# residuals.glmGamPoi: Extract Residuals of Gamma Poisson Model In glmGamPoi: Fit a Gamma-Poisson Generalized Linear Model

## Description

Extract Residuals of Gamma Poisson Model

## Usage

 ```1 2 3 4 5 6``` ```## S3 method for class 'glmGamPoi' residuals( object, type = c("deviance", "pearson", "randomized_quantile", "working", "response"), ... ) ```

## Arguments

 `object` a fit of type `glmGamPoi`. It is usually produced with a call to `glm_gp()`. `type` the type of residual that is calculated. See details for more information. Default: `"deviance"`. `...` currently ignored.

## Details

This method can calculate a range of different residuals:

deviance

The deviance for the Gamma-Poisson model is

dev = 2 * (1/theta * log((1 + m * theta) / (1 + y * theta)) - y log((m + y * theta) / (y + y * m * theta)))

and the residual accordingly is

res = sign(y - m) sqrt(dev).

pearson

The Pearson residual is res = (y - m) / sqrt(m + m^2 * theta)

randomized_quantile

The randomized quantile residual was originally developed by Dunn & Smyth, 1995. Please see that publication or `statmod::qresiduals()` for more information.

working

The working residuals are res = (y - m) / m.

response

The response residuals are res = y - m

## Value

a matrix with the same size as `fit\$data`. If `fit\$data` contains a `DelayedArray` than the result will be a `DelayedArray` as well.

`glm_gp()` and 'stats::residuals.glm()