How to specify informative prior only on one specific predictor in rstanarm

Question

I'm currently trying to fit a Bayesian multilevel model using rstanarm. I expect - and there's evidence in literature - that the coefficient of my main predictor lies between 0.15 and 0.65. Therefore, I'd like to set an informative prior but only for this variable and keeping the weakly informative default for the others. Up to now I have:

   stan_glmer(isei_r ~ 1 + maxisei_cntr + agea + as.factor(gender) + as.factor(emp_status) + (1 + maxisei_cntr | country), 
            data = ess,
            seed = 349, 
            prior = normal(0.40, 0.25, autoscale=F))  

But in this way it applies the informative prior to all my covariates. Is it possible to specify an informative prior only for one predictor?

Thanks

Answer 1

Here is what I use to automate this process:

data = iris
formula = Sepal.Length ~ Species + Sepal.Width + Petal.Length

# get the coefficient terms, including expanded dummy columns for factors
formula_terms = colnames(
    model.matrix(
        formula,
        data=data
    )
)
# remove intercept (it can specified separately)
formula_terms = setdiff(formula_terms, '(Intercept)')

# create named vectors mapping some of the coefficients to priors
priors_location = c(
    'Speciesversicolor'=-1,
    'Speciesvirginica'=-1.5,
    'Petal.Length'=1
)
priors_scale = c(
    'Speciesversicolor'=5,
    'Speciesvirginica'=5,
    'Petal.Length'=8
)

Now, define a helper function, which can be put elsewhere:

priors_or_default_for = function(formula_terms, priors, default) {
    as.array(
        sapply(
            formula_terms,
            function(term) ifelse(term %in% names(priors), priors[term], default)
        )
    )
}

And use it to create the priors vector:

location = priors_or_default_for(formula_terms, priors_location, default=0)
scale = priors_or_default_for(formula_terms, priors_scale, default=10)

fit = rstanarm::stan_glm(
    formula,
    data=data,
    prior=normal(
        location=location,
        scale=scale
    )
)

# (recommended) check that the priors were properly assigned
parameters::parameters(fit)

Parameter	Median	89% CI	pd	% in ROPE	Rhat	ESS	Prior
(Intercept)	2.40	[ 1.97, 2.79]	100%	0%	1.000	2556.00	Normal (5.84 +- 2.07)
Speciesversicolor	-0.95	[-1.31, -0.61]	100%	0%	1.002	1274.00	Normal (-1.00 +- 5.00)
Speciesvirginica	-1.39	[-1.86, -0.93]	100%	0%	1.003	1285.00	Normal (-1.50 +- 5.00)
Sepal.Width	0.43	[ 0.29, 0.55]	100%	0%	1.001	1803.00	Normal (0.00 +- 10.00)
Petal.Length	0.77	[ 0.67, 0.88]	100%	0%	1.002	1359.00	Normal (1.00 +- 8.00)

Answer 2

Yes, it is but you need to pass a vector of prior locations and / or scales whose size(s) are equal to the number of coefficients (excluding the intercept). So, in your example it might be something like:

stan_glmer(..., prior = normal(location = c(0, 0.4, 0, 0),
                               scale = c(10, 0.25, 10, 10))