residuals.betareg {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 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., and Zeileis, A. (2010). Beta Regression in R. Journal of Statistical Software, 34(2), 1–24. doi:10.18637/jss.v034.i02

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

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

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

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

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)