ML.BE3 {RBE3} | R Documentation |
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 ( |
tau |
the quantile of the distribution to be modelled ( |
link.mu |
link function to be used for |
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)