`semimrGen' is used to generate data for a two-component semiparametric mixture of regression models:
$$p m_1(x) + (1-p) m_2(x),$$
where \(m_1(x) = 4 -\sin(2\pi x)\) and \(m_2(x) = 1.5 + \cos(3\pi x).\)
This function is used in the examples for the semimrLocal and semimrGlobal functions.
See the examples for details.
Usage
semimrGen(n, p = 0.5, var = c(.1, .1), u)
Value
A list containing the following elements:
x
vector of length n, which represents the explanatory variable
that is randomly generated from Uniform(0,1).
y
vector of length n, which represent the response variable
that is generated based on the mean functions \(m_1(x)\) and \(m_2(x)\),
with the addition of normal errors having a mean of 0 and a standard deviation specified by the user.
true_mu
n by 2 matrix containing the values of \(m_1(x)\) and \(m_2(x)\) at x.
true_mu_u
length(u) by 2 matrix containing the values of \(m_1(x)\) and \(m_2(x)\) at u.
Arguments
n
a scalar, specifying the number of observations in \(x\).
p
a scalar, specifying the probability of an observation belonging to the first component,
i.e., \(p\) in the model.
var
a vector of variances of observations for the two components.
u
a vector of grid points for \(x\). If some specific explanatory variable are needed, create a vector and assign to u.
n = 100u = seq(from = 0, to = 1, length = 100)
true_p = c(0.3, 0.7)
true_var = c(0.09, 0.16)
out = semimrGen(n = n, p = true_p[1], var = true_var, u = u)