Simulation Model

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

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)