env.example {cap}R Documentation

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,…,n, t=1,…,T), y_{it}=(y_{it1},…,y_{itp}) was generated from a p-dimensional normal distribution with mean zero and covariance Σ, where

Σ=ΦΛΦ,

Φ is an orthonormal matrix and Λ=\mathrm{diag}(λ_{1},…,λ_{p}) is a diagonal matrix. The eigenvalues λ_{ij} (j=1,…,p) satisfies the following log-linear model

log(λ_{ij})=x_{i}^\topβ_{j},

where β_{j} is the jth column of beta.

Examples

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

[Package cap version 1.0 Index]