Per-trial outlier probabilities

Posterior probability that each response was generated by the outlier component rather than by the decision process, for a model fitted with any family built on the outlier mixture - cogmod_lognormal(), cogmod_loggamma(), cogmod_lnr() and the rest listed in the Supported families section of cogmod_priors(). This is the mixture responsibility poutlier * g(rt) / (poutlier * g(rt) + (1 - poutlier) * f(rt - ndt)), averaged over posterior draws.

Responses faster than ndt come out at 1, responses in the heart of the distribution near 0, and responses in either tail somewhere in between - the model discriminates by evidence rather than by a cutoff. A response in the middle can still be an outlier; a low probability means the data cannot tell, not that the trial is clean.

Averaging the responsibility over draws gives P(trial i came from the outlier component | data) directly, so the posterior mean is the quantity of interest and there is no interval to report alongside it. Pass summary = FALSE for the raw draws if you need the spread.

Usage

p_outlier(object, summary = TRUE)

Arguments

object

A brmsfit fitted with cogmod_lognormal(), cogmod_loggamma() or any other family built on the outlier mixture - see the Supported families section of cogmod_priors().

summary

Logical; if TRUE (default) returns a data frame with one row per observation. If FALSE, returns the full draws x observations matrix.

Value

A data frame with columns rt and p_outlier, in the order the observations appear in the model frame, or a draws x observations matrix if summary = FALSE.

Examples

# \donttest{
# Fitting needs cmdstanr, which lives outside CRAN - see the package website.
if (requireNamespace("cmdstanr", quietly = TRUE) &&
    !is.null(cmdstanr::cmdstan_version(error_on_NA = FALSE))) {
  df <- data.frame(RT = rcogmod_lognormal(200, ndt = 0.3, poutlier = 0.05))
  f <- brms::bf(RT ~ 1, ndt ~ 1, poutlier ~ 1, family = cogmod_lognormal())
  m <- brms::brm(f,
    data = df, stanvars = cogmod_stanvars(f),
    prior = cogmod_priors(f, df), init = cogmod_inits(f, df),
    backend = "cmdstanr", chains = 1, iter = 500, refresh = 0
  )
  head(p_outlier(m))
}
# }