Hello all,

I’m trying to set up a Bayesian Logistic Regression of my thesis data, which uses three variables (see block below for more details). The code I’ve included here works perfectly and maps directly on to the results I got via your run-of-the-mill SPSS analysis. However, I have a theoretical question about model specification: should I be specifying different priors for each parameter in my model?

For example, the Guilt variable’s estimated Odds Ratio is 13.5, while Discount’s ratios range between 3.5 and 4.5. Incidentally, shouldn’t I also then be setting priors for each *level* of my parameters? Going back to the Discount variable, the number guilty plea acceptances (my DV) rose dramatically as I increased the Discount percentage, so I would expect very different results between levels in future studies.

Any advice on if this is necessary/warranted (and if so, how) would be greatly appreciated!

Potential Trial Sentence (PTS): a two level factor representing the two possible threatened trial sentences in my study (5 years | 25 years)

Discount: a three level factor that indicates the reduction from the initial threatened sentence above (20% | 50% | 70%) offered in the plea deal

Guilt status: two level factor of the defendant’s factual guilt (Innocent | Guilty)

```
model1=stan_glm(Accept_Reject~Discount+PTS+Guilt,
family = binomial(link = "logit"),
data=pubdata,
#x = FALSE,
#y = TRUE,
prior = normal(location = 1.1,scale = 2.5,autoscale = FALSE),
#prior_intercept = normal(),
#prior_PD = FALSE,
algorithm = c("sampling"),
mean_PPD = TRUE,
adapt_delta = 0.95,
#QR = FALSE,
#sparse = FALSE,
chains=3,iter=50000,cores=3)
```