<p>It is difficult to overstate the extent to which analysis of variance-based linear modeling based for different groups dominates the cognitive sciences. A recent methodological review of the psychology literature suggesting that these analyses are used to test hypotheses in as much as 95% of studies (citation pending me recovering it). There <em>are</em> alternatives in working memory, but they often have more limited empirical support due to the dominance of the aforementioned analyses.</p>

<h1>Hierarchical models</h1>

<p>One alternative that doesn't veer <em>too</em> far from established practices is to use a hierarchical modeling approach, as you suggest. For example, Lee and Webb (2005) proposed a Bayesian hierarchical modeling of working memory which accounted for both individual differences and aggregated group data. The main benefit here is to take advantage of both individual- and group-level variability, but we ultimately end up with a linear model.</p>

<blockquote>
  <p><strong>Many evaluations of cognitive models rely on data that have been averaged or aggregated across all experimental subjects</strong>, and so fail to consider the possibility of important individual differences between subjects. <strong>Other evaluations are done at the single-subject level</strong>, and so fail to benefit from the reduction of noise that data averaging or aggregation potentially provides. To overcome these weaknesses, <strong>we have developed a general approach to modeling individual differences using families of cognitive models in which different groups of subjects are identified as having different psychological behavior.</strong> Separate models with separate parameterizations are applied to each group of subjects, and Bayesian model selection is used to determine the appropriate number of groups.</p>
</blockquote>

<h1>Topology</h1>

<p>An emerging, but currently more niche approach is to use topology. <strong>Topology is making some exciting inroads in the psychological methodology literature</strong> (e.g., Butner et al., 2014), but so far has not managed to see substantial use in the empirical WM literature. However, there are a few early birds who've made some attempts to capture WM within a topological context, namely <strong>Glassman's work on a "theory of relativity" for working memory</strong> (Glassman, 1999; Glassman, 2003). </p>

<p>In the succeeding excerpt, he explains why human verbal memory capacity is 3-4 items from a topological perspective:</p>

<blockquote>
  <p>Thus,
  a moment’s WM is hypothesized here to reside in myriad activated cortical planar “patches,” each subdivided into up to four amoeboid “subpatches.” Two different lines of topological reasoning suggest orderly associations of such representations. <strong>(1)</strong> The four-color principle of map topology, and the related K4 is planar theorem of graph theory, imply that if a small cortical area is dynamically subdivided into no more than four, discretely bounded planar subareas, then each such segment has ample free access to each of the others. <strong>(2)</strong> A hypothetical alternative to such associative adjacency of simultaneously active cortical representations of chunk-attributes is associative overlap, whereby, in dense cortical neuropil, activated subpatches behave like Venn diagrams of intersecting sets. As the number of Venn-like coactive subpatches
  within a patch increases, maintaining ad hoc associativity among all combinations requires exponentially proliferating intersections. <strong>Beyond four, serpentine subpatch shapes are required, which could easily lead to pathologies of omission or commission.</strong> </p>
</blockquote>

<h1>Others</h1>

<p>I am tangentially aware of related attempts to develop a theory of (working) memory as a form of <a href="http://www.scientificamerican.com/article/memory-foraging/" rel="nofollow">foraging behavior</a>, but not sufficiently to give a summary of it. Hopefully, the link is instructive.</p>

<h2>References</h2>

<ul>
<li><a href="http://www.psych.utah.edu/research/upforreview/butner/article3_butner.pdf" rel="nofollow">Butner, J. E., Gagnon, K. T., Geuss, M. N., Lessard, D. A., &amp; Story, T. N. (2014). Utilizing Topology to Generate and Test Theories of Change. Psychological methods.</a></li>
<li><a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.128.1309&amp;rep=rep1&amp;type=pdf" rel="nofollow">Lee, M. D., &amp; Webb, M. R. (2005). Modeling individual differences in cognition. Psychonomic Bulletin &amp; Review, 12(4), 605–621. doi:10.3758/BF03196751</a></li>
<li>Glassman, R. B. (1999). A working memory “theory of relativity”: elasticity in temporal, spatial, and modality dimensions conserves item capacity in radial maze, verbal tasks, and other cognition. Brain Research Bulletin, 48(5), 475–489. doi:10.1016/S0361-9230(99)00026-X</li>
<li>Glassman, R. B. (2003). Topology and graph theory applied to cortical anatomy may help explain working memory capacity for three or four simultaneous items. Brain Research Bulletin, 60(1-2), 25–42. doi:10.1016/S0361-9230(03)00030-3</li>
</ul>

CC BY-SA 3.0
2015-05-03T11:07:33.053Z
You mean, this 'topology' that is a part of mathematics?
Lil'Lobster
CC BY-SA 3.0
2015-05-03T11:16:47.290Z
@Lili That's the one.
Christian Hummeluhr
CC BY-SA 3.0
2015-05-03T12:15:55.577Z
To my knowledge, topology is a family of open sets and I don't know what that has in common with WM... but I have downloaded the article.
Lil'Lobster
CC BY-SA 3.0
2015-05-03T12:29:25.853Z
@Lili Well, it is that, but that's not all topology is. I've fixed the broken link to the Butner article, which clarifies the relationship to cognitive science research (including WM).
Christian Hummeluhr
CC BY-SA 3.0
2015-05-01T12:05:49.450Z
2015-05-03T12:28:43.917Z
2015-05-03T12:28:43.917Z
Christian Hummeluhr
<p>I mean, by cognitive psychologists. I skimmed over a few articles from <em>Journal of Cognitive Neuroscience</em> and <em>Trends in Cognitive Science</em> and concluded that ANOVAs and t-tests are mostly used (without effect sizes). I'm sure that there are more scientific journals of cognitive psychology than these two, and I guess, that there are also more advanced statistical tools than comparing groups. For example, in social psychology, structural equations modelling and mediation analysis are in fashion.</p>

<p>When asking this question, I had <strong>working memory</strong> in mind. 
Common methods to measure working memory empirically are, among others: dual task paradigms, n-back tasks and composites of simple memory measures. The main statistical tools that are applied to these measures seem to be mainly ANOVAs, t-tests, and other variations on traditional linear modeling, but what are the alternatives?</p>

<p><strong>What are the most used statistical methods in WM research besides (generalized) linear modeling?</strong></p>

CC BY-SA 3.0
2015-02-25T08:23:42.393Z
Statistical methods should be chosen based on the purpose, not on the discipline. If you can provide us with a more detailed question that would be great. For now, I vote to close this question because it is too broad.
AliceD
CC BY-SA 3.0
2015-02-25T10:52:00.057Z
@ChrisStronks I tried to improve it, but if it still to broad, don't hesitate to close it.
Lil'Lobster
CC BY-SA 3.0
2015-02-25T11:17:05.350Z
I think this greatly improves the question, thanks. I retracted my close-vote. +1 Good luck!
AliceD
CC BY-SA 3.0
2015-02-25T12:19:30.960Z
To reiterate @Chris' comment, the choice of analysis is completely dependant on the design of the experiment, and what the DV is, not the domain being studied. If you're looking at a continuous DV between groups, you use t tests/ANOVA (paired or unpaired), if you're looking at binary outcomes, you use logistic regression, and if you're looking at complex, nested, or unbalanced designs, you use mixed models. You'll really need to specify what kind of experiment you're thinking about, and consider posting on [CrossValidated](http://stats.stackexchange.com/)
Eoin
CC BY-SA 3.0
2015-03-23T13:30:29.463Z
@Lili I have revised the question to be more general and amenable to answering. I have strived to preserve the intent of your question, but the changes were substantial, so please roll back or comment on my edit if anything went missing.
Christian Hummeluhr
CC BY-SA 3.0
2015-03-23T15:02:08.607Z
@ChristianHummeluhr Thank you very much. I hope it helps. However soon it will turn out, that I'm gonna answer this question myself, by reviewing many psychological articles on my own...
Lil'Lobster
<methodology><statistics><working-memory>
What are the most used statistical methods in WM research besides (generalized) linear modeling?
Lil'Lobster
# What are the most used statistical methods in WM research besides (generalized) linear modeling?

(Asked by: username_0 on 2015-02-22)

I mean, by cognitive psychologists. I skimmed over a few articles from *Journal of Cognitive Neuroscience* and *Trends in Cognitive Science* and concluded that ANOVAs and t-tests are mostly used (without effect sizes). I'm sure that there are more scientific journals of cognitive psychology than these two, and I guess, that there are also more advanced statistical tools than comparing groups. For example, in social psychology, structural equations modelling and mediation analysis are in fashion.

When asking this question, I had **working memory** in mind.
Common methods to measure working memory empirically are, among others: dual task paradigms, n-back tasks and composites of simple memory measures. The main statistical tools that are applied to these measures seem to be mainly ANOVAs, t-tests, and other variations on traditional linear modeling, but what are the alternatives?

**What are the most used statistical methods in WM research besides (generalized) linear modeling?**

**Tags:** methodology, statistics, working-memory

> **Comments:**
> **username_1**: Statistical methods should be chosen based on the purpose, not on the discipline. If you can provide us with a more detailed question that would be great. For now, I vote to close this question because it is too broad.  
> **username_0**: @ChrisStronks I tried to improve it, but if it still to broad, don't hesitate to close it.  
> **username_1**: I think this greatly improves the question, thanks. I retracted my close-vote. +1 Good luck!  
> **username_2**: To reiterate @Chris' comment, the choice of analysis is completely dependant on the design of the experiment, and what the DV is, not the domain being studied. If you're looking at a continuous DV between groups, you use t tests/ANOVA (paired or unpaired), if you're looking at binary outcomes, you use logistic regression, and if you're looking at complex, nested, or unbalanced designs, you use mixed models. You'll really need to specify what kind of experiment you're thinking about, and consider posting on [CrossValidated](http://stats.stackexchange.com/)  
> **username_3**: @Lili I have revised the question to be more general and amenable to answering. I have strived to preserve the intent of your question, but the changes were substantial, so please roll back or comment on my edit if anything went missing.  
> **username_0**: @ChristianHummeluhr Thank you very much. I hope it helps. However soon it will turn out, that I'm gonna answer this question myself, by reviewing many psychological articles on my own...  

---

## 1 answers

### Answer by username_3 on 2015-05-01. Score: 2

It is difficult to overstate the extent to which analysis of variance-based linear modeling based for different groups dominates the cognitive sciences. A recent methodological review of the psychology literature suggesting that these analyses are used to test hypotheses in as much as 95% of studies (citation pending me recovering it). There *are* alternatives in working memory, but they often have more limited empirical support due to the dominance of the aforementioned analyses.

# Hierarchical models

One alternative that doesn't veer *too* far from established practices is to use a hierarchical modeling approach, as you suggest. For example, Lee and Webb (2005) proposed a Bayesian hierarchical modeling of working memory which accounted for both individual differences and aggregated group data. The main benefit here is to take advantage of both individual- and group-level variability, but we ultimately end up with a linear model.

> **Many evaluations of cognitive models rely on data that have been averaged or aggregated across all experimental subjects**, and so fail to consider the possibility of important individual differences between subjects. **Other evaluations are done at the single-subject level**, and so fail to benefit from the reduction of noise that data averaging or aggregation potentially provides. To overcome these weaknesses, **we have developed a general approach to modeling individual differences using families of cognitive models in which different groups of subjects are identified as having different psychological behavior.** Separate models with separate parameterizations are applied to each group of subjects, and Bayesian model selection is used to determine the appropriate number of groups.

# Topology

An emerging, but currently more niche approach is to use topology. **Topology is making some exciting inroads in the psychological methodology literature** (e.g., Butner et al., 2014), but so far has not managed to see substantial use in the empirical WM literature. However, there are a few early birds who've made some attempts to capture WM within a topological context, namely **Glassman's work on a "theory of relativity" for working memory** (Glassman, 1999; Glassman, 2003).

In the succeeding excerpt, he explains why human verbal memory capacity is 3-4 items from a topological perspective:

> Thus,
> a moment’s WM is hypothesized here to reside in myriad activated cortical planar “patches,” each subdivided into up to four amoeboid “subpatches.” Two different lines of topological reasoning suggest orderly associations of such representations. **(1)** The four-color principle of map topology, and the related K4 is planar theorem of graph theory, imply that if a small cortical area is dynamically subdivided into no more than four, discretely bounded planar subareas, then each such segment has ample free access to each of the others. **(2)** A hypothetical alternative to such associative adjacency of simultaneously active cortical representations of chunk-attributes is associative overlap, whereby, in dense cortical neuropil, activated subpatches behave like Venn diagrams of intersecting sets. As the number of Venn-like coactive subpatches
> within a patch increases, maintaining ad hoc associativity among all combinations requires exponentially proliferating intersections. **Beyond four, serpentine subpatch shapes are required, which could easily lead to pathologies of omission or commission.**

# Others

I am tangentially aware of related attempts to develop a theory of (working) memory as a form of [foraging behavior](http://www.scientificamerican.com/article/memory-foraging/), but not sufficiently to give a summary of it. Hopefully, the link is instructive.

## References

* [Butner, J. E., Gagnon, K. T., Geuss, M. N., Lessard, D. A., & Story, T. N. (2014). Utilizing Topology to Generate and Test Theories of Change. Psychological methods.](http://www.psych.utah.edu/research/upforreview/butner/article3_butner.pdf)
* [Lee, M. D., & Webb, M. R. (2005). Modeling individual differences in cognition. Psychonomic Bulletin & Review, 12(4), 605–621. doi:10.3758/BF03196751](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.128.1309&rep=rep1&type=pdf)
* Glassman, R. B. (1999). A working memory “theory of relativity”: elasticity in temporal, spatial, and modality dimensions conserves item capacity in radial maze, verbal tasks, and other cognition. Brain Research Bulletin, 48(5), 475–489. doi:10.1016/S0361-9230(99)00026-X
* Glassman, R. B. (2003). Topology and graph theory applied to cortical anatomy may help explain working memory capacity for three or four simultaneous items. Brain Research Bulletin, 60(1-2), 25–42. doi:10.1016/S0361-9230(03)00030-3

> **Comments:**
> **username_0**: You mean, this 'topology' that is a part of mathematics?  
> **username_3**: @Lili That's the one.  
> **username_0**: To my knowledge, topology is a family of open sets and I don't know what that has in common with WM... but I have downloaded the article.  
> **username_3**: @Lili Well, it is that, but that's not all topology is. I've fixed the broken link to the Butner article, which clarifies the relationship to cognitive science research (including WM).  

---

