data: simulated data for demonstrating the features of mixedBayes

In mixedBayes: Bayesian Longitudinal Regularized Quantile Mixed Model

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 (main and interaction effects) 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 the m-dimensional vector G_{ij} to denote measurements of genetics factors for the ith subject at time point j, where G_{ij} = (G_{ij1},...,G_{ijm})^\top. Also, we use p-dimensional vector E_{ij} to denote the environment factors, where E_{ij} = (E_{ij1},...,E_{ijp})^\top. X_{ij} = (1, T_{ij})^\top, where T_{ij}^\top 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. In a typical one-way repeated measure ANOVA with a fixed number (say four) of factor levels, the environment (or treatment) factor is modelled as a group of three dummy variables. Therefore, gene-environment (or treatment) interaction leads to variable selections on individual levels (main effects) and group levels (interaction effect) simultaneously. Considering the genetics factors, environment (or treatment) factors and their interactions that are jointly associated with the longitudinal phenotype, we have the following mixed-effects model:

Y_{ij} = X_{ij}^\top\gamma_{0}+E_{ij}^\top\gamma_{1}+G_{ij}^\top\gamma_{2}+(G_{ij}\bigotimes E_{ij})^\top\gamma_{3}+Z_{ij}^\top\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. In addition, \gamma_0 is the coefficient vector for X_{ij}. The gene–environment interactions that can be expressed as a Kronecker product between the two types of main effects as a mp-dimensional vector:

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

The above model also includes Z_{ij} with random effects \alpha_{i} to account for intra-correlations among repeated measurements. For random intercept-and-slope model, Z_{ij}^\top = (1,j) and \alpha_{i} = (\alpha_{i1},\alpha_{i2})^\top. For random intercept model, Z_{ij}^\top = 1 and \alpha_{i} = \alpha_{i1}.

See Also

mixedBayes

Examples

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

mixedBayes documentation built on June 8, 2025, 11:04 a.m.