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 (2024). Extended-Support Beta Regression for [0, 1] Responses. 2409.07233, arXiv.org E-Print Archive. doi:10.48550/arXiv.2409.07233
See Also
betareg
Examples
library("betareg")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)
