pqrBayes (version 1.1.2)

data: Simulated data under high-dimensional linear, group LASSO and quantile varying coefficient models

Description

Simulated data under high-dimensional linear, group LASSO and quantile varying coefficient models

Format

The data_linear object consists of 4 components: g, y, e and coeff. coeff contains the true values of parameters used for generating the response variable \(y\). The data_group object consists of 4 components: g, y, e and coeff. coeff contains the true values of parameters used for generating the response variable \(y\). The data_varying object consists of five components: g, y, u, e and coeff. coeff contains the true values of parameters used for generating the response variable \(y\).

Details

Generating Y using a sparse linear (quantile) regression model

The true data generating model under sparse linear regression: $$Y_i=\beta_0+\beta_{1}X_{i1}+\beta_{2}X_{i2}+\beta_{3}X_{i3}+\epsilon_i,$$ where \(\epsilon_i\sim N(0,1)\), \(\beta_{0}=0\), \(\beta_{1}=1 \), \(\beta_{2}=1.5\) and \(\beta_3=2\).

Generating Y using a high-dimensional group LASSO model

The true data generating model under a group LASSO model: $$Y_i=\beta_0+\beta_{1}X_{i1}+\beta_{2}X_{i2}+\beta_{3}X_{i3}+\beta_{7}X_{i7}+\beta_{8}X_{i8}+\beta_{9}X_{i9}+\epsilon_i,$$ where \(\epsilon_i\sim N(0,1)\), \(\beta_{0}=0\), \(\beta_{1}=0.6\), \(\beta_{2}=0.7\),\(\beta_{3}=0.8\),\(\beta_{7}=0.65\), \(\beta_{8}=0.75\) and \(\beta_{9}=0.85\).

Generating Y using a (quantile) varying coefficient model

Data generation under sparse (quantile) VC model: $$Y_i=\gamma_0(v_i)+\gamma_1(v_i)X_{i1}+\gamma_2(v_i)X_{i2}+\gamma_3(v_i)X_{i3}+\epsilon_i,$$ where \(\epsilon_i\sim N(0,1)\), \(\gamma_{0}(v_i)=1.5\sin(0.2\pi*v_i\)), \(\gamma_{1}(v_i)=2\exp(0.2v_i-1)-1.5 \), \(\gamma_{2}(v_i)=2-2v_i \) and \(\gamma_3(v_i)=-4+(v_i-2)^3/6\).

See Also

pqrBayes

Examples

data(data)
data = data$data_linear
g=data$g
dim(g)
y=data$y
coeff=data$coeff
print(coeff)

data = data$data_group
g=data$g
dim(g)
y=data$y
coeff=data$coeff
print(coeff)

data = data$data_varying
g=data$g
dim(g)
coeff=data$coeff
print(coeff)