residuals | R Documentation |
residuals is a method which extracts model residuals from a "glm_hP"
or "glm_CMP"
object, commonly returned by glm.hP
or
glm.CMP
. Optionally, it produces a half normal plot with a
simulated envelope of the residuals.
## S3 method for class 'glm_hP'
residuals(
object,
type = c("pearson", "response", "quantile"),
envelope = FALSE,
rep = 19,
title = "Simulated Envelope of Residuals",
...
)
## S3 method for class 'glm_CMP'
residuals(
object,
type = c("pearson", "response", "quantile"),
envelope = FALSE,
rep = 19,
title = "Simulated Envelope of Residuals",
...
)
object |
an object of class |
type |
the type of residuals which should be returned. The alternatives are: "pearson" (default), "response" and "quantile". Can be abbreviated. |
envelope |
a logical value indicating whether the envelope should be computed. |
rep |
number of replications for envelope construction. Default is 19, that is the smallest 95 percent band that can be built. |
title |
a string indicating the main title of the envelope. |
... |
further arguments passed to or from other methods. |
The response residuals (r_i=y_i - \mu_i
), Pearson
residuals (r^P_i = r_i/\sigma_i
) or randomized
quantile residuals are computed. The randomized quantile residuals are
obtained computing the cumulative probabilities that the fitted model being
less than y and less or equal than y. A random value from a
uniform distribution between both probabilities is generated and the value of
the residual is the standard normal variate with the same cumulative
probability. Four replications of the quantile residuals are recommended
because of the random component (see Dunn and Smyth, 1996 for more details).
The functions plot.glm_hP
and plot.glm_CMP
generate a residuals against fitted values plot and a Normal Q-Q plot.
The Normal Q-Q plot may show an unsatisfactory pattern of the Pearson residuals of a fitted model: then we are led to think that the model is incorrectly specified. The half normal plot with simulated envelope indicates that, under the distribution of the response variable, the model is fine when only a few points fall off the envelope.
Residual values.
Peter K. Dunn and Gordon K. Smyth (1996). "Randomized quantile residuals". Journal of Computational and Graphical Statistics, 5(3), pp. 236-244.
A. C. Atkinson (1981). "Two graphical displays for outlying and influential observations in regression". Biometrika, 68(1), pp. 13–20.
plots
## Estimate a hyper-Poisson model
Bids$size.sq <- Bids$size ^ 2
hP.fit <- glm.hP(formula.mu = numbids ~ leglrest + rearest + finrest +
whtknght + bidprem + insthold + size + size.sq + regulatn,
formula.gamma = numbids ~ 1, data = Bids)
## Compute residuals
r <- residuals(hP.fit)
## Estimate a COM-Poisson model
Bids$size.sq <- Bids$size ^ 2
CMP.fit <- glm.CMP(formula.mu = numbids ~ leglrest + rearest + finrest +
whtknght + bidprem + insthold + size + size.sq + regulatn,
formula.nu = numbids ~ 1, data = Bids)
## Compute its residuals
r <- residuals(CMP.fit)
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