rrmix.sim.norm {rrMixture}

Simulation Data Generator

Description

‘rrmix.sim.norm’ is used to create synthetic data from the multivariate normal distribution, which is used in a numerical study of Kang et. al. (2022+).

Usage

rrmix.sim.norm(
  K = 2,
  n = 100,
  p = 5,
  q = 5,
  rho = 0.5,
  b = 1,
  shift = 1,
  r.star = NULL,
  sigma = NULL,
  pr = NULL,
  seed = NULL
)

Arguments

K

number of mixture components.

n

number of observations.

p

number of predictors including an intercept.

q

number of responses.

rho

correlation between predictors used to make a design matrix.

b

signal strength which controls the magnitude of coefficient matrices.

shift

mean shift which measures how separate the mixture components are.

r.star

vector of length K, specifying the true ranks of K coefficient matrices.

sigma

vector of length K, specifying the noise strength of K multivariate normal distributions.

pr

vector of length K, specifying the multinomial probabilities for the K mixture components.

seed

seed number for the reproducibility of results. Default is ‘NULL’.

Value

X

n by p design matrix.

Y

n by q response matrix.

E

p by q error matrix.

ind.true

vector of length n, specifying the true mixture membership for n observations.

para.true

array of length K. It consists of K lists, each of which contains a coefficient matrix and its true rank.

Author(s)

Suyeon Kang, University of California, Riverside, [e-mail]; Weixin Yao, University of California, Riverside, [e-mail]; Kun Chen, University of Connecticut, [e-mail].

References

Kang, S., Chen, K., and Yao, W. (2022+). "Reduced rank estimation in mixtures of multivariate linear regression".

Examples

#-----------------------------------------------------------#
# Simulation 1: Two Components Case
#-----------------------------------------------------------#
K2mod <- rrmix.sim.norm(K = 2, n = 100, p = 5, q = 5, rho = .5,
         b = 1, shift = 1, r.star = c(1, 3), sigma = c(1, 1),
         pr = c(.5, .5), seed = 1215)

#-----------------------------------------------------------#
# Simulation 2: Four Components Case
#-----------------------------------------------------------#
K4mod <- rrmix.sim.norm(K = 4, n = 600, p = 15, q = 15,
         rho = .5, b = 1, shift = 1, r.star = c(1, 1, 3, 3),
         sigma = c(1, 1, 1, 1), pr = c(.25, .25, .25, .25),
         seed = 1215)