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I wonder under what condition I should use Bayesian logistic regression instead of standard logistic regression, or vice verse?

I have individual-level data regarding whether a person purchase a particular item online (say, 11 inch MacBook Air) or not (dependent variable y=1 if purchase, 0 otherwise), meanwhile, I have information regarding each person's past online experience across different categories (independent variable x1=# of total past experience) but I don't know if such experience contains purchasing experience of MacBook Air or not. Also, I have info regarding different stores' feature (such as x2=shipping fee, x3=seller's reputation, etc.), I don't know if it's worth applying Bayesian framework on this problem since I never used Bayesian statistics before but really interested in knowing?

Any advice would be appreciated!

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    $\begingroup$ I don't think its a question of whether or not one method is better than the other, but more so do you believe in the Bayesian paradigm (i.e., do you believe in the notion of prior information or not). Both Bayesian and non-Bayesian (Frequentist) regression will work but the choice of which to use is more fundamental to your beliefs in statistics. $\endgroup$
    – user25658
    Sep 20, 2013 at 5:54
  • $\begingroup$ I am really curious if there is any advantage of doing bayesian logit over frequentist logit regression, but based on your comment, I guess the answer is no... $\endgroup$
    – user001
    Sep 20, 2013 at 6:45
  • $\begingroup$ I think that conclusion is incorrect. There can be situations where Bayesian statistics has an edge. There can be other situations where freqentist statistics has an edge. There is a large field where both can be meaningfully applied. A more detailed discussion of when what would be most useful would require a book. $\endgroup$
    – Maarten Buis
    Sep 20, 2013 at 7:25

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Arguably, Bayesian logistic/probit regression would be better if you had informative prior, or if there was perfect or quasi-perfect separation or if you wanted to fit a hierarchical model.

If you have an informative prior, then use it. And nothing better than use it in a Bayesian approach. If there is perfect separation, a good prior (even if only weakly informative) may help you to deal with this problem. Last, but not least, I think Bayes excels with hierarchical models.

And yet, I'd still favor a Bayesian approach even if none of the above is true. And for one simple reason: It's easier to interpret Bayesian results than frequentist ones.

As it is known, it's hard to correctly compute standard errors for interaction terms in logistic/probit regression. However, it's quite easy to compute the uncertainty of interaction terms with a Bayesian approach. See the chosen answer to this question of mine about interaction terms in logistic regression. Also, with Bayes you can use posterior predictive checks to check the fit of your model, a great bonus!

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