Calculating model fit

• To calculate the fit of a model, consider the area under the curve to the right of $G^2$ for the appropriate degrees of freedom (CHIDIST($G^2$,$df$)): the smaller the $G^2$ the better.
  • `What is the chance of getting at least this much deviance if the model is correct?'
  • Small $G^2$ moderate/high probability.

• To calculate the significance of an improvement, consider the area to the right of the $\Delta G^2$ for $\Delta df$ (CHIDIST($\Delta G^2$,$\Delta df$)): the bigger the drop in $G^2$ the better.
  • `What is the chance of getting this much reduction in deviance if the second model is not actually better than the first?'
  • Big $\Delta G^2$ means small probability (high significance).

• The fit of a single model can also be considered as how much the saturated model could improve on it (saturated model has $G^2 = 0$).
  • If the model has a small deviance ($G^2$) reducing it to zero will only constitute a small improvement.