Metacognitive efficiency (M-ratio) from a fitted meta-d' SDT model

Extracts the posterior of the M-ratio (\(\mathrm{meta\text{-}d'}/d'\)) and of meta-d' from a sdt_rating() model fit with version = "metad". That model estimates the log M-ratio (logmratio) directly, so the M-ratio is exp(logmratio) and meta-d' is exp(logmratio) * d. The M-ratio is the standard measure of metacognitive efficiency (Maniscalco & Lau, 2012; Fleming, 2017): 1 is ideal metacognition, below 1 is inefficiency, and above 1 is hyper-efficiency. Type-1 and type-2 sensitivity are reported on one scale, \(d'\) or, once sdratio is estimated, \(d_a\) (see sdt_sensitivity()), so the ratio is unaffected by sdratio. The type-1 criterion keeps its location in the meta-d' space, as in the HMeta-d model equations (Fleming, 2017, Appendix); maximum-likelihood meta-d' constrains meta-c' = c' (Maniscalco & Lau, 2014), so the two differ when the criterion is far from the midpoint.

Usage

mratio(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 M-ratio. Its columns must be population-level predictors of logmratio or d in the formula; grouping variables of random effects are refused. If NULL (default), unique predictor combinations are derived from the data, and a fit without such a predictor gives one row.

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_mratio" summarising the posterior: columns parameter ("mratio" or "metad"), mean, median, lower, upper (the credible-interval bounds at probs), and any condition columns. The full per-draw posteriors are kept in the draws attribute (long format: parameter, value, .draw, plus condition columns) for downstream computation such as plotting or condition contrasts.

References

Maniscalco, B., & Lau, H. (2012). A signal detection theoretic approach for estimating metacognitive sensitivity from confidence ratings. Consciousness and Cognition, 21(1), 422–430. doi:10.1016/j.concog.2011.09.021

Maniscalco, B., & Lau, H. (2014). Signal detection theory analysis of type 1 and type 2 data: meta-d', response-specific meta-d', and the unequal variance SDT model. In S. M. Fleming & C. D. Frith (Eds.), The cognitive neuroscience of metacognition (pp. 25–66). Springer.

Fleming, S. M. (2017). HMeta-d: hierarchical Bayesian estimation of metacognitive efficiency from confidence ratings. Neuroscience of Consciousness, 2017(1), nix007. doi:10.1093/nc/nix007

See also

sdt_rating(), latent_sdt()