Best model in multinomial logistics regression model

[#1]

Hello

What models use to select variables in a multinomial logistics regression model to have the best AIC ? and select the best variables ?
I tried with the regression step by step but I don't understand that doesn't work, I have a less good confusion matrix than with my model of nominal logistic regression with all my variables

Thank you

[#2]

The goal of model is selection is generalization, not best fit. You can over-fit the training data such that the prediction of new observations (or hold out data) is poor. The model was trained to include noise in the features as information, but the new observations have different (random) noise, so the predictions do not generalize to new data.

Does that answer explain your case?

[#3]

I would caution you not to focus too much on the confusion matrix.  There are 2 problems with it - first, it depends on the cutoff probability for the classifications, so it will change if you change this probability.  Second, and related, is the fact that most problems are not symmetric in the cost of mis-classification errors.  So, a "better" confusion matrix depends both on the nature of the problem you are analyzing and the probability cutoff you choose.