data {roben}

simulated data for demonstrating the features of roben

Description

Simulated gene expression data for demonstrating the features of roben.

Usage

data("GxE_small")
data("GxE_large")

Format

GxE_small consists of five components: X, Y, E, clin and coeff. coeff contains the true values of parameters used for generating Y.

GxE_large contains larger datasets: X2, Y2, E2 and clin2

Details

The data model for generating Y

Use subscript i to denote the ith subject. Let (X_{i}, Y_{i}, E_{i}, Clin_{i}), (i=1,\ldots,n) be independent and identically distributed random vectors. Y_{i} is a continuous response variable representing the disease phenotype. X_{i} is the p–dimensional vector of G factors. The environmental factors and clinical covariates are denoted as the k-dimensional vector E_{i} and the q-dimensional vector Clin_{i}, respectively. The \epsilon follows some heavy-tailed distribution. Considering the following model:

Y_{i} = \alpha_{0} + \sum_{t=1}^{q}\alpha_{t}Clin_{it} + \sum_{m=1}^{k}\theta_{m}E_{im} + \sum_{j=1}^{p}\gamma_{j}X_{ij} + \sum_{j=1}^{p}\sum_{m=1}^{k}\zeta_{jm}E_{im}X_{ij} +\epsilon_{i},

where \alpha_{0} is the intercept; \alpha_{t}'s, \theta_{m}'s, \gamma_{j}'s and \zeta_{jm}'s are the regression coefficients for the clinical covariates, environmental factors, genetic factors and G\timesE interactions, respectively.

Define \beta_{j}=(\gamma_{j}, \zeta_{j1},\ldots,\zeta_{jk})^\top \equiv (\beta_{j1},\ldots,\beta_{jL})^\top and U_{ij}=(X_{ij},X_{ij}E_{i1}\ldots,X_{ij}E_{ik})^\top \equiv (U_{ij1},\dots,U_{ijL})^\top, where L=k+1. The model can be written as

Y_{i} = \alpha_{0} + \sum_{t=1}^{q}\alpha_{t}Clin_{it} + \sum_{m=1}^{k}\theta_{m}E_{im} + \sum_{j=1}^{p} \big(U_{ij}^\top\beta_{j}\big) +\epsilon_{i},

where the coefficient vector \beta_{j} represents all the main and interaction effects corresponding to the jth genetic measurement.

The object coeff in GxE_small is a list of four components, corresponding to \alpha_{0}, \alpha_{t}'s, \theta_{m}'s and \beta_{j}'s.

See Also

roben

Examples

data(GxE_small)
dim(X)
print(coeff)

data(GxE_large)
dim(X)
print(coeff)