I have some ordinal response $y$ that I modeled using both ordinal logistic regression and multinomial logistic regression (to avoid the proportional odds assumption), using two continuous variables as predictors $x_1$ and $x_2$.
I tested different models by including the predictor variables one at a time and their interactions.
$$y \sim x_1 \\ y \sim x_2 \\ y \sim x_1 + x_2 \\ y \sim x_1 + x_2 + x_1x_2 $$
In this way I obtained 8 different models (4 models using ordinal, and 4 models using multinomial logistic regression) and therefore 8 AIC values. It turn out that the best model (the difference in AIC is like 200) is the multinomial logistic with the following predictors:
$$ y \sim x_1 + x_2 + x_1x_2 $$
As far as I know, this model provides the best fit amongst all the various options. Now, how do I quantify if this model is good for the data in an absolute sense (in order for it to be published)?
I can do the regression both using frequentist glm and bayesian glm (so far I did frequentist way because it was more computationally cheap). Ideally I'd like to have the methodology that is most honest and convincing.
EDIT:
I'm more interested to assess model fit in terms of inference rather than prediction. In my specific problem, one of the classes is much more probable than the others on a wide range of the parameters, so prediction is unfeasible. But I'm still interested in discovering how appropriate are the estimates of the underlying probabilities.