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.
Thanks in advance for your help.