Regression trees with an ordinal response variable

Hi,

I am working on a regression tree in Rpart that uses a continuous response
variable that is ordered.  I read a previous response by Pfr. Ripley to a
inquiry regarding the ability of rpart to handle ordinal responses in
2003.  At that time rpart was unable to implement an algorithm to handle
ordinal responses.  Has there been any effort to rectify this in recent
years?

### ordinal regression
mammoct <- ctree(ME ~ ., data = mammoexp)

### estimated class probabilities
treeresponse(mammoct, newdata = mammoexp[1:5, ])

sessionInfo()

Thanks!

Stacey



On Mon, 2 Jun 2003, Andreas Christmann wrote:

1. RE: Ordinal data - Regression Trees & Proportional Odds

(Liaw, Andy)

AFAIK there's no implementation (or description) of tree algorithm
that handles ordinal response.

Regression trees with an ordinal response variable can be computed with
SPSS Answer Tree 3.0.

They *can* be handled by tree or rpart in R.
I think Andy's point was that there is no consensus as to the right way to
handle them: certainly using the codes of categories works and may often
be reasonable, and treating ordinal responses as categorical is also very
often perfectly adequate.
Note that rpart is user-extensible, so it would be reasonably easy to
write
an extension for a proportional-odds logistic regression model, if that is
thought appropriate (and it seems strange to me to impose such strong
structure on the model with such a general `linear predictor': POLR
models are often in my experience a poor reflection of real problems).
--
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

Den Fr, 2007-02-02, 06:03 skrev Stacey Buckelew:

Hi,

I am working on a regression tree in Rpart that uses a continuous response
variable that is ordered.  I read a previous response by Pfr. Ripley to a
inquiry regarding the ability of rpart to handle ordinal responses in
2003.  At that time rpart was unable to implement an algorithm to handle
ordinal responses.  Has there been any effort to rectify this in recent
years?

The `ctree' function in the `party' package is able to handle ordered
responses, but note that there are fundamental differences between the
former and `rpart'. Reading the package vignette and the relevant
references will help.

However, at the moment there seems to be a problem related to the ordinal
case (predicted probabilities > 1) and I've CC:ed the package's maintainer
(Torsten Hothorn).

HTH,
Henric

- - - - -

Torsten, consider the following:

### ordinal regression
mammoct <- ctree(ME ~ ., data = mammoexp)

Warning message:
no admissible split found

### estimated class probabilities
treeresponse(mammoct, newdata = mammoexp[1:5, ])

[[1]]
[1] 1.822115

[[2]]
[1] 1.265487

[[3]]
[1] 1.822115

[[4]]
[1] 1.560440

[[5]]
[1] 1.822115

sessionInfo()

R version 2.4.1 Patched (2007-01-06 r40399)
i386-pc-mingw32

locale:
LC_COLLATE=Swedish_Sweden.1252;LC_CTYPE=Swedish_Sweden.1252;LC_MONETARY=Swedish_Sweden.1252;LC_NUMERIC=C;LC_TIME=Swedish_Sweden.1252

attached base packages:
[1] "stats4"    "grid"      "splines"   "stats"     "graphics"  "grDevices"
[7] "utils"     "datasets"  "methods"   "base"

other attached packages:
     party         vcd  colorspace        MASS strucchange    sandwich
   "0.9-8"     "1.0-2"      "0.95"    "7.2-31"     "1.3-1"     "2.0-1"
       zoo        coin     mvtnorm  modeltools    survival
   "1.2-2"     "0.5-2"     "0.7-5"    "0.2-10"      "2.30"

Thanks!

Stacey



On Mon, 2 Jun 2003, Andreas Christmann wrote:

1. RE: Ordinal data - Regression Trees & Proportional Odds

(Liaw, Andy)

AFAIK there's no implementation (or description) of tree algorithm
that handles ordinal response.

Regression trees with an ordinal response variable can be computed with
SPSS Answer Tree 3.0.

They *can* be handled by tree or rpart in R.
I think Andy's point was that there is no consensus as to the right way to
handle them: certainly using the codes of categories works and may often
be reasonable, and treating ordinal responses as categorical is also very
often perfectly adequate.
Note that rpart is user-extensible, so it would be reasonably easy to
write
an extension for a proportional-odds logistic regression model, if that is
thought appropriate (and it seems strange to me to impose such strong
structure on the model with such a general `linear predictor': POLR
models are often in my experience a poor reflection of real problems).
--
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

Torsten, consider the following:

### ordinal regression
mammoct <- ctree(ME ~ ., data = mammoexp)

Warning message:
no admissible split found

### estimated class probabilities
treeresponse(mammoct, newdata = mammoexp[1:5, ])

[[1]]
[1] 1.822115

[[2]]
[1] 1.265487

[[3]]
[1] 1.822115

[[4]]
[1] 1.560440

[[5]]
[1] 1.822115