Data generating function for univariate beta plsR models

This function generates a single univariate rate response value \(Y\) and a vector of explanatory variables \((X_1,\ldots,X_{totdim})\) drawn from a model with a given number of latent components.

Usage

simul_data_UniYX_beta(
  totdim,
  ncomp,
  disp = 1,
  link = "logit",
  type = "a",
  phi0 = 20
)

Arguments

totdim

Number of columns of the X vector (from ncomp to hardware limits)

ncomp

Number of latent components in the model (from 2 to 6)

disp

Tune the shape of the beta distribution (defaults to 1)

link

Character specification of the link function in the mean model (mu). Currently, "logit", "probit", "cloglog", "cauchit", "log", "loglog" are supported. Alternatively, an object of class "link-glm" can be supplied.

type

Simulation scheme

phi0

Simulation scheme "a" parameter

Value

vector

\((Y,X_1,\ldots,X_{totdim})\)

Details

This function should be combined with the replicate function to give rise to a larger dataset. The algorithm used is a modification of a port of the one described in the article of Li which is a multivariate generalization of the algorithm of Naes and Martens.

References

Frédéric Bertrand, Nicolas Meyer, Michèle Beau-Faller, Karim El Bayed, Izzie-Jacques Namer, Myriam Maumy-Bertrand (2013). Régression Bêta PLS. Journal de la Société Française de Statistique, 154(3):143-159. https://ojs-test.apps.ocp.math.cnrs.fr/index.php/J-SFdS/article/view/215

T. Naes, H. Martens (1985). Comparison of prediction methods for multicollinear data. Commun. Stat., Simul., 14:545-576. <doi:10.1080/03610918508812458>

Baibing Li, Julian Morris, Elaine B. Martin (2002). Model selection for partial least squares regression, Chemometrics and Intelligent Laboratory Systems, 64:79-89. <doi:110.1016/S0169-7439(02)00051-5>

See also

simul_data_UniYX

Author

Frédéric Bertrand
frederic.bertrand@lecnam.net
https://fbertran.github.io/homepage/

Examples

# \donttest{
# logit link
layout(matrix(1:4,nrow=2))
hist(t(replicate(100,simul_data_UniYX_beta(4,4)))[,1])
hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=3)))[,1])
hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=5)))[,1])
hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=15)))[,1])

layout(1)

# probit link
layout(matrix(1:4,nrow=2))
hist(t(replicate(100,simul_data_UniYX_beta(4,4,link="probit")))[,1])
hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=3,link="probit")))[,1])
hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=5,link="probit")))[,1])
hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=15,link="probit")))[,1])

layout(1)

# cloglog link
layout(matrix(1:4,nrow=2))
hist(t(replicate(100,simul_data_UniYX_beta(4,4,link="cloglog")))[,1])
hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=3,link="cloglog")))[,1])
hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=5,link="cloglog")))[,1])
hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=15,link="cloglog")))[,1])

layout(1)

# cauchit link
layout(matrix(1:4,nrow=2))
hist(t(replicate(100,simul_data_UniYX_beta(4,4,link="cauchit")))[,1])
hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=3,link="cauchit")))[,1])
hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=5,link="cauchit")))[,1])
hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=15,link="cauchit")))[,1])

layout(1)

# loglog link
layout(matrix(1:4,nrow=2))
hist(t(replicate(100,simul_data_UniYX_beta(4,4,link="loglog")))[,1])
hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=3,link="loglog")))[,1])
hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=5,link="loglog")))[,1])
hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=15,link="loglog")))[,1])

layout(1)

# log link
layout(matrix(1:4,nrow=2))
hist(t(replicate(100,simul_data_UniYX_beta(4,4,link="log")))[,1])
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hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=3,link="log")))[,1])
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hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=5,link="log")))[,1])
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hist(t(replicate(100,simul_data_UniYX_beta(4,4,disp=15,link="log")))[,1])
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layout(1)
# }