varset: 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

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.

starting values.

Value

A list containing the following arguments
explanatoryN*2 matrix of 2 explanatory variables.
intermediateN*2 matrix of 2 intermediate variables.
responseresponse vectors with values 0 or 1.

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 = (\binom{u_{1}^{⊤}}{u_{2}^{⊤}}) * 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} = (\binom{u_{1, 1}}{u_{1, 2}}), u_{2} = (\binom{u_{2, 1}}{u_{2, 2}}), | | u_{1} | | = | | u_{2} | | = 1,

i.e. a matrix of two normalised vectors.

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

Run this code

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)

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