Hi all,
First of all, thanks to the authors for putting together this software and indeed making the forum as well! Also, apologies that this might be a very naive question - I'm not a psychophysicist by training (although I have now ordered the textbook!) but I've been tasked with trying to understand and adapt someone else's code.
In the PAL_gumbel function, is the threshold value (alpha) expected to be a 75% threshold, some other threshold or does it not make a difference? Sorry if this is really basic!
Many thanks in advance,
Hugo
PAL_gumbel function - what threshold to use?
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Nick Prins
- Site Admin
- Posts: 28
- Joined: Sun Feb 13, 2022 8:55 pm
Re: PAL_gumbel function - what threshold to use?
Hi Hugo,
What a function will evaluate to when the intensity equals it's 'threshold' parameter (alpha) depends on the form of the function (Gumbel, cumulative normal, etc.) the guess rate (gamma) and lapse rate (lambda). Most functions evaluate to gamma + (1 - gamma - lambda)*0.5 at threshold. The Gumbel (and it's close associate the Weibull) are exceptions. They evaluate to gamma + (1 - gamma - lambda)*(1 - e^-1) [i.e., gamma + (1 - gamma - lambda)*0.6321] at threshold. You can always figure the expected proportion of positive responses (e.g., 'correct') at the threshold value by using, e.g.,:
thresholdProp = PAL_Gumbel([1 1 gamma lambda],1) %evaluates to 0.8161 when using gamma = 0.5 and lambda = 0
The above evaluates to 0.8161 when using gamma = 0.5 and lambda = 0 (based on you asking about 75% threshold, we assume you're using gamma = 0.5 and lambda = 0). If you prefer 0.75, you can use the logQuick function, which is merely a shifted version of the Gumbel such that it evaluates to gamma + (1 - gamma - lambda)*0.5 at threshold.
thresholdProp = PAL_logQuick([1 1 gamma lambda],1) %evaluates to 0.75 when using gamma = 0.5 and lambda = 0
The relation between the Gumbel and the logQuick function (not to mention the Weibull and Quick functions) leads to a lot of confusion in the field. So much so that we dedicated a page to them: https://www.palamedestoolbox.org/weibullandfriends.html
Given a data set, using the logQuick or the Gumbel will fit the exact same function, just parameterized differently (see the page referenced above).
Hope that answers your question. If not, feel free to follow up.
What a function will evaluate to when the intensity equals it's 'threshold' parameter (alpha) depends on the form of the function (Gumbel, cumulative normal, etc.) the guess rate (gamma) and lapse rate (lambda). Most functions evaluate to gamma + (1 - gamma - lambda)*0.5 at threshold. The Gumbel (and it's close associate the Weibull) are exceptions. They evaluate to gamma + (1 - gamma - lambda)*(1 - e^-1) [i.e., gamma + (1 - gamma - lambda)*0.6321] at threshold. You can always figure the expected proportion of positive responses (e.g., 'correct') at the threshold value by using, e.g.,:
thresholdProp = PAL_Gumbel([1 1 gamma lambda],1) %evaluates to 0.8161 when using gamma = 0.5 and lambda = 0
The above evaluates to 0.8161 when using gamma = 0.5 and lambda = 0 (based on you asking about 75% threshold, we assume you're using gamma = 0.5 and lambda = 0). If you prefer 0.75, you can use the logQuick function, which is merely a shifted version of the Gumbel such that it evaluates to gamma + (1 - gamma - lambda)*0.5 at threshold.
thresholdProp = PAL_logQuick([1 1 gamma lambda],1) %evaluates to 0.75 when using gamma = 0.5 and lambda = 0
The relation between the Gumbel and the logQuick function (not to mention the Weibull and Quick functions) leads to a lot of confusion in the field. So much so that we dedicated a page to them: https://www.palamedestoolbox.org/weibullandfriends.html
Given a data set, using the logQuick or the Gumbel will fit the exact same function, just parameterized differently (see the page referenced above).
Hope that answers your question. If not, feel free to follow up.
Nick Prins, Administrator