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