Extract Informative Priors from a Fitted Bayesian IRT Model — posterior_to

Takes a fitted brmsfit object and constructs a brmsprior object in which each item parameter receives a normal(mean, sd) prior derived from its posterior distribution. The person-level random effect SD prior is also updated. The returned prior can be passed directly to update (or brm) to refit the model with empirical Bayes / informative priors — useful for anchoring scales, warm-starting a model on new data, or regularising estimation with small samples.

Usage

posterior_to_prior(
  model,
  item_var = item,
  person_var = id,
  mult = 1,
  target_link = c("source", "logit", "probit")
)

Arguments

model

A fitted brmsfit object. Supported parameterisations:

Polytomous ordinal: e.g., family = acat with thres(gr = item), producing item-specific thresholds.
Dichotomous Rasch (random items): e.g., response ~ 1 + (1 | item) + (1 | id) with family = bernoulli().
Dichotomous 1PL (fixed items): e.g., response ~ 0 + item + (1 | id) with family = bernoulli().

item_var

An unquoted variable name identifying the item grouping variable in the model data. Default is item.

person_var

An unquoted variable name identifying the person grouping variable in the model data. Default is id.

mult

Numeric multiplier applied to each posterior SD before it is used as the prior SD. Values > 1 widen the priors (less informative); values < 1 tighten them. Default is 1 (use posterior SD directly).

target_link

Character string specifying the link function of the model the priors will be used with. One of "logit", "probit", or "source" (the default). When "source", the link function of the fitted model is used and no transformation is applied. When different from the source model's link, all location and scale parameters are rescaled using the approximation \(\beta_{\text{probit}} \approx \beta_{\text{logit}} / 1.7\). This is useful when transferring priors from a logit-fitted model to a probit model or vice versa.

Value

A brmsprior object that can be supplied to the prior argument of brm or update.

Details

The function extracts all posterior draws via as_draws_df, computes the mean and SD of each parameter's marginal posterior, and constructs normal(mean, sd * mult) priors.

Polytomous ordinal models with grouped thresholds (thres(gr = item)): each threshold receives its own prior via brms::set_prior("normal(...)", class = "Intercept", group = item, coef = threshold_index).

Dichotomous Rasch models parameterised as response ~ 1 + (1 | item) + (1 | id): priors are set on the global intercept (class = "Intercept"), the item-level SD (class = "sd", group = item_var), and the person-level SD.

Dichotomous 1PL models parameterised as response ~ 0 + item + (1 | id): each item-specific fixed effect (e.g., b_itemI1) receives its own normal(mean, sd) prior via brms::set_prior(..., class = "b", coef = "itemI1").

In all cases the person-level SD receives a normal(mean, sd * mult) prior (brms applies the lower bound of zero automatically for SD parameters).

Link function transformation: When target_link differs from the source model's link function, all parameters (means and SDs) are rescaled by a factor of approximately 1.7. This uses the well-known approximation that \(\Phi(x) \approx \text{logistic}(1.7 \, x)\), so logit-scale parameters can be converted to probit-scale by dividing by 1.7, and vice versa. The approximation is excellent for parameters in the range \(|\beta| < 3\) and adequate beyond that range.

Examples

# \donttest{
library(brms)
library(dplyr)
library(tidyr)
library(tibble)

# --- Partial Credit Model ---

df_pcm <- eRm::pcmdat2 %>%
  mutate(across(everything(), ~ .x + 1)) %>%
  rownames_to_column("id") %>%
  pivot_longer(!id, names_to = "item", values_to = "response")

fit_pcm <- brm(
  response | thres(gr = item) ~ 1 + (1 | id),
  data   = df_pcm,
  family = acat,
  chains = 4, cores = 2, iter = 1000 # use more iter (and cores if you have)
)
#> Compiling Stan program...
#> Error in .fun(model_code = .x1): Boost not found; call install.packages('BH')

# Extract posterior-informed priors (same link)
new_priors <- posterior_to_prior(fit_pcm)
#> Error: object 'fit_pcm' not found
new_priors
#> Error: object 'new_priors' not found

# Narrow the prior's sd by a factor of 0.5
wide_priors <- posterior_to_prior(fit_pcm, mult = 0.5)
#> Error: object 'fit_pcm' not found

# Extract priors for use with a probit model
probit_priors <- posterior_to_prior(fit_pcm, target_link = "probit")
#> Error: object 'fit_pcm' not found

# --- Dichotomous 1PL (fixed item effects) ---

df_rm <- eRm::raschdat3 %>%
  as.data.frame() %>%
  rownames_to_column("id") %>%
  pivot_longer(!id, names_to = "item", values_to = "response")

fit_1pl <- brm(
  response ~ 0 + item + (1 | id),
  data   = df_rm,
  family = bernoulli(),
  chains = 4, cores = 2, iter = 1000 # use more iter (and cores if you have)
)
#> Compiling Stan program...
#> Error in .fun(model_code = .x1): Boost not found; call install.packages('BH')

priors_1pl <- posterior_to_prior(fit_1pl)
#> Error: object 'fit_1pl' not found
priors_1pl
#> Error: object 'priors_1pl' not found

# Transfer logit priors to a probit refit
priors_probit <- posterior_to_prior(fit_1pl, target_link = "probit")
#> Error: object 'fit_1pl' not found
# }