env.example {cap}

Simulated data

Description

"env.example" is an R environment containing the data generated from the proposed model with p=2.

Usage

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 jth column of beta.

Examples

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