residuals-methods: 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 glimML
residuals(object, type = c("pearson", "response"), …)
  # S4 method for 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.

Value

A numeric vector of residuals.

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 $y - \hat{y}$.

Examples

Run this code

# NOT RUN {
  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)
  
# }