In recognition memory, ROCs are typically asymmetric, which requires Gaussian distributions with unequal variance. One problem with the unequal-variance model is that it predicts below chance performance for items with very low familiarity (i.e., studying makes some items less familiar). - ThreadSky

singmann.bsky.social • 39 days ago

In recognition memory, ROCs are typically asymmetric, which requires Gaussian distributions with unequal variance. One problem with the unequal-variance model is that it predicts below chance performance for items with very low familiarity (i.e., studying makes some items less familiar).

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singmann.bsky.social•39 days ago

We consider an SDT model assuming Gumbel-min (i.e., minimum extreme-value) distributions. The Gumbel-min model avoids the problrms of the Gaussian model, predicts asymmetric ROCs assuming equal variances, and allows calculating measures of discriminability and response bias, g′ and kappa.

singmann.bsky.social•39 days ago

The Gumbel-min model implies a behavioural principle: the probability of choosing a new item remains constant as choice sets grow. An experiment confirms this principle with constant accuracy for new item detection (2M-min). For old-item detection (2M-max), accuracy increase with choice set.

singmann.bsky.social•39 days ago

We compared the descriptive performance of both models across 35 datasets from four different recognition memory paradigms. The Gumbel-min model fits the data nearly as well as the Gaussian model. Once model complexity was penalized via AIC, the Gumbel-min model matched or outperformed the Gaussian.

singmann.bsky.social•39 days ago

We also evaluated the predictive performance of both models: Identify a relevant portion of the data that that can be omitted. Leave it out, and test each model’s predictions against it. Across all predictive tests, a pattern was clear—the Gumbel-min model outperformed the Gaussian.

singmann.bsky.social•39 days ago

A particularly noteworthy example of a Gumbel-min prediction is shown here. The ROC predicted from g' (calculated from a single yes/no point) closely matches the ROC reconstruction derived independently from forced-choice judgments. The Gaussian model cannot even make a prediction in this case.

singmann.bsky.social•39 days ago

In short: SDT doesn't have to be Gaussian. Gumbel-min SDT provides a principled, powerful, and empirically supported alternative—a “parametric road not taken” that's well worth exploring. Its performance index, g', clearly outperforms d' in recognition memory and should be preferred going forward.

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