bisimrel function

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

Returns

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

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

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.