This command is available with the Predictive Analytics Module. Click here for more information about how to activate the module.

Assume there are
*m* predictors in a training data set, denoted as
*x*_{1},
*x*_{2}, ...,
*x*_{m}. First, sort the distinct values of predictor
*x*_{1} in the training data set in increasing order. Denote
*x*_{11} as the first distinct value of
*x*_{1}. Then,
*x*_{11} is the x-coordinate for the leftmost point on the plot.

The y-coordinate at
*x*_{1} =
*x*_{11} equals

Term | Description |
---|---|

N | the total number of rows in the training data set |

the observed values for in the training data set | |

j | each
individual row of the
J rows |

the fitted value from the model when
x_{1} =
x_{11},
x_{2} =
x_{2j},....,
x_{m} =
x_{mj} |

Replacing
*x*_{11} by each of the distinct values of
*x*_{1}, we get the y-coordinates for the rest of the points on
the plot. The calculations for the rest of the predictors are done similarly.

Calculations of all the y-coordinates for all distinct values of x can be
time consuming with large data sets. For TreeNet^{®}, there is a faster
way to do the calculations. Refer to Friedman, J. H. (2001). Greedy function
approximation: A gradient boosting machine.
The Annals of Statistics, 29(5), page 1221.

The calculations for multinomial response case are similar. Here the fitted value is from the model for each individual class.

Assume there are
*m* predictors in a training data set, denoted as
*x*_{1},
*x*_{2}, ...,
*x*_{m}. First, sort the distinct values of predictors
*x*_{1},
*x*_{2} in the training data set in increasing order. Denote
*x*_{11},
*x*_{21} as one of the distinct pairs. Then, each pair makes the
x and y-coordinates for a point on the surface plot.

The z-coordinate at
*x*_{1} =
*x*_{11},
*x*_{2} =
*x*_{21} equals

Term | Description |
---|---|

N | the total number of rows in the training
data set that all share the commonality of
x_{1} =
x_{11},
x_{2} =
x_{21} |

the observed values for in the training data set | |

j | each
individual row of the
J rows |

the fitted value from the model when
x_{1} =
x_{11},
x_{2} =
x_{21},
x_{3} =
x_{3j}....,
x_{m} =
x_{mj} |

The completion of the calculations for all distinct value combinations of
*x*_{1} and
*x*_{2} produces all the z-coordinates for the contour or
surface plot. For large data sets, the calculations for all distinct pairs of x
and y are time consuming. For TreeNet^{®} models, there is a faster way
to do the calculations. Refer to Friedman, J. H. (2001). Greedy function
approximation: A gradient boosting machine.
The Annals of Statistics, 29(5), page 1221.