RBE3 (version 1.1)

BE3.backward: backward stepwise regression for RBE3 model based on the AIC criterion or significance.

Description

BE3.backward.crit implements the covariates selection based on backward and the Akaike's information criteria (AIC). BE3.backward.sign implements the covariates selection based on backward and significance of the covariates.

Usage

BE3.backward.crit(data, tau = 0.5, link.mu = "logit")

Value

A list containg the covariates to be included for modelling \(\mu\), \(\alpha\) and \(\beta\), respectively.

Arguments

data

a list containing the response vector (\(y\)), and the matrices to model \(\mu\), the \(\tau\)-quantile of distribution, and the shape parameters \(\alpha\) and \(\beta\), labeled as \(Z_1, Z_2\) and \(Z_3\), respectively.

tau

the quantile of the distribution to be modelled (\(0<\tau<1\)).

link.mu

link function to be used for \(\mu\): logit (default), probit, loglog or cloglog.

Author

Diego Gallardo and Marcelo Bourguignon.

Examples

##Simulating two covariates
set.seed(2100)
x1<-rnorm(200); x2<-rbinom(200, size=1, prob=0.5)
##Desing matrices: Z1 includes x1 and x2, 
##Z2 includes only x1 and Z3 includes only x2
Z1=model.matrix(~x1+x2);Z2=model.matrix(~x1);Z3=model.matrix(~x2)
##Fixing parameters
theta=c(1, 0.2, -0.5); nu=c(0.5,-0.2); eta=c(-0.5, 0.3); tau=0.4
mu=plogis(Z1%*%theta); alpha=exp(Z2%*%nu); beta=exp(Z3%*%eta)
y=rBE3(200, mu, alpha, beta, tau=tau)
data=list(y=y, Z1=Z1, Z2=Z2, Z3=Z3)
BE3.backward.crit(data, tau = tau)