# Residuals Method for betareg Objects

### Description

Extract various types of residuals from beta regression models: raw response residuals (observed - fitted), Pearson residuals (raw residuals scaled by square root of variance function), deviance residuals (scaled log-likelihood contributions), and different kinds of weighted residuals suggested by Espinheira et al. (2008).

### Usage

1 2 3 4 |

### Arguments

`object` |
fitted model object of class |

`type` |
character indicating type of residuals. |

`...` |
currently not used. |

### Details

The definitions of all residuals are provided in Espinheira et al. (2008):
Equation 2 for `"pearson"`

, last equation on page 409 for `"deviance"`

,
Equation 6 for `"weighted"`

, Equation 7 for `"sweighted"`

, and
Equation 8 for `"sweighted2"`

.

Espinheira et al. (2008) recommend to use `"sweighted2"`

, hence this is
the default in the `residuals()`

method. Note, however, that these are
rather burdensome to compute because they require operations of *O(n^2)*
and hence might be prohibitively costly in large sample.

### References

Cribari-Neto, F., and Zeileis, A. (2010). Beta Regression in R.
*Journal of Statistical Software*, **34**(2), 1–24.
http://www.jstatsoft.org/v34/i02/.

Espinheira, P.L., Ferrari, S.L.P., and Cribari-Neto, F. (2008).
On Beta Regression Residuals.
*Journal of Applied Statistics*, **35**(4), 407–419.

Ferrari, S.L.P., and Cribari-Neto, F. (2004).
Beta Regression for Modeling Rates and Proportions.
*Journal of Applied Statistics*, **31**(7), 799–815.

### See Also

`betareg`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
options(digits = 4)
data("GasolineYield", package = "betareg")
gy <- betareg(yield ~ gravity + pressure + temp10 + temp, data = GasolineYield)
gy_res <- cbind(
residuals(gy, type = "pearson"),
residuals(gy, type = "deviance"),
residuals(gy, type = "response"),
residuals(gy, type = "weighted"),
residuals(gy, type = "sweighted"),
residuals(gy, type = "sweighted2")
)
colnames(gy_res) <- c("pearson", "deviance", "response",
"weighted", "sweighted", "sweighted2")
pairs(gy_res)
``` |

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