simrel: Simulation of Multivariate Linear Model Data

In therimalaya/simulatr: Simulation of Multivariate Linear Model Data

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	Number of predictors related to each relevant components 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. For more detail on the return values see the individual simulation functions unisimrel, bisimrel and multisimrel.

Common returns from univariate, bivariate and multivariate simulation:

call	the matched call
X	simulated predictors
Y	simulated responses
beta	true regression coefficients
beta0	true regression intercept
relpred	position of relevant predictors
n	number of observations
p	number of predictors (as supplied in the arguments)
p	number of responses (as supplied in the arguments)
q	number of relevant predictors (as supplied in the arguments)
gamma	declining factor of eigenvalues of predictors (as supplied in the arguments)
lambda	eigenvalues corresponding to the predictors
R2	theoretical R-squared value (as supplied in the arguments)
relpos	position of relevant components (as supplied in the arguments)
minerror	minimum model error
Sigma	variance-Covariance matrix of response and predictors
testX	simulated test predictor (in univarite simulation TESTX)
testY	simulated test response (in univarite simulation TESTY)
Rotation	Random rotation matrix used to rotate latent components. Is equivalent to the transpose of eigenvector-matrix. In multivariate simulation, Xrotation (R) and Yrotation (Q) refers to this matrix corresponding to the predictor and response.
type	type of simrel object univariate, bivariate or multivariate

Returns from multivariate simulation:

eta	a declining factor of eigenvalues of response (Y) (as supplied in the arguments)
ntest	number of simulated test observations
W	simulated response components
Z	simulated predictor components
testW	test predictor components
testZ	test response components
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
RsqW	Coefficient of determination corresponding to response components
RsqY	Coefficient of determination corresponding to response variables

Note

The parameter q represetns the number of predictor variables that forms a basis for each of the relevant componetns. For example, for q = 8 and relevant components 1, 2, and 3 specified by parameter relpos then the randomly selected 8 predictor variables forms basis for these three relevant componets and thus in the model these 8 predictors will be revant for the response (outcome).

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.

therimalaya/simulatr documentation built on Nov. 20, 2022, 2:49 p.m.