<p>In addition to Mike's answer, see the Ratcliff diffusion model E.g.:</p>

<p>Ratcliff, R., &amp; Rouder, J. N. (1998). Modeling response times for two–choice decisions. Psychological Science, 9, 347–356.</p>

<p>Ratcliff, R., &amp; Tuerlinckx, F. (2002). Estimating parameters of the diffusion model: Approaches to dealing with contaminant reaction times and parameter variability. Psychonomic Bulletin &amp; Review, 9, 438–481.</p>

CC BY-SA 3.0
2012-03-04T04:27:10.557Z
2017-05-24T08:05:53.170Z
2017-05-24T08:05:53.170Z
Jake Westfall
<p>You should probably also check out:
Pleskac &amp; Busemeyer (2010). Two-stage dynamic signal detection: A theory of choice, decision time, and confidence. Psychological Review.</p>

<p>Also, I believe Busemeyer has a dynamic signal detection theory paper but I don't know that it has been published.  The Pleskac &amp; Busemeyer paper probably draws on this unpublished manuscript.</p>

CC BY-SA 3.0
2012-03-14T03:04:13.630Z
Curious, how do you know about this work? I've been interested in this paper for a while now.
Andy DeSoto
CC BY-SA 3.0
2012-03-07T21:26:44.623Z
2012-03-07T21:26:44.623Z
Ryan
<p>As per self-<a href="http://en.wikipedia.org/wiki/Regulatory_focus_theory" rel="nofollow">regulatory theory</a> people can have two types of regulatory focus: promotion and prevention. </p>

<p><strong>Promotion focus</strong> is an eagerness-strategy where if we draw an analogy with SDT, one is more eager to detect signals even though there may be a few false alarms. One is ok with errors of commission. This type of motivation will reflect in seeded responses and is in direct opposition to accuracy that is modeled by the other preventive focus.</p>

<p>In <strong>preventive focus</strong>, you are more vigilant and on-guard , more focused on avoiding failure or in terms of SDT, ready to miss the signal but not miss out a correct rejection. The more cautious approach will lead to less fast repose but more accurate response bias.</p>

<p>Thus, the way I think speed or response time is to be incorporated in SDT is by pitting it against accuracy and it measuring and indicating the propensity to detect signal even at the cost of false alarms.The more the response time is less for a subject the more eagerness or promotion related focus he has - of detecting signal or achieving success. </p>

<hr>

<p>Of course this is lay mans integration of response time/ speed  with SDT; if you are looking for more mathematical models , perhaps the other answers will work better.  </p>

CC BY-SA 3.0
2012-03-14T14:17:07.790Z
2012-04-27T12:41:21.880Z
2012-04-27T12:41:21.880Z
sandygautam
<p>I believe you may be looking for Fuzzy SDT which allows for the incorporation of response time  into SDT, among other things:</p>

<p>Hancock, P.A., Masalonis, A.J., &amp; Parasuraman, R. (2000) "On the theory of fuzzy signal detection: theoretical and practical considerations" Theor. Issues In Ergon. Sci. 1(3):207-230
<a href="http://stephenrice.us/papers/Hancock,%20Masalonis,%20Parasuraman%202000.pdf" rel="nofollow">pdf</a></p>

CC BY-SA 3.0
2012-03-13T15:44:48.153Z
2012-04-27T12:38:22.710Z
2012-04-27T12:38:22.710Z
Steven Estes
<p>I'd suggest checking out the <a href="http://linkinghub.elsevier.com/retrieve/pii/S0022249610001173" rel="nofollow noreferrer">Linear Ballistic Accumulator</a> (Donkin et al., 2011) model for a scenario like this. While LBA can be used to model any number of alternatives in a speeded choice task, to model signal detection you'd want to model just two accumulators, one for the "signal" response and one for the "no signal" response. With this scenario, response bias will manifest as a difference between the accumulators in terms of their distance from starting point to criterion, while discriminability will manifest as the mean drift rate (which will probably be the same across the two accumulators). </p>

<p><strong>References</strong></p>

<p>Donkin, C., Brown, S., &amp; Heathcote, A. (2011). Drawing conclusions
from choice response time models: A tutorial using the linear
Ballistic accumulator. <em>Journal of Mathematical Psychology</em>, <em>55</em>, 140-151.</p>

CC BY-SA 3.0
2012-03-03T19:12:04.200Z
2017-04-28T17:58:09.330Z
2017-04-28T17:58:09.330Z
Mike Lawrence
<p>In <a href="http://en.wikipedia.org/wiki/Detection_theory" rel="nofollow noreferrer">signal detection theory</a>, one typically uses "signal" and "no signal" responses to analyze the data (that is, the analysis is based on a discrete choice for each trial, generating the four possible outcomes "hit", "miss", "false alarm" and "correct rejection").</p>

<p>Is there any standard way to also incorporate response time into the signal detection analysis? </p>

<reference-request><methodology><experimental-psychology><statistics><signal-detection>
Can response time be incorporated into signal detection theory?
Speldosa
# Can response time be incorporated into signal detection theory?

(Asked by: username_0 on 2012-03-03)

In [signal detection theory](http://en.wikipedia.org/wiki/Detection_theory), one typically uses "signal" and "no signal" responses to analyze the data (that is, the analysis is based on a discrete choice for each trial, generating the four possible outcomes "hit", "miss", "false alarm" and "correct rejection").

Is there any standard way to also incorporate response time into the signal detection analysis?

**Tags:** reference-request, methodology, experimental-psychology, statistics, signal-detection


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## 5 answers

### Answer by username_6 on 2012-03-03. Score: 16 | Accepted answer

I'd suggest checking out the [Linear Ballistic Accumulator](http://linkinghub.elsevier.com/retrieve/pii/S0022249610001173) (Donkin et al., 2011) model for a scenario like this. While LBA can be used to model any number of alternatives in a speeded choice task, to model signal detection you'd want to model just two accumulators, one for the "signal" response and one for the "no signal" response. With this scenario, response bias will manifest as a difference between the accumulators in terms of their distance from starting point to criterion, while discriminability will manifest as the mean drift rate (which will probably be the same across the two accumulators).

**References**

Donkin, C., Brown, S., & Heathcote, A. (2011). Drawing conclusions
from choice response time models: A tutorial using the linear
Ballistic accumulator. *Journal of Mathematical Psychology*, *55*, 140-151.


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### Answer by username_1 on 2012-03-04. Score: 10

In addition to Mike's answer, see the Ratcliff diffusion model E.g.:

Ratcliff, R., & Rouder, J. N. (1998). Modeling response times for two–choice decisions. Psychological Science, 9, 347–356.

Ratcliff, R., & Tuerlinckx, F. (2002). Estimating parameters of the diffusion model: Approaches to dealing with contaminant reaction times and parameter variability. Psychonomic Bulletin & Review, 9, 438–481.


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### Answer by username_2 on 2012-03-07. Score: 6

You should probably also check out:
Pleskac & Busemeyer (2010). Two-stage dynamic signal detection: A theory of choice, decision time, and confidence. Psychological Review.

Also, I believe Busemeyer has a dynamic signal detection theory paper but I don't know that it has been published. The Pleskac & Busemeyer paper probably draws on this unpublished manuscript.

> **Comments:**
> **username_3**: Curious, how do you know about this work? I've been interested in this paper for a while now.  

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### Answer by username_4 on 2012-03-14. Score: 3

As per self-[regulatory theory](http://en.wikipedia.org/wiki/Regulatory_focus_theory) people can have two types of regulatory focus: promotion and prevention.

**Promotion focus** is an eagerness-strategy where if we draw an analogy with SDT, one is more eager to detect signals even though there may be a few false alarms. One is ok with errors of commission. This type of motivation will reflect in seeded responses and is in direct opposition to accuracy that is modeled by the other preventive focus.

In **preventive focus**, you are more vigilant and on-guard , more focused on avoiding failure or in terms of SDT, ready to miss the signal but not miss out a correct rejection. The more cautious approach will lead to less fast repose but more accurate response bias.

Thus, the way I think speed or response time is to be incorporated in SDT is by pitting it against accuracy and it measuring and indicating the propensity to detect signal even at the cost of false alarms.The more the response time is less for a subject the more eagerness or promotion related focus he has - of detecting signal or achieving success.

---

Of course this is lay mans integration of response time/ speed with SDT; if you are looking for more mathematical models , perhaps the other answers will work better.


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### Answer by username_5 on 2012-03-13. Score: 3

I believe you may be looking for Fuzzy SDT which allows for the incorporation of response time into SDT, among other things:

Hancock, P.A., Masalonis, A.J., & Parasuraman, R. (2000) "On the theory of fuzzy signal detection: theoretical and practical considerations" Theor. Issues In Ergon. Sci. 1(3):207-230
[pdf](http://stephenrice.us/papers/Hancock,%20Masalonis,%20Parasuraman%202000.pdf)


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