# WAIC and model selection

I'm trying to compare 7 nested models at time. These are all Bayesian logistic regression estimated with stan. Some predictors will enter for sure in the model, while others have a polynomial structure. Thus I want to choose the polynomial degree. $$\ln\left(\frac{\pi}{1-\pi}\right)=\beta_0 +X\mathbf{\beta} + \beta_{n+1} z + \beta_{n+2}z^2+...$$ I'm using WAIC and LOO as criteria. In one case I have "clearly" different values:

     WAIC       LOO
1   13067,6    13067,6
2   13042,8    13042,9
3   13016,2    13016,3
4   12997,4    12997,5
5   12999,9    13000,0
6   12999,8    12999,9
7   13000,7    13000,8


In the other one the difference among the values are just few decimals.

  WAIC      LOO
1 8408,2    8408,7
2 8408,8    8409,5
3 8407,7    8408,1
4 8408,1    8408,7
5 8407,3    8407,7
6 8407,8    8408,2
7 8407,9    8408,6


I was wondering if there is a rule to determine if the differences are large enough. I haven't found anything online. Clearly this are not the only tools I'm using. I also checked the convergence of the chains and other diagnostic tools and, in both cases, looking at them, I would exclude the models 5-6-7. But I don't know how to choose among the remaining ones.