Algorithm to select predictors in logistic regression? I need to find a computer-driven way to come up with a model in logistic regression for an exploratory study using R. Usually I would just use the leaps or bestglm packages to find the best subset, but I have more than 300 potential predictor variables so none of them can go through the 2^300 potential models.
Are there any other computer-driven methods to select covariates for logistic regression that someone might recommend? If you could suggest the R package that implements them would be ideal.  
What I have been doing so far is running bestglm in groups of 10 predictors at a time, taking note of the ones that appear in the best models and hope that I can reduce the demand on computer power. Not ideal, but I don't know how else to tackle this.
 A: This represents questionable statistical practice.  On what statistical principle is that algorithm based?  Why do you need to do "model selection" as opposed to stating a model and fitting it?  Your approach will result in quite volatile models, i.e., you will find that bootstrapping the process would reveal a great deal of confusion about which predictors are selected.
A: Are you trying to examine the effects within your sample (ie. explanatory model) or are you using this data as a training set to build a model that can be used externally (ie. predictive model)? 
If the goal is to "find relationships among this variable and these 300+ predictors", I tend to agree with a regularized regression approach like LASSO and trying to establish some sort of "variable importance hierarchy". It's possible that all your variables are poor predictors, but I believe you can vary a cut-point in the LASSO to establish a relative importance. Multicollinearity may be an issue here, in which case you can try something like principal components regression or structured equation modeling approach.
If you're trying to build a predictive model, as others have mentioned, you cannot train the model AND assess model performance on the same dataset by simply using % accuracy without an external validation method (eg. train/test set split, cross validation, bootstrap). Random forest seems like a good option here, given the many predictors. 
