I have compared two logistic regression models using the function anova(mod1,mod2,test="Chisq") in R. The result that I obtained is the following:
Model 1: Status ~ Added.genes.var Model 2: Status ~ Added.genes.var + mult_genes Resid. Df Resid. Dev Df Deviance Pr(>Chi) 1 887 1218.0 2 886 1184.2 1 33.805 6.093e-09 ***
As far as I understand, this means that adding the 'mult_genes' predictor variable to the model, significantly improves its fit. For this reason, when checking the area under the curve (AUC) with the function auc() of the package pROC, I was expecting to see a significant difference in that as well, but I obtained, for model 1 and 2 respectively:
Area under the curve: 0.6147 Area under the curve: 0.6158
I believe 0.61 is quite low as AUC...does this mean that both models perform poorly? And how is it possible to get such a significant result when comparing models with anova(), and so similar AUCs at the same time?
Thanks a lot!