Maximum number of independent variables in Logistic Regression Is there a measure in logistic regression that maybe penalizes you for having too many independent variables like in multiple regression with the adjusted R squared?
That is, does having too many independent variables in a logistic regression hurt the model?
What about dummy variables? Can you have too many of those to the point of unpredictability? 
 A: Having too many parameters compared to observations may lead to overfitting. Various adjustments or measures can be used to correct for this. AIC for example accounts for both the number of variables and the number of observations in your dataset and is probably most often used. AIC itself doesn't adjust the model, but serves as a tool to select the best model if you construct multiple ones. It's basically a tradeoff between residual error and model complexity.
You can furthermore take a look at other "information criteria" or more advanced techniques like crossvalidation, penalized logistic regression ("penalized" package in R), ...
A: If the number of independent variables is not very large, you can just do “all subsets” regression in which all possible models are fit. The model the model with the highest F statistic or proportion of explained variation (PVE) (note: the concept was established with linear regression but can be applied to logistic regression as well) is selected. But this often results that we will choose the full model. So we need to penalize models with many variables that don’t ﬁt much better than models with fewer variables with Akaike Information Criterion (AIC). Lower AIC values usually indicate a better model that we will finally select.
If the number of independent variables is large. The strategy is, select the best model with only one variable, then select another variable so that the best model with two variables is obtained, then select the 3rd variable...so on and so forth. The selection stops once AIC increases. Usually the complexity is around O(n^2) rather than O(2^n) in all subsets regression.
A: For the typical low signal:noise ratio we see in most problems, a common rule of thumb is that you need about 15 times as many events and 15 times as many non-events as there are parameters that you entertain putting into the model.  The rationale for that "rule" is that it results in a model performance metric that is likely to be as good or as bad in new data as it appears to be in the training data.  But you need 96 observations just to estimate the intercept so that the overall predicted risk is within a $\pm 0.1$ margin of error of the true risk with 0.95 confidence.
