| residuals.unitquantreg {unitquantreg} | R Documentation |
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 |
type |
character indicating type of residuals. The options are
|
... |
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.