env.historical {cfma}

Simulated data from the historical influence mediation model

Description

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

Usage

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)