Question

In chapter 2 of BYSH (Broaden Your Statistical Horizon), what is the recommended way to compare

a) 2 nested models?

b) 2 non-nested models?

Answer 1

a) Nested means one model is a special case of the other model. We can compare nested models fit to the same dataset with the F test. A chi-square difference test also know as likelihood ratio test can be conducted using chi-square values and degrees of freedom from any two nested models. A nested model is a model that uses the same variables (and cases!) as another model but specifies at least one additional parameter to be estimated.

b. If the models are non nested, we cannot use the F-ratio or any likelihood-ratio test for that matter. In this case, one can use Akaike’s Information Criterion (AIC) after testing for plausibility of each model using e.g., a chi-square or some generalized likelihood method.