residuals-methods {aod}

Residuals for Maximum-Likelihood and Quasi-Likelihood Models

Description

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

Usage

  ## 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:

\frac{y - n * \hat{p}}{\sqrt{n * \hat{p} * (1 - \hat{p}) * (1 + (n - 1) * \hat{\phi})}}

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

\frac{y - \hat{y}}{\sqrt{\hat{y} + \hat{\phi} * \hat{y}^2}}

where y and \hat{y} are the observed and fitted counts, respectively. Response residuals are computed as y - \hat{y}.

Value

A numeric vector of residuals.

Author(s)

Matthieu Lesnoff [e-mail], Renaud Lancelot [e-mail]

See Also

residuals.glm

Examples

  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)