simrel: Simulation of Multivariate Linear Model Data

In simrel: Simulation of Multivariate Linear Model Data

Description

Simulation of Multivariate Linear Model Data

Usage

simrel(n, p, q, relpos, gamma, R2, type = "univariate", ...)

Arguments

n	Number of observations.
p	Number of variables.
q	An integer for univariate, a vector of 3 integers for bivariate and 3 or more for multivariate simulation (for details see Notes).
relpos	A list (vector in case of univariate simulation) of position of relevant component for predictor variables corresponding to each response.
gamma	A declining (decaying) factor of eigenvalues 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.
type	Type of simulation - univariate, bivariate and multivariate
...	Since this is a wrapper function to simulate univariate, bivariate or multivariate, it calls their respective function. This parameter should contain all the necessary arguements for respective simulations. See unisimrel, bisimrel and multisimrel

Value

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.

simrel documentation built on Sept. 17, 2021, 5:06 p.m.