-project.org 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. Received on Thu 20 Dec 2007 - 20:03:12 GMT

Archive maintained by Robert King, hosted by
the discipline of
statistics at the
University of Newcastle,
Australia.

Archive generated by hypermail 2.2.0, at Fri 21 Dec 2007 - 00:30:20 GMT.

*
Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help.
Please read the posting
guide before posting to the list.
*