# residuals: Residuals for Maximum-Likelihood and Quasi-Likelihood Models In aod: Analysis of Overdispersed Data

## Description

Residuals of models fitted with functions `betabin` and `negbin` (formal class “glimML”), or `quasibin` and `quasipois` (formal class “glimQL”).

## Usage

 ```1 2 3 4 5``` ``` ## S4 method for signature 'glimML' residuals(object, type = c("pearson", "response"), ...) ## S4 method for signature 'glimQL' residuals(object, type = c("pearson", "response"), ...) ```

## Arguments

 `object` Fitted model of formal class “glimML” or “glimQL”. `type` Character string for the type of residual: “pearson” (default) or “response”. `...` Further arguments to be passed to the function, such as `na.action`.

## Details

For models fitted with `betabin` or `quasibin`, Pearson's residuals are computed as:

(y - n * p.fit) / (n * p.fit * (1 - p.fit) * (1 + (n - 1) * φ))^{0.5}

where y and n are respectively the numerator and the denominator of the response, p.fit is the fitted probability and φ is the fitted overdispersion parameter. When n = 0, the residual is set to 0. Response residuals are computed as y/n - p.fit.
For models fitted with `negbin` or `quasipois`, Pearson's residuals are computed as:

(y - y.fit) / (y.fit + φ * y.fit^2)^{0.5}

where y and y.fit are the observed and fitted counts, respectively. Response residuals are computed as y - y.fit.

## Value

A numeric vector of residuals.

## Author(s)

Matthieu Lesnoff [email protected], Renaud Lancelot [email protected]

`residuals.glm`
 ```1 2 3 4 5 6``` ``` data(orob2) fm <- betabin(cbind(y, n - y) ~ seed, ~ 1, link = "logit", data = orob2) #Pearson's chi-squared goodness-of-fit statistic sum(residuals(fm, type = "pearson")^2) ```