The **robustbetareg** package allows fitting robust beta
regression. Currently, four types of robust estimators are supported.
They depend on a tuning constant which may be fixed or selected by a
data-driven algorithm also implemented in the package. Diagnostic tools
associated with the fitted model, such as the residuals and
goodness-of-fit statistics, are implemented. Robust Wald-type tests are
available.

You can install the development version of
**robustbetareg** from GitHub with:

```
# install.packages("devtools")
::install_github("yurimaluf/robustbetareg") devtools
```

The main function of the \(\textbf{robustbetareg}\) package is
`robustbetareg()`, which allows fitting robust beta regression to
proportional data on the unit interval \((0,1)\). The arguments of
`robustbetareg()` are:

```
robustbetareg(formula, data, alpha, type = c("LSMLE", "LMDPDE", "SMLE", "MDPDE"),
link = c("logit", "probit", "cloglog", "cauchit", "loglog"), link.phi = NULL,
control = robustbetareg.control(...), model = TRUE, ... )
```

The `robustbetareg()` function returns an object of class
“`robustbetareg`”, similar to “`betareg`” and
“`glm`” objects, for which some methods are available. The
`summary()` method returns a standard output, with coefficient
estimates, standard errors, partial Wald-type tests and p values for the
regression coefficients, the pseudo \(R^2\), etc.. The `type` argument in
`robustbetareg()` specifies the type of estimators to be used.
The `plot()` method draws graphs for diagnostic analyses.

```
library(robustbetareg)
## basic example code
```

In the following, an example is presented to illustrate the
capacities of \(\textbf{robustbetareg}\) package. We use
the `Firm` dataset, available in the package.

`data("Firm", package = "robustbetareg)`

The response variable is `FIRMCOST` and the covariates are the
logarithm of total assets (`SIZELOG`) and a measure of the firm’s
industry risk (`INDCOST`). In the following, we fit the beta
regression model using the maximum likelihood estimator and the LSMLE, a
robust estimator, with tuning constant selected by the data-driven
algorithm.

```
# MLE fit (fixed alpha equal to zero)
<- robustbetareg(FIRMCOST ~ SIZELOG + INDCOST,
fit_MLE data = Firm, type = "LSMLE", alpha = 0,
link.phi = "log")
summary(fit_MLE)
# LSMLE fit (choosing alpha via the data-driven algorithm)
<- robustbetareg(FIRMCOST ~ SIZELOG + INDCOST,
fit_LSMLE data = Firm, type = "LSMLE",
link.phi = "log")
```

The goodness of fit is assessed using diagnostic graphs through the plot method.

`plot(fit_LSMLE)`

Further details and examples on the R package \(\textbf{robustbetareg}\) can be found using the help on R by typing:

`help("robustbetareg")`

Maluf, Y.S., Ferrari, S.L.P., and Queiroz, F.F. (2022). Robust beta regression through the logit transformation. \(\textit{arXiv}\):2209.11315.