residuals.unitquantreg: Residuals method for 'unitquantreg' objects

In unitquantreg: Parametric Quantile Regression Models for Bounded Data

Residuals method for unitquantreg objects

Description

Extract various types of residuals from unit quantile regression models.

Usage

## S3 method for class 'unitquantreg'
residuals(object, type = c("quantile", "cox-snell", "working", "partial"), ...)

Arguments

object	fitted model object of class unitquantreg.
type	character indicating type of residuals. The options are "quantile", "cox-snell", "working" and "partial".
...	currently not used.

Details

The residuals method can compute quantile and Cox-Snell residuals. These residuals are defined, respectively, by

r_{Q} = \Phi^{-1}\left[ F(y_i \mid \widehat{\mu}_i, \widehat{\theta}_i)\right]

and

r_{CS} = -\log\left[1- F(y_i \mid \widehat{\mu}_i, \widehat{\theta}_i)\right]

where \widehat{\mu}_i and \widehat{\theta}_i are the fitted values of parameters \mu and \theta, F(\cdot \mid \cdot, \cdot) is the cumulative distribution function (c.d.f.) and \Phi(\cdot) is the c.d.f. of standard Normal distribution.

Apart from the variability due the estimates of parameters,if the fitted regression model is correctly specified then the quantile residuals, r_Q, follow a standard Normal distribution and the Cox-Snell residuals, r_{CS}, follow a standard exponential distribution.

Value

Numeric vector of residuals extract from an object of class unitquantreg.

Author(s)

André F. B. Menezes

References

Cox, D. R. and Snell E. J., (1968). A general definition of residuals. Journal of the Royal Statistical Society - Series B, 30(2), 248–265.

Dunn, P. K. and Smyth, G. K., (1996). Randomized quantile residuals. Journal of Computational and Graphical Statistics, 5(3), 236–244.

unitquantreg documentation built on Sept. 8, 2023, 5:40 p.m.