residuals {DGLMExtPois}

Extract and Visualize hyper-Poisson and COM-Poisson Model Residuals

Description

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.

Usage

## 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",
  ...
)

Arguments

object

an object of class "glm_hP" or "glm_CMP", typically the result of a call to glm.hP or glm.CMP.

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.

Details

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.

Value

Residual values.

References

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.

See Also

plots

Examples

## 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)