data {mixedBayes}

simulated data for demonstrating the features of mixedBayes

Description

Simulated gene expression data for demonstrating the features of mixedBayes.

Format

The data object consists of seven components: y, e, X, g, w ,k and coeff. coeff contains the true values of parameters used for generating Y.

Details

The data and model setting

Consider a longitudinal study on n subjects with k repeated measurement for each subject. Let Y_{ij} be the measurement for the ith subject at each time point j(1\leq i \leq n, 1\leq j \leq k) .We use a m-dimensional vector G_{ij} to denote the genetics factors, where G_{ij} = (G_{ij1},...,G_{ijm})^{T}. Also, we use p-dimensional vector E_{ij} to denote the environment factors, where E_{ij} = (E_{ij1},...,E_{ijp})^{T}. X_{ij} = (1, T_{ij})^{T}, where T_{ij}^{T} is a vector of time effects . Z_{ij} is a h \times 1 covariate associated with random effects and \alpha_{i} is a h\times 1 vector of random effects. At the beginning, the interaction effects is modeled as the product of genomics features and environment factors with 4 different levels. After representing the environment factors as three dummy variables, the identification of the gene by environment interaction needs to be performed as group level. Combing the genetics factors, environment factors and their interactions that associated with the longitudinal phenotype, we have the following mixed-effects model:

Y_{ij} = X_{ij}^{T}\gamma_{0}+E_{ij}^{T}\gamma_{1}+G_{ij}^{T}\gamma_{2}+(G_{ij}\bigotimes E_{ij})^{T}\gamma_{3}+Z_{ij}^{T}\alpha_{i}+\epsilon_{ij}.

where \gamma_{1},\gamma_{2},\gamma_{3} are p,m and mp dimensional vectors that represent the coefficients of the environment effects, the genetics effects and interactions effects, respectively. Accommodating the Kronecker product of the m - dimensional vector G_{ij} and the p-dimensional vector E_{ij}, the interactions between genetics and environment factors can be expressed as a mp-dimensional vector, denoted as the following form:

G_{ij}\bigotimes E_{ij} = [E_{ij1}E_{ij1},E_{ij2}E_{ij2},...,E_{ij1}E_{ijp},E_{ij2}E_{ij1},...,E_{ijm}E_{ijp}]^{T}.

For random intercept and slope model, Z_{ij}^{T} = (1,j) and \alpha_{i} = (\alpha_{i1},\alpha_{i2})^{T}. For random intercept model, Z_{ij}^{T} = 1 and \alpha_{i} = \alpha_{i1}.

See Also

mixedBayes

Examples

data(data)
dim(y)
dim(g)
dim(e)
dim(w)
print(k)
print(X)
print(coeff)