Description Usage Arguments Details Value Author(s) References Examples
This function generates a two-level dataset with given parameters.
1 2 | sim.data.ts.two(Z.list, N, theta, Sigma, W, Delta = NULL, p = NULL,
Lambda = diag(rep(1, 3)), nburn = 100)
|
Z.list |
a list of data. Each list is a vector containing the treatment/exposure assignment at each time point for the subject. |
N |
an integer, indicates the number of subjects. |
theta |
a vector of length 3, contains the population level causal effect coefficients. |
Sigma |
a 2 by 2 matrix, is the covariance matrix of the two Gaussian white noise processes in the single level model. |
W |
a 2p by 2 matrix, is the transition matrix in the single level model. |
Delta |
a 2 by 2 matrix, is the covariance matrix of the initial condition in the single level model. Default is |
p |
an integer, indicates the order of the vector autoregressive (VAR) model in the single level model. Default is |
Lambda |
the covariance matrix of the model errors in the linear model of the model coefficients. Default is a 3 by 3 identity matrix. |
nburn |
a integer indicating the number of burning sample in the single level model. Default is 100. |
For the time series of length n_{i} of subject i, the single level GMA model is
M_{i_{t}}=Z_{i_{t}}A_{i}+E_{i_{1t}},
R_{i_{t}}=Z_{i_{t}}C_{i}+M_{i_{t}}B_{i}+E_{i_{2t}},
and
E_{i_{1t}}=∑_{j=1}^{p}ω_{i_{11_{j}}}E_{i_{1,t-j}}+∑_{j=1}^{p}ω_{i_{21_{j}}}E_{i_{2,t-j}}+ε_{i_{1t}},
E_{i_{2t}}=∑_{j=1}^{p}ω_{i_{12_{j}}}E_{i_{1,t-j}}+∑_{j=1}^{p}ω_{i_{22_{j}}}E_{i_{2,t-j}}+ε_{i_{2t}},
where Sigma
is the covariance matrix of (ε_{i_{1t}},ε_{i_{2t}}) (for simplicity, Sigma
is the same across subjects). For coefficients A_{i}, B_{i} and C_{i}, we assume a multivariate regression model. The model errors are from a trivariate normal distribution with mean zero and covariance Lambda
.
data |
a list of data. Each list is a data frame of (Z_{t},M_{t},R_{t}). |
error |
a list of data. Each list is a data frame of (E_{1t},E_{2t}). |
A |
a vector of length |
B |
a vector of length |
C |
a vector of length |
type |
a character indicates the type of the dataset. |
Yi Zhao, Brown University, zhaoyi1026@gmail.com; Xi Luo, Brown University, xi.rossi.luo@gmail.com
Zhao, Y., & Luo, X. (2017). Granger Mediation Analysis of Multiple Time Series with an Application to fMRI. arXiv preprint arXiv:1709.05328.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | ###################################################
# Generate a two-level dataset
# covariance matrix of errors
delta<-0.5
Sigma<-matrix(c(1,2*delta,2*delta,4),2,2)
# model coefficients
A0<-0.5
B0<--1
C0<-0.5
theta<-c(A0,B0,C0)
# number of time points
N<-50
set.seed(2000)
n<-matrix(rpois(N,100),N,1)
# treatment assignment list
set.seed(1000)
Z.list<-list()
for(i in 1:N)
{
Z.list[[i]]<-matrix(rbinom(n[i,1],size=1,prob=0.5),n[i,1],1)
}
# Lambda
Lambda<-diag(0.5,3)
# VAR(1) model
p<-1
# Delta and W matrices
Delta<-matrix(c(2,delta*sqrt(2*8),delta*sqrt(2*8),8),2,2)
W<-matrix(c(-0.809,0.154,-0.618,-0.5),2,2)
# number of burning samples
nburn<-1000
# set.seed(2000)
# data2<-sim.data.ts.two(Z.list,N,theta=theta,Sigma,W,Delta,p,Lambda,nburn)
###################################################
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