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So I have been reading some books (or parts of them) on modeling (F. Harrell's "Regression Modeling Strategies" among others), since my current situation right now is that I need to do a logistic model based on binary response data. I have both continuous, categorical, and binary data (predictors) in my data set. Basically I have around 100 predictors right now, which obviously is way too many for a good model. Also, many of these predictors are kind of related, since they are often based on the same metric, although a bit different.

Anyhow, what I have been reading, using univariate regression and step-wise techniques is some of the worst things you can do in order to reduce the amount of predictors. I think the LASSO technique is quite okay (if I understood that correctly), but obviously you just can't use that on 100 predictors and think any good will come of that.

So what are my options here ? Do I really just have to sit down, talk to all my supervisors, and smart people at work, and really think about what the top 5 best predictors could/should be (we might be wrong), or which approach(es) should I consider instead ?

And yes, I also know that this topic is heavily discussed (online and in books), but it sometimes seems a bit overwhelming when you are kind of new in this modeling field.

+1 for "sometimes seems a bit overwhelming". It really depends (as Harrell clearly states; see the section at the end of Chapter 4) whether you want to do

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  confirmatory analysis ($to$ reduce your predictor complexity to a reasonable level without looking at the responses, by PCA or subject-area considerations or ...)


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  predictive analysis ($to$ use appropriate penalization methods). Lasso could very well work OK with 100 predictors, if you have a reasonably large sample. Feature selection will be unstable, but that's OK if all you care about is prediction. I have a personal preference for ridge-like approaches that don't technically "select features" (because they never reduce any parameter to exactly zero), but whatever works ...

  
  
  

  You'll have to use cross-validation to choose the degree of penalization, which will destroy your ability to do inference (construct confidence intervals on predictions) unless you use cutting-edge high-dimensional inference methods (e.g. Dezeure et al 2015; I have not tried these approaches but they seem sensible ...)

  
  


• 
  exploratory analysis: have fun, be transparent and honest, don't quote any p-values.

There are many different approaches. What I would recommend is trying some simple ones, in the following order:

• L1 regularization (with increasing penalty; the larger the regularization coefficient, the more features will be eliminated)


• Recursive Feature Elimination (https://scikit-learn.org/stable/modules/feature_selection.html#recursive-feature-elimination) -- removes features incrementally by eliminating the features associated with the smallest model coefficients (assuming that those are the least important once; obviously, it's very crucial here to normalize the input features)


• Sequential Feature Selection (http://rasbt.github.io/mlxtend/user_guide/feature_selection/SequentialFeatureSelector/) -- removes features based on how important they are for predictive performance