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
## S3 method for class 'glimML':
residuals(object, type = c("pearson", "response"), ...)
## S3 method for class '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 $y - \hat{y}$.
data(orob2)
fm <- betabin(cbind(y, n - y) ~ seed, ~ 1,
link = "logit", data = orob2)
#Pearson's chi-squared goodness-of-fit statisticsum(residuals(fm, type = "pearson")^2)