# Classification trees for ordinal responses

### Description

This function allows the user to build classification trees for ordinal responses within the CART framework. The trees are grown using the Generalized Gini impurity function, where the misclassification costs are given by the absolute or squared differences in scores assigned to the categories of the response. Pruning is based on the total misclassification rate or on the total misclassification cost.

### Usage

1 2 3 4 |

### Arguments

`formula` |
a formula, as in the |

`data` |
an optional data frame in which to interpret the variables named in the formula. |

`weights` |
optional case weights. |

`subset` |
optional expression saying that only a subset of the rows of the data should be used in the fit. |

`na.action` |
The default action deletes all observations for which |

`split` |
One of |

`prune` |
One of |

`model` |
if logical: keep a copy of the model frame in the result? If the input value for model is a model frame (likely from an earlier call to the |

`x` |
keep a copy of the |

`y` |
keep a copy of the dependent variable in the result. If missing and |

`control` |
options that control details of the |

`...` |
arguments to |

### Details

The use of this function is almost the same as the `rpart`

function.

It is assumed that a set of (not necessarily linear) numerical scores has been assigned to the ordered categories of the response.

The main difference with respect to the `rpart`

function is the presence of two
arguments (`split`

and `prune`

) instead of the `method`

argument.

The argument `split`

controls the splitting function used to grow the classification tree, by setting the
misclassification costs in the generalized Gini impurity function equal to the absolute (`"abs"`

- is the default option) or to the squared
(`"quad"`

) differences in scores.

The argument `prune`

allows the user to select the prediction performance measure used to prune the classification tree,
and can take two values: `"mr"`

(total misclassification rate) or `"mc"`

(total misclassification cost - is the default option).

### Value

An object of class `rpart`

, a superset of class `tree`

.

### Author(s)

Giuliano Galimberti, Gabriele Soffritti, Matteo Di Maso

### References

Breiman L., Friedman J.H., Olshen R.A., Stone C.J. 1984 *Classification and Regression Trees*. Wadsworth International.

Galimberti G., Soffritti G., Di Maso M. 2012 Classification Trees for Ordinal Responses in **R**: The `rpartScore`

Package.
*Journal of Statistical Software*, **47**(10), 1-25.
URL http://www.jstatsoft.org/v47/i10/.

Piccarreta R. 2008 Classication Trees for Ordinal Variables. *Computational Statistics*, **23**, 407-427.

Therneau T.M., Atkinson E.J. 1997 An Introduction to Recursive Partitioning Using rpart Routines.
*Technical Report 61*, Section of Biostatistics, Mayo Clinic, Rochester. URL http://www.mayo.edu/hsr/techrpt/61.pdf.

### See Also

`rpart`

,`rpart.control`

,
`rpart.object`

,`summary.rpart`

,
`print.rpart`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
data("birthwt",package="MASS")
birthwt$Category.s <- ifelse(birthwt$bwt <= 2500, 3,
ifelse(birthwt$bwt <= 3000, 2,
ifelse(birthwt$bwt <= 3500, 1, 0)))
T.abs.mc <- rpartScore(Category.s ~ age + lwt + race + smoke +
ptl + ht + ui + ftv, data = birthwt)
plotcp(T.abs.mc)
T.abs.mc.pruned<-prune(T.abs.mc,cp=0.02)
plot(T.abs.mc.pruned)
text(T.abs.mc.pruned)
T.abs.mr <- rpartScore(Category.s ~ age + lwt + race + smoke +
ptl + ht + ui + ftv, data = birthwt, prune = "mr")
T.quad.mc <- rpartScore(Category.s ~ age + lwt + race + smoke +
ptl + ht + ui + ftv, split = "quad", data = birthwt)
T.quad.mr <- rpartScore(Category.s ~ age + lwt + race + smoke + ptl + ht +
ui + ftv, split = "quad", prune = "mr", data = birthwt)
``` |

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