Simulated data from the historical influence mediation model

"env.historical" is an R environment containing the data generated from a historical influence mediation model.

data("env.historical")

Format

An R environment

Z

a \(n\times T\) data matrix, treatment trajectory of \(n\) subjects for \(T\) time points.

M

a \(n\times T\) data matrix, mediator trajectory of \(n\) subjects for \(T\) time points.

Y

a \(n\times T\) data matrix, outcome trajectory of \(n\) subjects for \(T\) time points.

alpha

a \(T\times T\) matrix model coefficient.

beta

a \(T\times T\) matrix model coefficient.

gamma

a \(T\times T\) matrix model coefficient.

Details

The data was generated from the historical influence mediation model $$M(t)=\int_{\Omega_{t}^{1}}Z(s)\alpha(s,t)ds+\epsilon_{1}(t),$$ $$Y(t)=\int_{\Omega_{t}^{2}}Z(s)\gamma(s,t)ds+\int_{\Omega_{t}^{3}}M(s)\beta(s,t)ds+\epsilon_{2}(t),$$ where \(\alpha(s,t)\), \(\beta(s,t)\), \(\gamma(s,t)\) are coefficient curves; \(\Omega_{t}^{j}=[(t-\delta_{j})\vee 0,t]\) for \(j=1,2,3\). \(Z(t)\) is the convolution of hemodynamic response function (HRF) and event onsets.

Examples

data(env.historical)
Z<-get("Z",env.historical)
M<-get("M",env.historical)
Y<-get("Y",env.historical)