How to select best model out of linear, quadratic, and a model involving an exponential? Are the models nested?

I'm examining the growth rate of species en function of ion carbonate. For each specie, I have different measured of ion carbonate, it can be in different temperature or pH.

For each measure, I'm doing graphics:

• x - ion carbonate;
• y - growth rate.

I know that for each measure I can have one of this models:

1. y=ax+b
2. y=ax^2+bx +c
3. y=a*(1-exp(-x/b)) + c

so I have to choose which one to select. I'm doing this with AIC. But AIC is only for nested models, is my 3 model is nested? 1 and 2 are nested I think.

If not, how can I select what is the "best" model for my data?

3 Answers

Model 1 is nested in model 2, but neither model 1 or 2 is nested in 3 because of the transformation on your x variable. Decisions about types of models/shapes of relationships should depend more on understanding the science that produced the data and the questions to be answered than on canned formulas.

• And I believe the specific justification for saying it's nested is that you can create 1 from 2 by restricting parameters: Fix 2's a=0 and you get 1. – Wayne Oct 6 '11 at 18:06

As Eric said, AIC is not for Nested model. There is no harm to use AIC for model selection in this case. However, it would be quite interesting if you consider more than one criteria, such as, BIC, Cp, and Cross-validation criteria for model selection. For more information please see the following Wikipedia URL.

My understanding is that, no, AIC is not for nested models, it was developed specifically for helping choose between models that are not nested.