Residuals Method for betareg Objects

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

# S3 method for class 'betareg'
residuals(object, type = c("quantile",
  "deviance", "pearson", "response", "weighted", "sweighted", "sweighted2"),
  ...)

Arguments

object

fitted model object of class "betareg".

type

character indicating type of residuals.

...

currently not used.

Details

The default residuals (starting from version 3.2-0) are quantile residuals as proposed by Dunn and Smyth (1996) and explored in the context of beta regression by Pereira (2017). In case of extended-support beta regression with boundary observations at 0 and/or 1, the quantile residuals for the boundary observations are randomized.

The definitions of all other 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 was the default prior to version 3.2-0. However, these are rather burdensome to compute because they require operations of \(O(n^2)\) and hence are typically prohibitively costly in large sample. Also they are not available for extended-support beta regression. Finally, Pereira (2017) found quantile residuals to have better distributional properties.

References

Cribari-Neto F, Zeileis A (2010). Beta Regression in R. Journal of Statistical Software, 34(2), 1–24. doi:10.18637/jss.v034.i02

Dunn PK, Smyth GK (1996). Randomized Quantile Residuals. Journal of Computational and Graphical Statistics, 5(3), 236–244. doi:10.2307/1390802

Espinheira PL, Ferrari SLP, Cribari-Neto F (2008). On Beta Regression Residuals. Journal of Applied Statistics, 35(4), 407–419. doi:10.1080/02664760701834931

Ferrari SLP, Cribari-Neto F (2004). Beta Regression for Modeling Rates and Proportions. Journal of Applied Statistics, 31(7), 799–815. doi:10.1080/0266476042000214501

Pereira GHA (2017). On Quantile Residuals in Beta Regression. Communications in Statistics – Simulation and Computation, 48(1), 302–316. doi:10.1080/03610918.2017.1381740

Kosmidis I, Zeileis A (2026). Extended-Support Beta Regression for [0, 1] Responses. Journal of the Royal Statistical Society C, 75(1), 139–157. doi:10.1093/jrsssc/qlaf039

See also

betareg

Examples

options(digits = 4)

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

gy <- betareg(yield ~ gravity + pressure + temp10 + temp, data = GasolineYield)

gy_res <- cbind(
  "quantile"   = residuals(gy, type = "quantile"),
  "pearson"    = residuals(gy, type = "pearson"),
  "deviance"   = residuals(gy, type = "deviance"),
  "response"   = residuals(gy, type = "response"),
  "weighted"   = residuals(gy, type = "weighted"),
  "sweighted"  = residuals(gy, type = "sweighted"),
  "sweighted2" = residuals(gy, type = "sweighted2")
)
pairs(gy_res)


cor(gy_res)
#>            quantile pearson deviance response weighted sweighted sweighted2
#> quantile     1.0000  0.9980   0.9997   0.9659   0.9995    0.9995     0.9980
#> pearson      0.9980  1.0000   0.9984   0.9739   0.9956    0.9956     0.9941
#> deviance     0.9997  0.9984   1.0000   0.9682   0.9989    0.9989     0.9976
#> response     0.9659  0.9739   0.9682   1.0000   0.9609    0.9609     0.9652
#> weighted     0.9995  0.9956   0.9989   0.9609   1.0000    1.0000     0.9985
#> sweighted    0.9995  0.9956   0.9989   0.9609   1.0000    1.0000     0.9985
#> sweighted2   0.9980  0.9941   0.9976   0.9652   0.9985    0.9985     1.0000