standardize_parameters(method = "posthoc") does not scale continuous predictors by SD(x) for brmsfit models

For the same model and data, standardize_parameters(method = "posthoc") produces different conventions depending on the Bayesian backend: the stanreg path scales continuous coefficients by SD(x) as documented, the brmsfit path does not.

library(brms); library(rstanarm); library(effectsize)
d <- lme4::sleepstudy
d$grp <- factor(rep(c("a", "b", "c"), 60))

set.seed(1)
bf <- brm(Reaction ~ Days + grp, data = d, chains = 1, iter = 600,
          backend = "rstan", refresh = 0)
set.seed(1)
sf <- stan_glm(Reaction ~ Days + grp, data = d, chains = 1,
               iter = 600, refresh = 0)

standardize_parameters(sf, method = "posthoc")
#> Days ~ 0.536  == median(Days draws) * sd(Days) / sd(Reaction)   [expected]
standardize_parameters(bf, method = "posthoc")
#> b_Days ~ 0.185 == median(b_Days draws) / sd(Reaction)           [sd(Days) missing]

The ratio between the two (unrounded) outputs is exactly sd(Days) = 2.88. method = "basic" agrees between the two backends (and with the algebra), so the discrepancy is specific to the posthoc path for brmsfit.

The mechanism seems to be in standardize_info(): for a brmsfit, Deviation_Smart is 1 for continuous predictors while Deviation_Basic correctly finds SD(x), and .standardize_posteriors_posthoc() takes its predictor deviation from the Deviation_Smart column — so the posthoc factor collapses to 1/SD(y). Minimal probe (a smaller model, to keep the output short):

set.seed(1)
bf0 <- brm(Reaction ~ Days, data = lme4::sleepstudy, chains = 1,
           iter = 400, backend = "rstan", refresh = 0)
parameters::standardize_info(bf0)[, c("Parameter", "Deviation_Smart", "Deviation_Basic")]
#>     Parameter Deviation_Smart Deviation_Basic
#> 1 b_Intercept               0        0.000000
#> 2      b_Days               1        2.880293   <-- Smart expected to be 2.88 too
#> 3       sigma               1              NA

set.seed(1)
sf0 <- rstanarm::stan_glm(Reaction ~ Days, data = lme4::sleepstudy,
                          chains = 1, iter = 400, refresh = 0)
parameters::standardize_info(sf0)[, c("Parameter", "Deviation_Smart", "Deviation_Basic")]
#>     Parameter Deviation_Smart Deviation_Basic
#> 1 (Intercept)        0.000000        0.000000
#> 2        Days        2.880293        2.880293

The stanreg parameter is named Days and gets Deviation_Smart = 2.88; the brmsfit parameter is named b_Days and falls back to 1, so the b_ prefix may be what breaks the smart-deviation lookup.

Expected: identical standardization for identical models regardless of backend. Happy to provide more probes if useful.

Versions: parameters 0.29.2, effectsize 1.0.3, insight 1.5.2, datawizard 1.3.1, brms 2.23.0, rstanarm 2.32.2, R 4.6.1, Windows 11.

(Found while cross-validating standardized coefficients in a downstream table package; we use method = "basic" as the oracle there since it is backend-invariant.)

Reproduce the minimal brmsfit and stanreg probes, then inspect standardize_info() and .standardize_posteriors_posthoc(), especially how the b_ prefix is matched for predictor deviations. Compare Deviation_Smart with Deviation_Basic and confirm that posthoc standardization gives the same result for both backends. Done means the reported continuous-predictor scaling is backend-invariant without changing the existing basic behavior.