varset: Simulation Model

In ipred: Improved Predictors

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.

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)

ipred documentation built on March 31, 2023, 11:08 p.m.