I'm a college student and pursuing (in part, at least) a statistics and data science track. Much of my coursework beyond the introductory statistics sequence has involved topics like multiple regression, logistic regression (and probit and tobit), discriminant analysis, clustering techniques, etc. However, the issue with these courses is that they tend to introduce the motivation behind each topic and then move straight into implementation and interpretation. The last time I actually understood the mathematics behind a methodology was linear least squares, and I want to be able to derive the equations for the coefficients for logistic regression or for discriminant analysis.

Where can I learn to do this? Is there a good statistics manual or "encyclopedia" of sorts that collects reference material on all sorts of statistical methods? Ideally, I'd also envision some source that I can look to years down the road, when I'm rusty and need a refresher on how a certain estimator is derived or can quickly look at what the assumptions for a model are without having to sift through paragraphs of explanation.

I've looked through Introduction to Statistical Learning, but it's fairly surface-level (and also pretty focused on how to use R, and not even a very modern approach to R); I'm working through Elements of Statistical Learning and it seems to be closer to what I want, but it still doesn't seem to have the treatment I want of certain topics (mostly topics that fall under the realm of traditional statistics, such as MANOVA, rather than modern data mining/machine learning).

For specificity purposes, let's say that right now, I want to learn the underlying theory behind logistic and probit regression. What's the best place for me to do that?

  • $\begingroup$ Hi, and welcome! I took the liberty of retagging your question. Searching for previous threads with both tags yields a number of results that may be helpful, like this one and this one and this one and this one. $\endgroup$ Apr 26 '19 at 7:22
  • $\begingroup$ I'll VTC as a duplicate of the first one. If that one does not answer your question, perhaps you could edit your question to focus on a more specific technique you'd like to have more mathematical background on. (Right now, your question is rather broad.) $\endgroup$ Apr 26 '19 at 7:23
  • $\begingroup$ @StephanKolassa Thanks for your help, and apologies for not applying the right tags. I'll take a look at those links when I get a chance, and in the meantime I've edited my question to ask specifically about logistic and probit regression. (Did I do that correctly?) $\endgroup$
    – Daniel
    Apr 26 '19 at 7:31
  • 2
    $\begingroup$ No need to apologize, improving posts is what we are here for. Yes, your edit is very good (I boldfaced it to draw attention to it). I'd say this is now at least specific enough not to be closed as "too broad" and have retracted my close vote. If you find that the links answer your question, perhaps you could vote to close yourself. (But please don't delete the question. We like duplicates. They help people find answers to differently-worded-but-similar questions.) $\endgroup$ Apr 26 '19 at 7:39