Prior standard deviations from a fit's priors

The standard deviation on the link scale that each parameter's prior implies, for the priors that have one in closed form. Pass the result as prior_sd to recover() or recovery_grid() to get the contraction of each posterior against its prior without fitting the prior alone.

Usage

prior_sd_table(x, group = "id", ...)

Arguments

x

A fit (a brmsfit or bmmfit, read through brms::prior_summary()), or a prior table with the columns of one: prior, class, coef, group, and nlpar or dpar, as bmm::default_prior(formula, data, model) returns before anything is fitted.

group

The grouping factor whose standard deviations are wanted, as in extract_estimates().

...

Not used.

Value

A tibble with the columns term, level ("population", "effect" or "sd"), prior (the prior as brms writes it) and prior_sd_link, one row per estimated parameter, named as extract_estimates() names it.

Details

A coefficient whose own prior is empty takes the prior of its class, as brms does. The closed forms are, for coefficients (class b): normal(mu, sigma) gives sigma, logistic(mu, s) gives s * pi / sqrt(3), and student_t(nu, mu, sigma) gives sigma * sqrt(nu / (nu - 2)) for nu > 2. For standard deviations (class sd), which brms bounds at 0, the prior is the half of a distribution centred on 0, except exponential(lambda), bmm's default there, which gives 1 / lambda. Half-normal gives sigma * sqrt(1 - 2 / pi) and half-Student-t, for nu > 2, the square root of sigma^2 * nu / (nu - 2) minus its squared mean 2 * sigma * sqrt(nu) * gamma((nu + 1) / 2) / (sqrt(pi) * gamma(nu / 2) * (nu - 1)).

Any other prior is NA — a flat prior, a prior with bounds on a coefficient, a Student t with nu <= 2 (whose variance is infinite), a half prior not centred on 0, another family — and one message names those terms. A prior-only fit covers them: pass it, or a prior_check(), as prior_sd instead. Fixed parameters (constant()) have no row, as they have no estimate.

A Student t prior on a standard deviation with nu = 3, brms's default, has an infinite fourth moment, so the SD of a prior-only fit's draws converges slowly; the closed form is exact.

See also

recover() for contraction, which this feeds.

Examples

prior_sd_table(bmm::default_prior(
  bmm::bmf(kappa ~ 1 + (1 | id), thetat ~ 1 + (1 | id)),
  data = data.frame(
    y = c(0.1, -0.2, 0.3, 0.05), id = factor(c(1, 1, 2, 2))
  ),
  model = bmm::mixture2p(resp_error = "y")
))
#> # A tibble: 4 × 4
#>   term   level      prior          prior_sd_link
#>   <chr>  <chr>      <chr>                  <dbl>
#> 1 kappa  population normal(2, 1)            1   
#> 2 thetat population logistic(0, 1)          1.81
#> 3 kappa  sd         exponential(1)          1   
#> 4 thetat sd         exponential(1)          1