varset {ipred} | R Documentation |

## Simulation Model

### Description

Three sets of variables are calculated: explanatory, intermediate and response variables.

### Usage

varset(N, sigma=0.1, theta=90, threshold=0, u=1:3)

### Arguments

`N` |
number of simulated observations. |

`sigma` |
standard deviation of the error term. |

`theta` |
angle between two u vectors. |

`threshold` |
cutpoint for classifying to 0 or 1. |

`u` |
starting values. |

### Details

For each observation values of two explanatory variables *x = (x_1, x_2)^{top}* and of two responses *y = (y_1, y_2)^{top}* are simulated, following the formula:

*
y = U*x+e = ({u_1^{top} atop u_2^{top}})*x+e
*

where x is the evaluation of as standard normal random variable and e is generated by a normal variable with standard deviation `sigma`

. U is a 2*2 Matrix, where

*
u_1 = ({u_{1, 1} atop u_{1, 2}}),
u_2 = ({u_{2, 1} atop u_{2, 2}}),
||u_1|| = ||u_2|| = 1,
*

i.e. a matrix of two normalised vectors.

### Value

A list containing the following arguments

`explanatory` |
N*2 matrix of 2 explanatory variables. |

`intermediate` |
N*2 matrix of 2 intermediate variables. |

`response` |
response vectors with values 0 or 1. |

### Author(s)

Andrea Peters <Peters.Andrea@imbe.imed.uni-erlangen.de>

### References

David J. Hand, Hua Gui Li, Niall M. Adams (2001),
Supervised classification with structured class definitions.
*Computational Statistics & Data Analysis* **36**,
209–225.

### Examples

theta90 <- varset(N = 1000, sigma = 0.1, theta = 90, threshold = 0)
theta0 <- varset(N = 1000, sigma = 0.1, theta = 0, threshold = 0)
par(mfrow = c(1, 2))
plot(theta0$intermediate)
plot(theta90$intermediate)

[Package

*ipred* version 0.8-1

Index]