# How to assess if a model is good in multinomial logistic regression?

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.

• It is expected as the best model you found is also the most flexible. You should evaluate each model on a held out dataset to see which is the best. – Vladislavs Dovgalecs Apr 7 '15 at 20:08
• Well, I wouldn't choose frequentist vs bayesian based on model fit. That is a choice based on a number of factors, model fit not likely high on the list. – robin.datadrivers Apr 8 '15 at 2:42
• – mkt Jul 9 at 17:45