Many thanks for your informative posts, @jsocolar. After a night’s sleep, I was now able to comprehend your histogram example and what it illustrates, i.e. that the 0/1 coding causes the reference level of the binary covariate to be treated differently from the non-reference level, prior-wise. However, in my case the Intercept has a prior of N(0, 5) which is even more diffuse that the one on the beta. This prior is also based on the section of BDA3 mentioned earlier. Thus, when conducting your histogram experiment, I find that the prior probability distribution is highly U-shaped for both the reference category and the non-reference category. This doesn’t worry me particularly, given that at least one authoritative sources thinks it is not a problem:
This is good enough for me. In a perfect world, I would indeed scale at least the binary covariates – they can have only two values, and so I don’t see how interpretation could be badly compromised. But the problem is that then I’d have to also figure out a way to subject the multicategory covariates to the same scaling without the major complication of having to manually create dummies for every non-reference category of every multicategory covariate.
References:
Gelman, Andrew, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin (2014). Bayesian Data Analysis. 3rd ed. CRC Press.
Agresti, Alan (2013). Categorical Data Analysis. 3rd ed. Hoboken, New Jersey: John Wiley & Sons.