simrel | R Documentation |
Simulation of Multivariate Linear Model Data
simrel(n, p, q, relpos, gamma, R2, type = "univariate", ...)
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 |
R2 |
Vector of coefficient of determination (proportion of variation explained by predictor variable) for each relevant response components. |
type |
Type of simulation - |
... |
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 |
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 |
testY |
simulated test response (in univarite simulation |
Rotation |
Random rotation matrix used to rotate latent components. Is
equivalent to the transpose of eigenvector-matrix. In multivariate
simulation, |
type |
type of simrel object |
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 |
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).
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.
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