Interpret the AIC in logistic regression

Question

I'm doing logistic regression in R with binary data (0's and 1's), sample size around 300 : Predicting 1 target variable (varp)

If I use one independent variable ( varx), it's significant (p 0.03, the AIC is 200) : glm(formula = varp ~ varx, family = binomial, data = mydata)

 Coefficients:
                Estimate Std. Error z value   Pr(>|z|)    
    (Intercept)  -1.0251     0.2215  -4.681 0.00000245 ***
    indepvar1  -0.6551     0.3612  -2.118     0.0322 *  
Dispersion parameter for binomial family taken to be 1)
    Null deviance: 211.06  on 205  degrees of freedom
Residual deviance: 206.36  on 204  degrees of freedom
AIC: 200

But when I use multiple independent variables of interest the AIC becomes 170, glm(formula = varp ~ varx+varb+vargg+varkkk...., family = binomial, data = mydata)

How to select the model ( the one with 1 var or the group of vars) that best predict the varp ?:

1. the model with One independent variable (varx) with AIC 200 , or
2. a group of variables with AIC 170, in this group, the varx becomes non significant and instead another one is significant ...

Answer 1

First the answer: Well, based on your short explanation I would say 2, if you want to predict the dependent variable. If your goal is to model parsimony, then use AIC, if predictive power then adjusted R2. Notice, the adjusted as we in regular regression tend to look at adjusted R2 rather than just R2. You can maximize the predictive power of your model by evaluating prediction error metrics (MAE, RMSE, etc). And maybe don't compare AIC to R2, compare AIC with the change in adjusted R2 instead.

Second some food for thoughts: I do not get the reasoning for your choice of models. Why do you run a model with only one independent variable when you are in possession of more potentially descriptive variables? That does not make any sense in my opinion. Include all the variables in your predictive model instead and you do not have to compare it to anything else.

If it is because you want to know which variables to include or not you should look more into the tag feature-selection and maybe the glmnet package in which you can diminish insignificant independent variables to 0 and then get the feature selection.