betareg (version 3.2-3)

residuals.betareg: 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

# S3 method for 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. tools:::Rd_expr_doi("10.18637/jss.v034.i02")

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

Espinheira PL, Ferrari SLP, Cribari-Neto F (2008). On Beta Regression Residuals. Journal of Applied Statistics, 35(4), 407--419. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.1080/0266476042000214501")

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

Kosmidis I, Zeileis A (2024). Extended-Support Beta Regression for [0, 1] Responses. 2409.07233, arXiv.org E-Print Archive. tools:::Rd_expr_doi("10.48550/arXiv.2409.07233")

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)