Simulated data

data("env.example")

Format

An R environment

X

a $n\times q$ data matrix, the covariate matrix of $n$ subjects with $q-1$ predictors. The first column is all ones.

Y

a list of length $n$. Each list element is a $T\times p$ matrix, the data matrix of $T$ observations from $p$ features.

Phi

a $p\times p$ matrix, the true projection matrix used to generate the data.

beta

a $q\times p$ matrix, the true coefficient matrix used to generate the data.

Sigma

a $p\times p\times n$ array, the covariance matrix of the $n$ subjects.

Details

For subject $i$ observation $t$ ($i=1,\dots,n$, $t=1,\dots,T$), $y_{it}=(y_{it1},\dots,y_{itp})$ was generated from a $p$-dimensional normal distribution with mean zero and covariance $\Sigma$, where $$\Sigma=\Phi\Lambda\Phi,$$ $\Phi$ is an orthonormal matrix and $\Lambda=\mathrm{diag}(\lambda_{1},\dots,\lambda_{p})$ is a diagonal matrix. The eigenvalues $\lambda_{ij}$ ($j=1,\dots,p$) satisfies the following log-linear model $$log(\lambda_{ij})=x_{i}^\top\beta_{j},$$ where $\beta_{j}$ is the $j$th column of beta.

Examples

data(env.example)
X<-get("X",env.example)
Y<-get("Y",env.example)