betareg.control: Control Parameters for Beta Regression

Description

Various parameters that control fitting of beta regression models using betareg.

Usage

betareg.control(phi = TRUE, method = "BFGS", maxit = 5000,
  gradient = NULL, hessian = FALSE, trace = FALSE, start = NULL,
  fsmaxit = 200, fstol = 1e-8, quad = 20, ...)

Value

A list with the arguments specified.

Arguments

phi: logical indicating whether the precision parameter phi should be treated as a full model parameter (TRUE, default) or as a nuisance parameter.
method: characters string specifying the method argument passed to optim. Additionally, method = "nlminb" can be used to employ nlminb, instead.
maxit: integer specifying the maxit argument (maximal number of iterations) passed to optim.
trace: logical or integer controlling whether tracing information on the progress of the optimization should be produced (passed to optim).
gradient: logical. Should the analytical gradient be used for optimizing the log-likelihood? If set to FALSE a finite-difference approximation is used instead. The default of NULL signals that analytical gradients are only used for the classical "beta" distribution but not for "xbetax" or "xbeta".
hessian: logical. Should the numerical Hessian matrix from the optim output be used for estimation of the covariance matrix? By default the analytical solution is employed. For details see below.
start: an optional vector with starting values for all parameters (including phi).
fsmaxit: integer specifying maximal number of additional (quasi) Fisher scoring iterations. For details see below.
fstol: numeric tolerance for convergence in (quasi) Fisher scoring. For details see below.
quad: numeric. The number of quadrature points for numeric integration in case of dist = "xbetax" is used in the beta regression.
...: arguments passed to optim.

Details

All parameters in betareg are estimated by maximum likelihood using optim with control options set in betareg.control. Most arguments are passed on directly to optim, and start controls how optim is called.

After the optim maximization, an additional (quasi) Fisher scoring can be perfomed to further enhance the result or to perform additional bias reduction. If fsmaxit is greater than zero, this additional optimization is performed and it converges if the threshold fstol is attained for the cross-product of the step size.

Starting values can be supplied via start or estimated by lm.wfit, using the link-transformed response. Covariances are in general derived analytically. Only if type = "ML" and hessian = TRUE, they are determined numerically using the Hessian matrix returned by optim. In the latter case no Fisher scoring iterations are performed.

The main parameters of interest are the coefficients in the linear predictor of the model and the additional precision parameter phi which can either be treated as a full model parameter (default) or as a nuisance parameter. In the latter case the estimation does not change, only the reported information in output from print, summary, or coef (among others) will be different. See also examples.

Examples

Run this code

options(digits = 4)

data("GasolineYield", package = "betareg")

## regression with phi as full model parameter
gy1 <- betareg(yield ~ batch + temp, data = GasolineYield)
gy1

## regression with phi as nuisance parameter
gy2 <- betareg(yield ~ batch + temp, data = GasolineYield, phi = FALSE)
gy2

## compare reported output
coef(gy1)
coef(gy2)
summary(gy1)
summary(gy2)