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. - ThreadSky

singmann.bsky.social • 51 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.

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singmann.bsky.social•51 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•51 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•51 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•51 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.

nivreggev.bsky.social•50 days ago

This is super interesting!

Are you familiar with this work by Adva Levi, Caren Rotello & Yonatan Goshen-Gottstein?

https://osf.io/preprints/osf/9m3sr_v1

They show da is superior to many other measures. It would be interesting to see how the two measures complement each other

singmann.bsky.social•50 days ago

Yes & we discuss some shortcomings of d_a. As shown below, d_a does not permit an ordering of participants according to performance (d' and g' do). We also compare Type I error rates for g', d', and d_a for real H/FA-pairs where only response bias differs, only g' maintains 5% Type I errors (pp. 51)

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