data: Simulated data under high-dimensional linear, binary, group...

In pqrBayes: Bayesian Penalized Quantile Regression

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

Description

Simulated data under high-dimensional linear, binary, 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_binary 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 sparse binary (quantile) regression model

The true data generating model under sparse linear regression:

\tilde{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}=0.22 , \beta_{2}=0.18 and \beta_3=0.14.

Y_i=1 if \tilde{Y}_i>0 and Y_i=0 otherwise.

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$data_binary
g=data$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)

pqrBayes documentation built on June 8, 2025, 12:35 p.m.