Simulation of Multivariate Linear Model data with response

Simulation of Multivariate Linear Model data with response

bisimrel(
  n = 50,
  p = 100,
  q = c(10, 10, 5),
  rho = c(0.8, 0.4),
  relpos = list(c(1, 2), c(2, 3)),
  gamma = 0.5,
  R2 = c(0.8, 0.8),
  ntest = NULL,
  muY = NULL,
  muX = NULL,
  sim = NULL
)

Arguments

n	Number of training samples
p	Number of x-variables
q	Vector of number of relevant predictor variables for first, second and common to both responses
rho	A 2-element vector, unconditional and conditional correlation between y_1 and y_2
relpos	A list of position of relevant component for predictor variables. The list contains vectors of position index, one vector or each response
gamma	A declining (decaying) factor of eigen value of predictors (X). Higher the value of gamma, the decrease of eigenvalues will be steeper
R2	Vector of coefficient of determination for each response
ntest	Number of test observation
muY	Vector of average (mean) for each response variable
muX	Vector of average (mean) for each predictor variable
sim	A simrel object for reusing parameters setting

Value

A simrel object with all the input arguments along with following additional items

X

Simulated predictors

Y

Simulated responses

beta

True regression coefficients

beta0

True regression intercept

relpred

Position of relevant predictors

testX

Test Predictors

testY

Test Response

minerror

Minimum model error

Rotation

Rotation matrix of predictor (R)

type

Type of simrel object, in this case bivariate

lambda

Eigenvalues of predictors

Sigma

Variance-Covariance matrix of response and predictors

References

Sæbø, S., Almøy, T., & Helland, I. S. (2015). simrel—A versatile tool for linear model data simulation based on the concept of a relevant subspace and relevant predictors. Chemometrics and Intelligent Laboratory Systems, 146, 128-135.

Almøy, T. (1996). A simulation study on comparison of prediction methods when only a few components are relevant. Computational statistics & data analysis, 21(1), 87-107.

Examples

sobj <- bisimrel(
   n = 100,
   p = 10,
   q = c(5, 5, 3),
   rho = c(0.8, 0.4),
   relpos = list(c(1, 2, 3), c(2, 3, 4)),
   gamma = 0.7,
   R2 = c(0.8, 0.8)
)
# Regression Coefficients from this simulation
sobj$beta
#>             [,1]       [,2]
#>  [1,]  0.1976147  0.0000000
#>  [2,] -1.1352283 -1.2669424
#>  [3,]  0.6884604  0.5123310
#>  [4,]  0.0000000  0.3985812
#>  [5,]  0.0000000  0.0000000
#>  [6,]  0.0000000  0.0000000
#>  [7,]  0.4467680  0.7546115
#>  [8,]  0.0000000 -0.3985812
#>  [9,] -0.1976147  0.0000000
#> [10,]  0.0000000  0.0000000