Latent decision thresholds from a fitted rating SDT model

Extracts the \(K-1\) latent decision thresholds of a rating signal detection model fit with bmm(). Thresholds are not posterior parameters: they are reconstructed per draw from the criterion and the parameterization parameters (spacing and/or delta*), whose mapping to ordered thresholds depends on the model's threshold_type. This function returns those draws on the latent decision-variable scale together with a posterior summary, so threshold estimates are accessible without knowing the parameterization. Which threshold separates "noise" from "signal" responses depends on whether the number of categories is even or odd; see the section "Where criterion sits" in sdt_rating().

Usage

sdt_thresholds(fit, conditions = NULL, probs = c(0.025, 0.975), ...)

Arguments

fit

A bmmfit object returned by bmm() from an SDT model.

conditions

Optional data frame of predictor values at which to evaluate the model. Column names must match predictor variables used in the formula. If NULL (default), unique predictor combinations are derived from the data.

probs

Numeric vector of length 2. Lower and upper quantiles for the credible interval (default c(0.025, 0.975)).

...

Additional arguments passed to brms::posterior_linpred(), such as draw_ids to use a subset of the posterior draws. ndraws is refused: each parameter is drawn by its own call, so random subsets would not match across parameters.

Value

A data frame of class "bmm_sdt_thresholds" with columns marker (threshold label t1, t2, ...), position (latent location), .draw, and any condition columns. The object carries a summary attribute (marker, position posterior mean, lower, upper, plus condition columns). The position/lower/upper naming matches the lines attribute of latent_sdt(), which visualises the same quantities. The object also carries probs, model_class, dist and conditions.

See also

latent_sdt(), roc_sdt()

Examples

if (FALSE) { # \dontrun{
dat <- expand.grid(id = 1:20, stimulus = c(0L, 1L))
dat <- cbind(dat, rsdt_rating(nrow(dat), 200, dat$stimulus, d = 1.5,
                              thresholds = c(0.25, 0.75, 1.25), sdratio = 1.3))

fit <- bmm(
  formula = bmf(d ~ 1, criterion ~ 1, spacing ~ 1, sdratio ~ 1),
  data = dat,
  model = sdt_rating(response = c("r1", "r2", "r3", "r4"),
                     stimulus = "stimulus"),
  cores = 4,
  backend = "cmdstanr"
)

sdt_thresholds(fit)
} # }