Posterior mixture-component probabilities at the estimates

brms's pp_mixture() on a maximum-likelihood fit. For a mixture() fit, including a mixture of ordinal families, and for a fit of frmtmb.latent's mixture_mvn(), it gives the probability that each observation came from each component, given its response, with the parameters at their estimates. Estimate is mixture_probs(). The quantile columns are a Wald interval on the logit scale, so they stay inside (0, 1): the logit of the estimate plus a normal quantile times its delta-method standard error, taken over the estimated parameters and the group-level effects. Est.Error is the standard deviation of that same law, the probability plogis(Z) with Z normal around the logit, integrated numerically (100-point Gauss-Hermite, and adaptive quadrature where the law is wide). brms reports the mean, the SD and the quantiles of the same probability over the posterior draws; pp_mixture() on frmtmb.sample::frm_sample() draws does that here.

Usage

pp_mixture(x, ...)

# S3 method for class 'frmtmb_fit'
pp_mixture(
  x,
  newdata = NULL,
  re_formula = NULL,
  resp = NULL,
  ndraws = NULL,
  draw_ids = NULL,
  log = FALSE,
  summary = TRUE,
  robust = FALSE,
  probs = c(0.025, 0.975),
  ...
)

Arguments

x: A frmtmb_fit with a mixture family.
...: Refused: an argument the method does not have is an error naming it.
newdata, re_formula: brms's arguments, in brms's positions. newdata is refused: the probabilities classify the rows the model was fitted on. re_formula = NULL (the default) conditions on the group-level effects, which is what is computed; any other value is refused.
resp: The response, for brms's signature. A multivariate fit is refused.
ndraws, draw_ids, summary, robust: brms's draws arguments. A maximum-likelihood fit has no draws, so a value other than the default is refused by name with the reason.
log: If TRUE, log probabilities: the estimate and the interval ends are logged, and Est.Error is the standard deviation of the log under the same law.
probs: Probabilities of the quantile columns, as in brms.

Value

An observations x statistics x components array.

Details

Why not the delta-method standard error of the probability itself: a probability near 0 or 1 is far from linear in the parameters, and that first-order error understates the spread there by orders of magnitude. On a two-component gaussian mixture of 300 rows, against brms 2.23.0's pp_mixture() on the same data (4 chains of 1500 draws, brms's default priors), the delta-method error was a median 0.36 of brms's posterior SD over all 300 rows, and 0.008 within 1e-4 of an edge. Est.Error as reported here was a median 1.11 of brms's SD over all rows, and 0.84 to 1.27 (medians of bins by distance from the edge) for probabilities between 0.001 and 0.999. Within 0.001 of an edge it overstates: 2.4 and 4.8 times brms's SD (bin medians), where brms's is a median 0.015 and 0.007. The interval's width was a median 1.04 of brms's, and each of the 300 estimates was inside brms's 95% interval.

The array has brms's shape and names: observations by statistics by components, with the components named P(K = k | Y). For a group-level mixture (mixture(groups = )) the rows are groups, as in mixture_probs().

Examples