multisimrel function

Simulation of Multivariate Linear Model Data

multisimrel(
  n = 100,
  p = 15,
  q = c(5, 4, 3),
  m = 5,
  relpos = list(c(1, 2), c(3, 4, 6), c(5, 7)),
  gamma = 0.6,
  R2 = c(0.8, 0.7, 0.8),
  eta = 0,
  ntest = NULL,
  muX = NULL,
  muY = NULL,
  ypos = list(c(1), c(3, 4), c(2, 5))
)

Arguments

• n: Number of observations
• p: Number of variables
• q: Vector containing the number of relevant predictor variables for each relevant response components
• m: Number of response variables
• relpos: A list of position of relevant component for predictor variables. The list contains vectors of position index, one vector or each relevant response components
• 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 (proportion of variation explained by predictor variable) for each relevant response components
• eta: A declining (decaying) factor of eigenvalues of response (Y). Higher the value of eta, more will be the declining of eigenvalues of Y. eta = 0 refers that all eigenvalues of responses (Y) are 1.
• ntest: Number of test observation
• muX: Vector of average (mean) for each predictor variable
• muY: Vector of average (mean) for each response variable
• ypos: List of position of relevant response components that are combined to generate response variable during orthogonal rotation

Returns

A simrel object with all the input arguments along with following additional items - X: Simulated predictors

• Y: Simulated responses

• W: Simulated predictor components

• Z: Simulated response components

• beta: True regression coefficients

• beta0: True regression intercept

• relpred: Position of relevant predictors

• testX: Test Predictors

• testY: Test Response

• testW: Test predictor components

• testZ: Test response components

• minerror: Minimum model error

• Xrotation: Rotation matrix of predictor (R)

• Yrotation: Rotation matrix of response (Q)

• type: Type of simrel object univariate or multivariate

• lambda: Eigenvalues of predictors

• SigmaWZ: Variance-Covariance matrix of components of response and predictors

• SigmaWX: Covariance matrix of response components and predictors

• SigmaYZ: Covariance matrix of response and predictor components

• Sigma: Variance-Covariance matrix of response and predictors

• RsqW: Coefficient of determination corresponding to response components

• RsqY: Coefficient of determination corresponding to response variables

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.