simul_data_UniYX_beta() R function from [plsRbeta]

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.


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

Returns

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.

Examples


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

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. http://publications-sfds.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