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("sweighted2", "deviance", "pearson", "response", "weighted", "sweighted"),
  ...)

Arguments

object: fitted model object of class "betareg".
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. tools:::Rd_expr_doi("10.18637/jss.v034.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.

Examples

Run this code

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)