  This is a companion paper to Yarkoni and Westfall (2017), which describes the
Python package Bambi for estimating Bayesian generalized linear mixed models
using a simple interface. Here I give the statistical details underlying the
default, weakly informative priors used in all models when the user does not
specify the priors. Our approach is to first deduce what the variances of the
slopes would be if we were instead to have defined the priors on the partial
correlation scale, and then to set independent Normal priors on the slopes with
variances equal to these implied variances. Our approach is similar in spirit
to that of Zellner's g-prior (Zellner 1986), in that it involves a multivariate
normal prior on the regression slopes, with a tuning parameter to control the
width or informativeness of the priors irrespective of the scales of the data
and predictors. The primary differences are that here the tuning parameter is
directly interpretable as the standard deviation of the distribution of
plausible partial correlations, and that this tuning parameter can have
different values for different coefficients. The default priors for the
intercepts and random effects are ultimately based on the prior slope
variances.
