# How to choose a model? Residual deviance or AIC

I have two models of logistic regression with the same variables

in the first model I got:

Residual deviance:  61.097  on 73  degrees of freedom
AIC: 79.097


in the second model, I added interaction between some of the variables from the first model and got:

Residual deviance:  63.542  on 75  degrees of freedom
AIC: 77.542


so based on the AIC, the second model is better, but how can I explain the Residual deviance?

## 1 Answer

You may want to double check this but looking at the degrees of freedom it seems to me that the first model is more complex than the second (degrees of freedom: 73 vs 75). As a consequence of its higher complexity, the first model has lower deviance, i.e. it fits better to the data. However, the AIC is telling you that the increase in goodness of fit does not justify the increase in complexity. Therefore, the simpler model is preferable.

You may get better answers if you show the models and the output of summary(my.model)

• in the first model I have 8 explanatory variables, in the second model I have 6 because I took 2 interactions. so the second model is better based on the AIC? – ari6739 Jan 24 at 10:54
• Such well-organized assessments of added value of model terms is a good idea. But pause to ask yourself what you intend to do with the knowledge, in view of the fact that when we use the data to tell us to fit a smaller model the standard errors of parameter estimates are biased low due to model uncertainty. – Frank Harrell Jan 24 at 11:27