ML.BE3: Perform the parameter estimation for the Generalized beta...

In RBE3: Estimation and Additional Tools for Quantile Generalized Beta Regression Model

Perform the parameter estimation for the Generalized beta distribution

Description

ML.BE3 computes the maximum likelihood estimates based on the maximum likelihood method.

Usage

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

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.

Details

Covariates are included as g_1(\mu_i(\tau))=\mathbf{Z}_{1i}^\top {\bm \theta}(\tau), g_2(\alpha_i(\tau))=\mathbf{Z}_{2i}^\top {\bm \nu}(\tau) and g_3(\beta_i(\tau))=\mathbf{Z}_{3i}^\top {\bm \eta}(\tau), where {\bm \theta}(\tau)=(\theta_1(\tau),\ldots,\theta_{r_1}(\tau)), {\bm \nu}(\tau)=(\nu_1(\tau),\ldots,\nu_{r_2}(\tau)) and {\bm \eta}(\tau)=(\eta_1(\tau),\ldots,\eta_{r_3}(\tau)), where r_1, r_2 and r_3 are the dimensions of Z_1, Z_2 and Z_3, respectively. Initial values for {\bm \theta}(\tau) are used as the coefficients for the linear regresion in \mbox{logit}(y_i) using the elements of \mathbf{Z}_{1i}^\top as regressors. Initial values for the other coefficients are considered as zeros.

Value

a list containing the following elements

estimate	A matrix with the estimates
logLik	The maximum likelihood values attached by the estimates parameters

Author(s)

Diego Gallardo and Marcelo Bourguignon.

References

Bourguignon, M., Gallardo, D.I., Saulo, H. (2023) A parametric quantile beta regression for modeling case fatality rates of COVID-19. Submitted.

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)
ML.BE3(data, tau=tau)

RBE3 documentation built on May 29, 2024, 10:31 a.m.