env.two {gma}

Simulated two-level dataset

Description

"env.two" is an R environment containing a data list generated from 50 subjects, and the parameter settings used to generate the data.

Usage

data("env.two")

Format

An R environment.

data2

a list of length 50, each contains a data frame with 3 variables.

error2

a list of length 50, each contains a data frame with 2 columns.

theta

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

Sigma

a 2 by 2 matrix, which is the covariance matrix of the 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.

n

a 50 by 1 matrix, is the number of time points for each subject.

Lambda

the covariance matrix of the model errors in the coefficient regression model.

A

a vector of length 50, is the A value in the single-level for each subject.

B

a vector of length 50, is the B value in the single-level for each subject.

C

a vector of length 50, is the C value in the single-level for each subject.

Details

The true parameters are set as follows. The number of subjects i N = 50. For each subject, the number of time points is a random draw from a Poisson distribution with mean 100. The population level coefficients are set to be A = 0.5, C = 0.5 and B = -1, and the variances of the Gaussian white noise process are assumed to be the same across participants with \sigma_{1_{i}}^2 = 1, \sigma_{2_{i}}^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.two)
dt<-get("data2",env.two)