RRR_sim: Simulating data for Reduced-Rank Regression
In RRRR: Online Robust Reduced-Rank Regression Estimation

View source: R/simulation.R

RRR_sim

R Documentation

Simulating data for Reduced-Rank Regression

Description

Simulate data for Reduced-rank regression. See Detail for the formulation of the simulated data.

Usage

RRR_sim(
  N = 1000,
  P = 3,
  Q = 3,
  R = 1,
  r = 1,
  mu = rep(0.1, P),
  A = matrix(rnorm(P * r), ncol = r),
  B = matrix(rnorm(Q * r), ncol = r),
  D = matrix(rnorm(P * R), ncol = R),
  varcov = diag(P),
  innov = mvtnorm::rmvt(N, sigma = varcov, df = 3),
  mean_x = 0,
  mean_z = 0,
  x = NULL,
  z = NULL
)

Arguments

`N`	Integer. The total number of simulated realizations.
`P`	Integer. The dimension of the response variable matrix. See `Detail`.
`Q`	Integer. The dimension of the explanatory variable matrix to be projected. See `Detail`.
`R`	Integer. The dimension of the explanatory variable matrix not to be projected. See `Detail`.
`r`	Integer. The rank of the reduced rank coefficient matrix. See `Detail`.
`mu`	Vector with length P. The constants. Can be `NULL` to drop the term. See `Detail`.
`A`	Matrix with dimension P*r. The exposure matrix. See `Detail`.
`B`	Matrix with dimension Q*r. The factor matrix. See `Detail`.
`D`	Matrix with dimension P*R. The coefficient matrix for `z`. Can be `NULL` to drop the term. See `Detail`.
`varcov`	Matrix with dimension P*P. The covariance matrix of the innovation. See `Detail`.
`innov`	Matrix with dimension N*P. The innovations. Default to be simulated from a Student t distribution, See `Detail`.
`mean_x`	Integer. The mean of the normal distribution x is simulated from.
`mean_z`	Integer. The mean of the normal distribution z is simulated from.
`x`	Matrix with dimension N*Q. Can be used to specify x instead of simulating form a normal distribution.
`z`	Matrix with dimension N*R. Can be used to specify z instead of simulating form a normal distribution.

Details

The data simulated can be used for the standard reduced-rank regression testing with the following formulation

y = μ +AB' x + D z+innov,

where for each realization y is a vector of dimension P for the P response variables, x is a vector of dimension Q for the Q explanatory variables that will be projected to reduce the rank, z is a vector of dimension R for the R explanatory variables that will not be projected, μ is the constant vector of dimension P, innov is the innovation vector of dimension P, D is a coefficient matrix for z with dimension P*R, A is the so called exposure matrix with dimension P*r, and B is the so called factor matrix with dimension Q*r. The matrix resulted from AB' will be a reduced rank coefficient matrix with rank of r. The function simulates x, z from multivariate normal distribution and y by specifying parameters μ, A, B, D, and varcov, the covariance matrix of the innovation's distribution. The constant μ and the term Dz can be dropped by setting NULL for arguments mu and D. The innov in the argument is the collection of innovations of all the realizations.