The likelihood ratio test compares the fits of two nested models fit by Poisson regression. Nested means one model (the simpler one, model 1 below) is a special case of the other model (the more complicated one; model 2 below).

The Χ2 ratio quantifies the relative goodness of fit of the two models:

 Χ2=2ln(LR)

If the simpler model is correct you expect to get an LR ratio near 0, so Q will be near 2. If the ratio is much greater than 2.0, there are two possibilities:

•The more complicated model is correct.

•The simpler model is correct, but random scatter led the more complicated model to fit better. The P value tells you how rare this coincidence would be.

The P value is computed from Χ2 using the chi-square distribution. The degrees of freedom equals the difference between the df of the two models.

The P value answers this question:

If model 1 is really correct, what is the chance that you would randomly obtain data that fits model 2 so much better?