R help - Jul 2003 - Tree question

I was under the impression that the tree method (e.g. as implemented in
rpart) was insensitive to monotonic transformations of the dependent
variable.  e.g. Breiman Olshen et al. Classification and Regression
Trees  state "In a standard data structure [a tree] is invariant under
all monotone transformations of individual ordered varaibles" (p. 57)

However, I get very different results from
tr.hh.pri <- rpart((log(YPRISX+1)~AGE+DRUGUSEY+SEX+OBSXNUM))

and 

tr.hh.pri <- rpart(YPRISX~AGE+DRUGUSEY+SEX+OBSXNUM)

the former gives more splits and different splits.

Some notes:
The DV is a count variable, and highly skew, with some 0s, many 1s, and
a long right tail out to 99.
AGE ranges from 18-25
DRUGUSEY is ordered (hardest drug used)
and 
OBSXNUM is also ordered (proportion of your friends who object to your
having 'casual sex')

printing the first tree gives

 1) root 307 23.472040 0.7114605  
   2) AGE>=19.5 196 13.811070 0.6857971  
     4) OBSXNUM< 2.5 69  5.712526 0.6338252  
       8) DRUGUSEY>=1.5 15  2.261203 0.5161601 *
       9) DRUGUSEY< 1.5 54  3.185960 0.6665100 *
     5) OBSXNUM>=2.5 127  7.810911 0.7140339 *
   3) AGE< 19.5 111  9.303947 0.7567761  
     6) DRUGUSEY< 0.5 48  1.105266 0.6727132 *
     7) DRUGUSEY>=0.5 63  7.601052 0.8208239  
      14) SEX>=1.5 21  1.258395 0.7317629 *
      15) SEX< 1.5 42  6.092803 0.8653544 *


printing the second tree gives

 1) root 307 144.540700 1.1205210  
   2) AGE>=19.5 196  68.382650 1.0561220 *
   3) AGE< 19.5 111  73.909910 1.2342340  
     6) DRUGUSEY< 0.5 48   2.979167 0.9791667 *
     7) DRUGUSEY>=0.5 63  65.428570 1.4285710  
      14) SEX>=1.5 21   6.571429 1.1428570 *
      15) SEX< 1.5 42  56.285710 1.5714290 *


So, is this the 'exception that proves the rule'? Have I done something
wrong?  Or what?

Any ideas or thoughts?

Thanks in advance


Peter

Peter L. Flom, PhD
Assistant Director, Statistics and Data Analysis Core
Center for Drug Use and HIV Research
National Development and Research Institutes
71 W. 23rd St
www.peterflom.com
New York, NY 10010
(212) 845-4485 (voice)
(917) 438-0894 (fax)

That should be "in"dependent variable.  The CART book, in the sentence
you
quoted, did not make this clear.  But the following paragraph clearly
indicate that they are talking about the predictor variables, not the
response.

This is because the tree algorithm doesn't work on the original predictor
variables, but rather just the ranks of their unique values.  The possible
splits are all the "gaps" between the unique values, so the algorithm
only
need the ranks.  Ranks are clearly invariant to monotone transformation.

Andy
> -----Original Message-----
> From: Peter Flom [mailto:flom at ndri.org] 
> Sent: Tuesday, July 15, 2003 2:44 PM
> To: r-help at stat.math.ethz.ch
> Subject: [R] Tree question
> 
> 
> I was under the impression that the tree method (e.g. as 
> implemented in
> rpart) was insensitive to monotonic transformations of the 
> dependent variable.  e.g. Breiman Olshen et al. 
> Classification and Regression Trees  state "In a standard 
> data structure [a tree] is invariant under all monotone 
> transformations of individual ordered varaibles" (p. 57)
> 
> However, I get very different results from
> tr.hh.pri <- rpart((log(YPRISX+1)~AGE+DRUGUSEY+SEX+OBSXNUM))
> 
> and 
> 
> tr.hh.pri <- rpart(YPRISX~AGE+DRUGUSEY+SEX+OBSXNUM)
> 
> the former gives more splits and different splits.
> 
> Some notes:
> The DV is a count variable, and highly skew, with some 0s, 
> many 1s, and a long right tail out to 99. AGE ranges from 
> 18-25 DRUGUSEY is ordered (hardest drug used) and 
> OBSXNUM is also ordered (proportion of your friends who 
> object to your having 'casual sex')
> 
> printing the first tree gives
> 
>  1) root 307 23.472040 0.7114605  
>    2) AGE>=19.5 196 13.811070 0.6857971  
>      4) OBSXNUM< 2.5 69  5.712526 0.6338252  
>        8) DRUGUSEY>=1.5 15  2.261203 0.5161601 *
>        9) DRUGUSEY< 1.5 54  3.185960 0.6665100 *
>      5) OBSXNUM>=2.5 127  7.810911 0.7140339 *
>    3) AGE< 19.5 111  9.303947 0.7567761  
>      6) DRUGUSEY< 0.5 48  1.105266 0.6727132 *
>      7) DRUGUSEY>=0.5 63  7.601052 0.8208239  
>       14) SEX>=1.5 21  1.258395 0.7317629 *
>       15) SEX< 1.5 42  6.092803 0.8653544 *
> 
> 
> printing the second tree gives
> 
>  1) root 307 144.540700 1.1205210  
>    2) AGE>=19.5 196  68.382650 1.0561220 *
>    3) AGE< 19.5 111  73.909910 1.2342340  
>      6) DRUGUSEY< 0.5 48   2.979167 0.9791667 *
>      7) DRUGUSEY>=0.5 63  65.428570 1.4285710  
>       14) SEX>=1.5 21   6.571429 1.1428570 *
>       15) SEX< 1.5 42  56.285710 1.5714290 *
> 
> 
> So, is this the 'exception that proves the rule'? Have I done 
> something wrong?  Or what?
> 
> Any ideas or thoughts?
> 
> Thanks in advance
> 
> 
> Peter
> 
> Peter L. Flom, PhD
> Assistant Director, Statistics and Data Analysis Core
> Center for Drug Use and HIV Research
> National Development and Research Institutes
> 71 W. 23rd St
> www.peterflom.com
> New York, NY 10010
> (212) 845-4485 (voice)
> (917) 438-0894 (fax)
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list 
> https://www.stat.math.ethz.ch/mailman/listinfo> /r-help
> 
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