Comparing models

• An alternative way of examining how well models fit is to compare nested models.

• One model is `nested' within another when the other has all the parameters it has, plus some extra ones.

• When two models are nested, we test the effect on fit of adding the extra parameters as a block, to test whether the bigger model is a better fit than the one nested within it.

• We do this by taking the difference in $G^2$, and the difference in degrees of freedom, and comparing with the theoretical $\chi ^2$ distribution. When the reduction in $G^2$ is big relative to the reduction in degrees of freedom, the more complex model is an improvement over the simpler one.