data {pqrBayes}

simulated data for demonstrating the features of pqrBayes

Description

Simulated gene expression data for demonstrating the features of pqrBayes.

Format

The data 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

The model for generating Y

Use subscript i to denote the ith subject. Let (\boldsymbol X_{i}, Y_{i}, V_{i}, \boldsymbol E_{i}), (i=1,\ldots,n) be independent and identically distributed random vectors. Y_{i} is a continuous response variable representing the disease phenotype. \boldsymbol X_{i}=(X_{i0},...,X_{ip})^\top denotes a (1+p)–dimensional vector of predictors (e.g. genetic factors) with the first element X_{i0}=1. The environmental factor V_i \in \rm I\!R^1 is a univariate index variable. \boldsymbol E_{i}=(E_{i1},...,E_{iq})^\top is the q-dimensional vector of clinical covariates. At a given quantile level \tau, considering the following quantile varying coefficient model:

Y_{i}=\sum_{k=1}^{q} E_{ik} \beta_{k,\tau} +\sum_{j=0}^{p}\gamma_{j,\tau}(V_i)X_{ij} +\epsilon_{i,\tau},

where \beta_{k,\tau}'s are the regression coefficients for the clinical covariates and \gamma_{j,\tau}(\cdot)'s are unknown smooth varying-coefficient functions. The regression coefficients of \boldsymbol X vary with the univariate index variable \boldsymbol v=(v_1,...,v_n)^\top. The \epsilon_{i,\tau} is the random error. For simplicity of notation, the quantile level \tau has been suppressed hereafter.

The true model that we used to generate Y:

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}=1.5\sin(0.2\pi*v_i), \gamma_{1}=2\exp(0.2v_i-1)-1.5 , \gamma_{2}=2-2v_i and \gamma_3=-4+(v_i-2)^3/6.

See Also

pqrBayes

Examples

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