env.single {gma}

Simulated single-level dataset

Description

"env.single" is an R environment containing a data frame of data generated from 500 time points, and the true model parameters.

Usage

data("env.single")

Format

An R environment

data1

a data frame with Z the treatment assignment, M the mediator and R the interested outcome.

error1

a data frame with E1 and E2 the error time series of M and R, respectively.

theta

a 3 by 1 vector, which is the coefficients (A,B,C) of the model.

Sigma

a 2 by 2 matrix, which is the covariance matrix of two Gaussian white noise processes.

p

the order of the vector autoregressive (VAR) model.

W

a 2p by 2 matrix, which is the transition matrix of the VAR(p) model.

Delta

a 2 by 2 matrix, which is the covariance matrix of the initial condition of the Gaussian white noise processes.

Details

The true parameters are set as follows. The number of time points is 500. The coefficients are set to be A = 0.5, C = 0.5 and B = -1. The variances of the model errors are \sigma_1^2 = 1, \sigma_2^2 = 4 and the correlation is \delta = 0.5. For the VAR model, we consider the case p = 1, and the parameter settings satisfy the stationarity condition.

References

Zhao, Y., & Luo, X. (2017). Granger Mediation Analysis of Multiple Time Series with an Application to fMRI. arXiv preprint arXiv:1709.05328.

Examples

data(env.single)
dt<-get("data1",env.single)