beta4reg {betaBayes} | R Documentation |

This function fits Bayesian beta regression models. The response distribution can be either the beta with the support on (0,1) or the four-parameter beta with an unknown final support. The logarithm of the pseudo marginal likelihood (LPML), the deviance information criterion (DIC), and the Watanabe-Akaike information criterion (WAIC) are provided for model comparison.

```
beta4reg(formula, data, na.action, link="logit", model = "mode",
mcmc=list(nburn=3000, nsave=2000, nskip=0, ndisplay=500),
prior=NULL, start=NULL, Xpred=NULL)
```

`formula` |
a formula expression of the form |

`data` |
a data frame in which to interpret the variables named in the |

`na.action` |
a missing-data filter function, applied to the |

`link` |
a character string for the link function. Choices include |

`model` |
a character string for the regression type. The options include |

`mcmc` |
a list giving the MCMC parameters. The list must include the following elements: |

`prior` |
a list giving the prior information. The function itself provides all default priors. The following components can be specified here: |

`start` |
a list giving the starting values of the parameters. The function itself provides all default choices. The following components can be specified here: |

`Xpred` |
A new design matrix at which estimates of the response model or mean are required. The default is the design matrix returned by the argument |

This class of objects is returned by the `beta4reg`

function to represent a fitted Bayesian beta regression model. Objects of this class have methods for the functions `print`

and `summary`

.

The `beta4reg`

object is a list containing the following components:

`modelname` |
the name of the fitted model |

`terms` |
the |

`link` |
the link function used |

`model` |
the model fitted: mean or mode |

`coefficients` |
a named vector of coefficients. The last two elements are the estimates of theta1 and theta2 involved in the support of the four-parameter beta distribution. |

`call` |
the matched call |

`prior` |
the list of hyperparameters used in all priors. |

`start` |
the list of starting values used for all parameters. |

`mcmc` |
the list of MCMC parameters used |

`n` |
the number of row observations used in fitting the model |

`p` |
the number of columns in the model matrix |

`y` |
the response observations |

`X` |
the n by (p+1) orginal design matrix |

`beta` |
the (p+1) by nsave matrix of posterior samples for the coefficients in the |

`theta` |
the 2 by nsave matrix of posterior samples for theta1 and theta2 involved in the support. |

`phi` |
the vector of posterior samples for the precision parameter. |

`cpo` |
the length n vector of the stabilized estiamte of CPO; used for calculating LPML |

`pD` |
the effective number of parameters involved in DIC |

`DIC` |
the deviance information criterion (DIC) |

`pW` |
the effective number of parameters involved in WAIC |

`WAIC` |
the Watanabe-Akaike information criterion (WAIC) |

`ratetheta` |
the acceptance rate in the posterior sampling of theta vector involved in the support |

`ratebeta` |
the acceptance rate in the posterior sampling of beta coefficient vector |

`ratephi` |
the acceptance rate in the posterior sampling of precision parameter |

The use of the `summary`

function to the object will return new object with the following additional components:

`coeff` |
A table that presents the posterior summaries for the regression coefficients |

`bounds` |
A table that presents the posterior summaries for the support boundaries theta1 and theta2 |

`phivar` |
A table that presents the posterior summaries for the precision phi. |

Haiming Zhou and Xianzheng Huang

Zhou, H. and Huang, X. (2022). Bayesian beta regression for bounded responses with unknown supports. *Computational Statistics & Data Analysis*, 167, 107345.

```
library(betaBayes)
library(betareg)
## Data from Ferrari and Cribari-Neto (2004)
data("GasolineYield", package = "betareg")
data("FoodExpenditure", package = "betareg")
## four-parameter beta mean regression
mcmc=list(nburn=2000, nsave=1000, nskip=4, ndisplay=1000);
# Note larger nburn, nsave and nskip should be used in practice.
prior = list(th1a0 = 0, th2b0 = 1)
# here the natural bound (0,1) is used to specify the prior
# GasolineYield
set.seed(100)
gy_res1 <- beta4reg(yield ~ batch + temp, data = GasolineYield,
link = "logit", model = "mean",
mcmc = mcmc, prior = prior)
(gy_sfit1 <- summary(gy_res1))
cox.snell.beta4reg(gy_res1) # Cox-Snell plot
# FoodExpenditure
set.seed(100)
fe_res1 <- beta4reg(I(food/income) ~ income + persons, data = FoodExpenditure,
link = "logit", model = "mean",
mcmc = mcmc, prior = prior)
(fe_sfit1 <- summary(fe_res1))
cox.snell.beta4reg(fe_res1) # Cox-Snell plot
## two-parameter beta mean regression with support (0,1)
mcmc=list(nburn=2000, nsave=1000, nskip=4, ndisplay=1000);
# Note larger nburn, nsave and nskip should be used in practice.
prior = list(th1a0 = 0, th1b0 = 0, th2a0 = 1, th2b0 = 1)
# this setting forces the support to be (0,1)
# GasolineYield
set.seed(100)
gy_res2 <- beta4reg(yield ~ batch + temp, data = GasolineYield,
link = "logit", model = "mean",
mcmc = mcmc, prior = prior)
(gy_sfit2 <- summary(gy_res2))
cox.snell.beta4reg(gy_res2) # Cox-Snell plot
# FoodExpenditure
set.seed(100)
fe_res2 <- beta4reg(I(food/income) ~ income + persons, data = FoodExpenditure,
link = "logit", model = "mean",
mcmc = mcmc, prior = prior)
(fe_sfit2 <- summary(fe_res2))
cox.snell.beta4reg(fe_res2) # Cox-Snell plot
```

[Package *betaBayes* version 1.0.1 Index]