sim_model_ex1 {ehymet}

Function for generating functional data in one dimension

Description

Each dataset has 2 groups with n curves each, defined in the interval t=[0, 1] with p equidistant points. The first n curves are generated fron the following model X_1(t)=E_1(t)+e(t) where E_1(t)=E_1(X(t))=30t^{ \frac{3}{2}}(1-t) is the mean function and e(t) is a centered Gaussian process with covariance matrix Cov(e(t_i),e(t_j))=0.3 \exp(-\frac{\lvert t_i-t_j \rvert}{0.3}) The remaining 50 functions are generated from model i_sim with i_sim \in \{1, \ldots, 8\}. The first three models contain changes in the mean, while the covariance matrix does not change. Model 4 and 5 are obtained by multiplying the covariance matrix by a constant. Model 6 is obtained from adding to E_1(t) a centered Gaussian process h(t) whose covariance matrix is given by Cov(e(t_i),e(t_j))=0.5 \exp (-\frac{\lvert t_i-t_j\rvert}{0.2}). Model 7 and 8 are obtained by a different mean function.

Model 1.

X_1(t)=30t^{\frac{3}{2}}(1-t)+0.5+e(t).

Model 2.

X_2(t)=30t^{\frac{3}{2}}(1-t)+0.75+e(t).

Model 3.

X_3(t)=30t^{\frac{3}{2}}(1-t)+1+e(t).

Model 4.

X_4(t)=30t^{\frac{3}{2}}(1-t)+2 e(t).

Model 5.

X_5(t)=30t^{\frac{3}{2}}(1-t)+0.25 e(t).

Model 6.

X_6(t)=30t^{\frac{3}{2}}(1-t)+ h(t).

Model 7.

X_7(t)=30t{(1-t)}^2+ h(t).

Model 8.

X_8(t)=30t{(1-t)}^2+ e(t).

Usage

sim_model_ex1(n = 50, p = 30, i_sim = 1)

Arguments

n

Number of curves to generate for each of the two groups. Set to 50 by default.

p

Number of grid points of the curves. Curves are generated over the interval [0, 1]. Set to 30 grid point by default.

i_sim

Integer set to 1, \ldots, 8.

Value

data matrix of size 2n \times p.

Examples

sm1 <- sim_model_ex1()
dim(sm1)