To evaluate the goodness of fit of a generalized linear model, a common statistic that is computed is the so-called Deviance statistic. It is defined as:

Deviance = -2 * (Lm - Ls)

where Lm denotes the maximized log-likelihood value for the model of interest, and Ls is the log-likelihood for the saturated model, i.e., the most complex model given the current distribution and link function. For computational details, see Agresti (1996).

See also the description of the Generalized Linear/Nonlinear Model method of analysis.