Hot answers tagged mathematical-psychology
9
Here are a few options. I have not tried them yet personally.
LBA
Scott Brown has a copy of Donkin et al (2009) on his web page with some code in R, Excel, and WinBUGS for fitting the LBA model:
http://www.newcl.org/publications/DonkinAverellEtAl2009BRM.pdf
http://www.newcl.org/members/chris/fitLBA.zip
Diffusion model
The Diffussion model is ...
8
I would go with Physics.
Physicists study the world using mathematics, while mathematicians study mathematics itself which is a construct that does not necessarily exist in the real world (Albert Einstein once said: "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."). ...
7
Dehaene & Changeux (1991) made a neural-network model:
The coding units are clusters of neurons organized in layers, or assemblies. A sensonmotor loop enables the network to sort the input cards according to several criteria (color, form, etc.). A higher-level assembly of rule-coding clusters codes for the currently tested rule, which shifts when ...
5
Now that @ofri has presented a good argument for physics, I'll give a few arguments for the benefits of a course in maths, and particularly a math course that focuses heavily on statistics.
There are many areas of psychology where a good understanding of statistics is very helpful. Statistics is particularly useful in psychometrics, mathematical ...
4
The following are just my thoughts on what seems to make sense from first principles. I don't have a detailed understanding of what is standard practice in the wisdom of crowds literature. I've also only given what you've written a basic read. I.e., enough to understand the broad question, but not enough to follow exactly what you've done.
Let $y_i$ be the ...
4
For the diffusion model, there is also Eric-Jan Wagenmakers' "EZ-diffusion model", which you can find here.
This paper compares three different pieces of software for estimation of diffusion model parameters:
von Ravenzwaaij D., & Oberauer, K. (2009). How to use the diffusion
model: Parameter recovery of three methods: EZ, fast-dm, and DMAT.
...
3
Unfortunately, in psychology and cognitive sciences (and some parts of neuroscience) absolutely no mathematical training is given beyond the highschool level (intro stats, basics of linear algebra in $\mathbb{R}^2$ and $\mathbb{R}^3$, and intro calc). To make this relatable, I will compare understanding dynamics sytems to literature, where you have 3 levels: ...
3
Have you read this:
Fishbein, M., Middlestadt, S. (1995) Noncognitive Effects on Attitude Formation and Change: Fact or Artifact? Journal of Consumer Psychology, 4(2),181-202. [DOI]
Direct quote from page 187:
Note that the psychology of the double negative is an essential part of an expectancy-value formulation (Ajzen & Fishbein, 1980; Fishbein, ...
3
Related to this is several works on the integration or non-integration of computational models in general to cognitive science. For instance, the Tractable Cognition Thesis basically says that we can improve cognitive modeling if we limit cognitive models to those tractably implementable on a Turing machine.
Van Rooij, I. 2008. The Tractable Cognition ...
2
My colleagues have applied the COVIS model of category learning to the WCST. COVIS isn't a model of WCST performance per se, but can account for several known phenomena. See this Google Scholar search: http://scholar.google.com/scholar?hl=en&q=Helie+Paul+ashby&btnG=&as_sdt=1%2C5&as_sdtp=
2
Unless I'm mistaken, it sounds like you're actually interested in meta-cognition and type-2 signal detection theory (the form of SDT that Speldosa has pointed to is type-1 signal detection theory). It's used to study our ability to reflect on our own knowledge, or what we think about what we think.
This wikipedia article might get you started on ...
2
From my social psychology perspective, there has been some computational modelling work on things like attitudinal influence dynamics. See:
Nowak, A., Szamrej, J., & Latané, B. (1990). From private attitude to public opinion: a dynamic theory of social impact. Psychological Review, 97, 362-476.
Robin Vallacher and Andrzej Nowak crop up a lot in this ...
2
Recently Bayesian models of cognitive development have been very successful in at least formulating working hypotheses as to how abstract knowledge "regularizes" and guides learning and reasoning from sparse data. I was thinking for instance of the following paper:
Tenenbaum, J. B., Kemp, C., Griffiths, T. L., and Goodman, N. D. (2011). How to Grow a Mind: ...
1
The problem is fundamentally due to the level of likelihood you allocate to an event, that is variable $e_i$, should not be measured using a bi-polar scale. Instead, likelihoods should be associated with a percentage, between 0 and 100%. This is a more natural unit, as a "low likelihood" result usually means that the respondent thinks the probability of ...
1
Bogacz et al. (2006) provide the most comprehensive overview of models in this domain. This includes comparisons of the Drift Diffusion Model (Ratcliff, 1978), Ornstein–Uhlenbeck (O-U) Model (e.g. Busemeyer & Townsend, 1993; "Decision Field Theory"), race models without inhibition (e.g. Vickers, 1970), and race models with inhibition (e.g. Usher & ...
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