Mixing weakly informative and informative priors

Modeling
1

I’m fitting a logistic regression model with rstanarm, and for some predictors I have prior knowledge, for others not. Can I mix both priors in the prior-argument?

Here’s an example of how I specified my model, with agitation being continuous and dementia a 3-level factor (low, middle and high dementia severity). Now I know from literature research that a middle severity in dementia is associated with a 2fold higher chance of falling, and high severity has an odds ratio of 3.5. I have no prior knowledge about the other two predictors.

This is how I would specify my priors. Since the location is on the log-scale, I would use log(2) and log(3.5) as location parameter, while I leave the other two priors at default (i.e. 0):

stan_glm(
  falls ~ age + dementia + agitation,
  data = d,
  family = binomial("logit"),
  prior = normal(
    location = c(0, log(2), log(3.5), 0),
    scale = c(NULL, NULL, NULL, NULL)
  )
)

Is this correct? Do I need to set autoscale = FALSE? And what about the scale parameters?

I have tried to google for possible answers, but maybe I have used the wrong search terms…

Best
Daniel

2

location = c(0, log(2), log(3.5), 0), is consistent with what you said.

Usually, when you have informative priors, you would want to also specify autoscale = FALSE so that the priors are in raw units rather than standard deviations. But if you do that, you will need to put numbers in for scale rather than all NULL.