Use of different priors for groups of idepedent variables in a Bayesian Probit regression model (rstanarm)

Question

I am using the Bayesian logistic regression (probit) from the rstanarm package to train a model on default events. As inputs the model accepts some financial ratios and some qualitative data. Is there a way where I can actually regularise the coefficients, for the qualitative data only, to be always positive?

For example, when I use a single prior for everything I get these results (I calibrate the model using MCMC, with set.seed(12345) ):

prior <- rstanarm::normal(location = 0, scale = NULL, autoscale = TRUE)

model.formula <-
  formula(paste0('default_events ~ fin_ratio_1 + ',
                 'fin_ratio_2 + fin_ratio_3 +',
                 'fin_ratio_4 + fin_ratio_5 +',
                 'fin_ratio_6 + fin_ratio_7 +',
                 'fin_ratio_8 + Qual_1 + Qual_2 +',
                 'Qual_3 + Qual_4'))

bayesian.model <- rstanarm::stan_glm(model.formula,
                                     family = binomial(link = "probit"),
                                     data = as.data.frame(ds), prior = prior,
                                     prior_intercept = NULL,
                                     init_r = .1, iter=600, warmup=200)

The coefficients are the following:

summary(bayesian.model)

Estimates:
               mean    sd      2.5%    25%     50%     75%     97.5%
(Intercept)    -2.0     0.4    -2.7    -2.3    -2.0    -1.7    -1.3
fin_ratio_1    -0.7     0.1    -0.9    -0.8    -0.7    -0.6    -0.4
fin_ratio_2    -0.3     0.1    -0.5    -0.4    -0.3    -0.2    -0.1
fin_ratio_3     0.4     0.1     0.2     0.4     0.4     0.5     0.6
fin_ratio_4     0.3     0.1     0.1     0.2     0.3     0.3     0.4
fin_ratio_5     0.2     0.1     0.1     0.2     0.2     0.3     0.4
fin_ratio_6    -0.2     0.1    -0.4    -0.2    -0.2    -0.1     0.0
fin_ratio_7    -0.3     0.1    -0.5    -0.3    -0.3    -0.2    -0.1
fin_ratio_8    -0.2     0.1    -0.5    -0.3    -0.2    -0.1     0.0
Qual_1         -0.2     0.1    -0.3    -0.2    -0.2    -0.1    -0.1
Qual_2          0.0     0.1    -0.1    -0.1     0.0     0.0     0.1
Qual_3          0.2     0.0     0.1     0.1     0.2     0.2     0.3
Qual_4          0.0     0.2    -0.3    -0.1     0.0     0.1     0.3

The question is, can I use two different distributions? Like for fin_ratio_x variables to use normal and for Qual_x variables to use exponential or dirichlet?

Answer 1

Neither using different prior families nor inequality restrictions on coefficients are possible with the models supplied by the rstanarm package. Either or both is fairly easy to do with the brms package or by writing your own Stan program.