More reading suggests that I was overthinking this. The probability of something happening will be between 0-1, if a factor shifts this probability, the shift will also be between 0-1. If you use a logit link, this is an infinite space, but (-5,5) will cover probabilities between 0.01 and 0.99 and that's probably good enough for most cases in behavioural science.

I'll use a prior distribution that includes these values. The STAN wiki recommends a student t because of concerns about the gaussian.

I'm sure this could be refined in many ways but might work as a first pass. Will check using diagnostics.

[edited: Einar's reply goes one step further than what I come up with so I'm picking that one as the answer]

More reading suggests that I was overthinking this. The probability of something happening will be between 0-1, if a factor shifts this probability, the shift will also be between 0-1. If you use a logit link, this is an infinite space, but (-5,5) will cover probabilities between 0.01 and 0.99 and that's probably good enough for most cases in behavioural science.

I'll use a prior distribution that includes these values. The STAN wiki recommends a student t because of concerns about the gaussian.

I'm sure this could be refined in many ways but might work as a first pass. Will check using diagnostics.