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

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)
```