# Cognitive Models in Intelligence Research: Advantages and Recommendations for Their Application

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## Abstract

**:**

## 1. Introduction

## 2. Advantages of Cognitive Modeling in Intelligence Research

#### 2.1. Statistical Models

#### 2.2. Cognitive Models

## 3. Selecting Cognitive Models Suitable for Intelligence Research

#### 3.1. Different Cognitive Models of Interest for Intelligence Research

#### 3.1.1. The Drift Diffusion Model of Binary Decision Making

#### 3.1.2. The Time-Based Resource-Sharing Model of Working Memory

#### 3.1.3. The Shrinking Spotlight Model of Selective Attention

#### 3.2. Guidelines for Model Selection

## 4. Guidelines for Model Application

- Researchers should plan their data collection to meet requirements for reliable and stable parameter estimates.
- Model fit should be carefully evaluated after fitting the model to the empirical data.
- Model parameters should be adequately related to other individual differences variables of interest such as intelligence test performances.

#### 4.1. Design and Data Collection

#### 4.1.1. Reliability and Stability of Estimated Model Parameters

#### 4.1.2. Trait, Situation, and Task Characteristics of Model Parameters

#### 4.2. Evaluation of Model Fit

#### 4.2.1. Relative Model Fit: Which Model Provides the Best Account for the Data?

#### 4.2.2. Absolute Model Fit: How Well Does the Selected Model Describe the Data?

#### 4.3. Relating Model Parameters to Intelligence Test Performance

## 5. Interpretation of the Results

## 6. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Abbreviations

SOB-CS | Serial-Order in Box Model for Complex Span Tasks |

DDM | Drift-Diffusion Model |

LBA | Linear Ballistic Accumulator Model |

LCA | Leaky Competing Accumulator Model |

TBRS | Time-base resource sharing theory/model |

AIC | Akaike Information Criterion |

BIC | Bayesian Information Criterion |

GOF | Goodness-of-fit |

## References

- De Boeck, P. Intelligence, Where to Look, Where to Go? J. Intell.
**2013**, 1, 5–24. [Google Scholar] [CrossRef] [Green Version] - Thurstone, L. Primary Mental Abilities; University of Chicago Press: Chicago, IL, USA, 1938. [Google Scholar]
- Kievit, R.A.; Davis, S.W.; Griffiths, J.; Correia, M.M.; Henson, R.N. A watershed model of individual differences in fluid intelligence. Neuropsychologia
**2016**, 91, 186–198. [Google Scholar] [CrossRef] [PubMed] - Kovacs, K.; Conway, A.R.A. Process Overlap Theory: A Unified Account of the General Factor of Intelligence. Psychol. Inquiry
**2016**, 27, 151–177. [Google Scholar] [CrossRef] - Spearman, C. ‘General intelligence’, objectively determined and measured. Am. J. Psychol.
**1904**, 15, 201–293. [Google Scholar] [CrossRef] - Horn, J.L.; Cattell, R.B. Refinement and test of the theory of fluid and crystallized general intelligences. J. Educ. Psychol.
**1966**, 57, 253–270. [Google Scholar] [CrossRef] [PubMed] - Carroll, J.B. Human Cognitive Abilities: A Survey of Factor-Analytic Studies; Cambridge University Press: Cambridge, UK, 1993. [Google Scholar]
- McGrew, K. The Cattell-Horn-Carroll Theory of Cognitive Abilities: Past, Present, and Future. In Contemporary Intellectual Assessment: Theories, Tests, and Issues; The Guilford Press: New York, NY, USA, 2005. [Google Scholar]
- Jensen, A.R. Clocking the Mind: Mental Chronometry and Individual Differences; Elsevier: Amsterdam, The Netherlands, 2006. [Google Scholar]
- Kyllonen, P.C.; Zu, J. Use of Response Time for Measuring Cognitive Ability. J. Intell.
**2016**, 4, 14. [Google Scholar] [CrossRef] - Colom, R.; Abad, F.J.; Ángeles Quiroga, M.; Shih, P.C.; Flores-Mendoza, C. Working memory and intelligence are highly related constructs, but why? Intelligence
**2008**, 36, 584–606. [Google Scholar] [CrossRef] - Conway, A.R.; Cowan, N.; Bunting, M.F.; Therriault, D.J.; Minkoff, S.R. A latent variable analysis of working memory capacity, short-term memory capacity, processing speed, and general fluid intelligence. Intelligence
**2002**, 30, 163–183. [Google Scholar] [CrossRef] - Engle, R.W.; Tuholski, S.W.; Laughlin, J.E.; Conway, A.R. Working memory, short-term memory, and general fluid intelligence: A latent-variable approach. J. Exp. Psychol. Gen.
**1999**, 128, 309–331. [Google Scholar] [CrossRef] [PubMed] - Kyllonen, P.C.; Christal, R.E. Reasoning ability is (little more than) working-memory capacity? Intelligence
**1990**, 14, 389–433. [Google Scholar] [CrossRef] - Unsworth, N.; Engle, R.W. Simple and complex memory spans and their relation to fluid abilities: Evidence from list-length effects. J. Mem. Lang.
**2006**, 54, 68–80. [Google Scholar] [CrossRef] - Unsworth, N.; Engle, R.W. The nature of individual differences in working memory capacity: Active maintenance in primary memory and controlled search from secondary memory. Psychol. Rev.
**2007**, 114, 104–132. [Google Scholar] [CrossRef] [PubMed] - Miyake, A.; Friedman, N.P.; Emerson, M.J.; Witzki, A.H.; Howerter, A. The unity and diversity of executive functions and their contributions to complex ‘frontal lobe’ tasks: A latent variable analysis. Cognit. Psychol.
**2000**, 41, 49–100. [Google Scholar] [CrossRef] [PubMed] - Wongupparaj, P.; Kumari, V.; Morris, R.G. The relation between a multicomponent working memory and intelligence: The roles of central executive and short-term storage functions. Intelligence
**2015**, 53, 166–180. [Google Scholar] [CrossRef] - Thomson, G.H. A hierarchy without a general factor. Br. J. Psychol. 1904–1920
**1916**, 8, 271–281. [Google Scholar] [CrossRef] - Eriksen, B.A.; Eriksen, C.W. Effects of noise letters upon the identification of a target letter in a nonsearch task. Percept. Psychophys.
**1974**, 16, 143–149. [Google Scholar] [CrossRef] [Green Version] - Stroop, J.R. Studies of interference in serial verbal reactions. J. Exp. Psychol.
**1935**, 18, 643–662. [Google Scholar] [CrossRef] - Kane, M.J.; Meier, M.E.; Smeekens, B.A.; Gross, G.M.; Chun, C.A.; Silvia, P.J.; Kwapil, T.R. Individual differences in the executive control of attention, memory, and thought, and their associations with schizotypy. J. Exp. Psychol. Gen.
**2016**, 145, 1017–1048. [Google Scholar] [CrossRef] [PubMed] - McVay, J.C.; Kane, M.J. Why does working memory capacity predict variation in reading comprehension? On the influence of mind wandering and executive attention. J. Exp. Psychol. Gen.
**2012**, 141, 302–320. [Google Scholar] [CrossRef] [PubMed] - Donders, F. On the speed of mental processes. Acta Psychol.
**1969**, 30, 412–431. [Google Scholar] [CrossRef] - Friston, K.J.; Price, C.J.; Fletcher, P.; Moore, C.; Frackowiak, R.S.; Dolan, R.J. The trouble with cognitive subtraction. NeuroImage
**1996**, 4, 97–104. [Google Scholar] [CrossRef] [PubMed] - Schubert, A.L.; Hagemann, D.; Voss, A.; Schankin, A.; Bergmann, K. Decomposing the relationship between mental speed and mental abilities. Intelligence
**2015**, 51, 28–46. [Google Scholar] [CrossRef] - Cronbach, L.J.; Furby, L. How we should measure change: Or should we? Psychol. Bull.
**1970**, 74, 68–80. [Google Scholar] [CrossRef] - Hedge, C.; Powell, G.; Sumner, P. The reliability paradox: Why robust cognitive tasks do not produce reliable individual differences. Behav. Res. Methods
**2017**, 50, 1166–1186. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Borsboom, D. Measuring the Mind: Conceptual Issues in Contemporary Psychometrics; Cambridge University Press: Cambridge, UK, 2005. [Google Scholar]
- Lord, F.; Novick, M.; Birnbaum, A. Statistical Theories of Mental Test Scores; Addison-Wesley: Boston, MA, USA, 1968. [Google Scholar]
- Schmidt, F.L.; Hunter, J.E. Theory testing and measurement error. Intelligence
**1999**, 27, 183–198. [Google Scholar] [CrossRef] - Borsboom, D. Latent variable theory. Meas. Interdiscip. Res. Perspect.
**2008**, 6, 25–53. [Google Scholar] [CrossRef] - Borsboom, D.; Mellenbergh, G.J. True scores, latent variables and constructs: A comment on Schmidt and Hunter. Intelligence
**2002**, 30, 505–514. [Google Scholar] [CrossRef] - Schwarz, W. The ex-Wald distribution as a descriptive model of response times. Behav. Res. Methods Instrum. Comput.
**2001**, 33, 457–469. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Schwarz, W. On the Convolution of inverse Gaussian and exponential Random Variables. Commun. Stat. Theory Methods
**2002**, 31, 2113–2121. [Google Scholar] [CrossRef] - Miller, R.; Scherbaum, S.; Heck, D.W.; Goschke, T.; Enge, S. On the Relation Between the (Censored) Shifted Wald and the Wiener Distribution as Measurement Models for Choice Response Times. Appl. Psychol. Meas.
**2018**, 42, 116–135. [Google Scholar] [CrossRef] [PubMed] - Keats, J.A.; Lord, F.M. A theoretical distribution for mental test scores. Psychometrika
**1962**, 27, 59–72. [Google Scholar] [CrossRef] - Wilcox, R.R. Estimating true score in the compound binomial error model. Psychometrika
**1978**, 43, 245–258. [Google Scholar] [CrossRef] - Matzke, D.; Wagenmakers, E.J. Psychological interpretation of the ex-Gaussian and shifted Wald parameters: A diffusion model analysis. Psychon. Bull. Rev.
**2009**, 16, 798–817. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Farrell, S.; Lewandowsky, S. Computational Modeling of Cognition and Behavior; Cambridge University Press: Cambridge, UK, 2018. [Google Scholar]
- Heathcote, A.; Brown, S.; Wagenmakers, E. An Introduction to Good Practices in Cognitive Modeling. In An Introduction to Model-Based Cognitive Neuroscience; Forstmann, B., Wagenmakers, E., Eds.; Springer: New York, NY, USA, 2015. [Google Scholar]
- Oberauer, K.; Lin, H.Y. An interference model of visual working memory. Psychol. Rev.
**2017**, 124, 21–59. [Google Scholar] [CrossRef] [PubMed] - Zhang, W.; Luck, S.J. Discrete fixed-resolution representations in visual working memory. Nature
**2008**, 453, 233. [Google Scholar] [CrossRef] [PubMed] - Banks, W.P. Signal detection theory and human memory. Psychol. Bull.
**1970**, 74, 81–99. [Google Scholar] [CrossRef] - Oberauer, K.; Lewandowsky, S.; Farrell, S.; Jarrold, C.; Greaves, M. Modeling working memory: An interference model of complex span. Psychon. Bull. Rev.
**2012**, 19, 779–819. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Bröder, A.; Schütz, J. Recognition ROCs are curvilinear—Or are they? On premature arguments against the two-high-threshold model of recognition. J. Exp. Psychol. Learn. Mem. Cognit.
**2009**, 35, 587–606. [Google Scholar] [CrossRef] [PubMed] - Ratcliff, R. A theory of memory retrieval. Psychol. Rev.
**1978**, 85, 59–108. [Google Scholar] [CrossRef] - Oberauer, K.; Lewandowsky, S. Modeling working memory: A computational implementation of the Time-Based Resource-Sharing theory. Psychon. Bull. Rev.
**2011**, 18, 10–45. [Google Scholar] [CrossRef] [PubMed] - Carpenter, P.A.; Just, M.A.; Shell, P. What one intelligence test measures: A theoretical account of the processing in the Raven Progressive Matrices Test. Psychol. Rev.
**1990**, 97, 404–431. [Google Scholar] [CrossRef] [PubMed] - Schmiedek, F.; Oberauer, K.; Wilhelm, O.; Süß, H.M.; Wittmann, W.W. Individual differences in components of reaction time distributions and their relations to working memory and intelligence. J. Exp. Psychol. Gen.
**2007**, 136, 414–429. [Google Scholar] [CrossRef] [PubMed] - Ratcliff, R.; Schmiedek, F.; McKoon, G. A diffusion model explanation of the worst performance rule for reaction time and IQ. Intelligence
**2008**, 36, 10–17. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Schmitz, F.; Wilhelm, O. Modeling Mental Speed: Decomposing Response Time Distributions in Elementary Cognitive Tasks and Correlations with Working Memory Capacity and Fluid Intelligence. J. Intell.
**2016**, 4, 13. [Google Scholar] [CrossRef] - Ratcliff, R.; Tuerlinckx, F. Estimating parameters of the diffusion model: Approaches to dealing with contaminant reaction times and parameter variability. Psychon. Bull. Rev.
**2002**, 9, 438–481. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Van Ravenzwaaij, D.; Oberauer, K. How to use the diffusion model: Parameter recovery of three methods: EZ, fast-dm, and DMAT. J. Math. Psychol.
**2009**, 53, 463–473. [Google Scholar] [CrossRef] - Ratcliff, R.; McKoon, G. The diffusion decision model: Theory and data for two-choice decision tasks. Neural Comput.
**2008**, 20, 873–922. [Google Scholar] [CrossRef] [PubMed] - Voss, A.; Rothermund, K.; Voss, J. Interpreting the parameters of the diffusion model: An empirical validation. Mem. Cognit.
**2004**, 32, 1206–1220. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lerche, V.; Voss, A. Experimental validation of the diffusion model based on a slow response time paradigm. Psychol. Res.
**2017**. [Google Scholar] [CrossRef] [PubMed] - Lerche, V.; Voss, A. Retest reliability of the parameters of the Ratcliff diffusion model. Psychol. Res.
**2017**, 81, 629–652. [Google Scholar] [CrossRef] [PubMed] - Schubert, A.L.; Frischkorn, G.T.; Hagemann, D.; Voss, A. Trait Characteristics of Diffusion Model Parameters. J. Intell.
**2016**, 4, 7. [Google Scholar] [CrossRef] - Steyer, R.; Schmitt, M.; Eid, M. Latent state–trait theory and research in personality and individual differences. Eur. J. Personal.
**1999**, 13, 389–408. [Google Scholar] [CrossRef] - Longstreth, L.E. Jensen’s reaction-time investigations of intelligence: A critique. Intelligence
**1984**, 8, 139–160. [Google Scholar] [CrossRef] - Ratcliff, R.; Thapar, A.; McKoon, G. Individual differences, aging, and IQ in two-choice tasks. Cognit. Psychol.
**2010**, 60, 127–157. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ratcliff, R.; Thapar, A.; McKoon, G. Effects of aging and IQ on item and associative memory. J. Exp. Psychol.
**2011**, 140, 464–487. [Google Scholar] [CrossRef] [PubMed] - Schulz-Zhecheva, Y.; Voelkle, M.C.; Beauducel, A.; Biscaldi, M.; Klein, C. Predicting Fluid Intelligence by Components of Reaction Time Distributions from Simple Choice Reaction Time Tasks. J. Intell.
**2016**, 4, 8. [Google Scholar] [CrossRef] - Wagenmakers, E.J.; Van Der Maas, H.L.J.; Grasman, R.P.P.P. An EZ-diffusion model for response time and accuracy. Psychon. Bull. Rev.
**2007**, 14, 3–22. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Wagenmakers, E.J.; van der Maas, H.L.J.; Dolan, C.V.; Grasman, R.P.P.P. EZ does it! Extensions of the EZ-diffusion model. Psychon. Bull. Rev.
**2008**, 15, 1229–1235. [Google Scholar] [CrossRef] [PubMed] - Voss, A.; Voss, J. Fast-dm: A free program for efficient diffusion model analysis. Behav. Res. Methods
**2007**, 39, 767–775. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Brown, S.D.; Heathcote, A. The simplest complete model of choice response time: Linear ballistic accumulation. Cognit. Psychol.
**2008**, 57, 153–178. [Google Scholar] [CrossRef] [PubMed] - Usher, M.; McClelland, J.L. The time course of perceptual choice: The leaky, competing accumulator model. Psychol. Rev.
**2001**, 108, 550–592. [Google Scholar] [CrossRef] [PubMed] - Barrouillet, P.; Bernardin, S.; Camos, V. Time Constraints and Resource Sharing in Adults’ Working Memory Spans. J. Exp. Psychol. Gen.
**2004**, 133, 83–100. [Google Scholar] [CrossRef] [PubMed] - Barrouillet, P.; Bernardin, S.; Portrat, S.; Vergauwe, E.; Camos, V. Time and cognitive load in working memory. J. Exp. Psychol. Learn. Mem. Cognit.
**2007**, 33, 570–585. [Google Scholar] [CrossRef] [PubMed] - Vergauwe, E.; Barrouillet, P.; Camos, V. Visual and spatial working memory are not that dissociated after all: A time-based resource-sharing account. J. Exp. Psychol. Learn. Mem. Cognit.
**2009**, 35, 1012–1028. [Google Scholar] [CrossRef] [PubMed] - Vergauwe, E.; Camos, V.; Barrouillet, P. The impact of storage on processing: How is information maintained in working memory? J. Exp. Psychol. Learn. Mem. Cognit.
**2014**, 40, 1072–1095. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Barrouillet, P.; Portrat, S.; Camos, V. On the law relating processing to storage in working memory. Psychol. Rev.
**2011**, 118, 175–192. [Google Scholar] [CrossRef] [PubMed] - Gauvrit, N.; Mathy, F. Mathematical transcription of the ‘time–based resource sharing’ theory of working memory. Br. J. Math. Stat. Psychol.
**2018**, 71, 146–166. [Google Scholar] [CrossRef] [PubMed] - Colom, R.; Rebollo, I.; Palacios, A.; Juan-Espinosa, M.; Kyllonen, P.C. Working memory is (almost) perfectly predicted by g. Intelligence
**2004**, 32, 277–296. [Google Scholar] [CrossRef] - Gignac, G.E. Working memory and fluid intelligence are both identical to g? Reanalyses and critical evaluation. Psychol. Sci.
**2007**, 49, 187–207. [Google Scholar] - Oberauer, K.; Farrell, S.; Jarrold, C.; Lewandowsky, S. What limits working memory capacity? Psychol. Bull.
**2016**, 142, 758–799. [Google Scholar] [CrossRef] [PubMed] - Oberauer, K.; Lewandowsky, S. Simple Measurement Models for Complex Working-Memory Tasks. Available online: https://osf.io/vkhmu/ (accessed on 17 July 2018).
- White, C.N.; Ratcliff, R.; Starns, J.J. Diffusion models of the flanker task: Discrete versus gradual attentional selection. Cognit. Psychol.
**2011**, 63, 210–238. [Google Scholar] [CrossRef] [PubMed] [Green Version] - White, C.N.; Servant, M.; Logan, G.D. Testing the validity of conflict drift-diffusion models for use in estimating cognitive processes: A parameter-recovery study. Psychon. Bull. Rev.
**2018**, 25, 286–301. [Google Scholar] [CrossRef] [PubMed] - White, C.N.; Curl, R. A Spotlight Diffusion Model Analysis of the Attentional Networks Task. 2017. Available online: https://osf.io/h9b8v/ (accessed on 17 July 2018).
- Huebner, R.; Steinhauser, M.; Lehle, C. A dual-stage two-phase model of selective attention. Psychol. Rev.
**2010**, 117, 759–784. [Google Scholar] [CrossRef] [PubMed] - Huebner, R.; Tobel, L. Does attentional selectivity in the flanker task improve discretely or gradually? Front. Psychol.
**2012**, 3, 434. [Google Scholar] - Grange, J.A. Flankr: An R package implementing computational models of attentional selectivity. Behav. Res. Methods
**2016**, 48, 528–541. [Google Scholar] [CrossRef] [PubMed] - Rogers, R.D.; Monsell, S. Costs of a predictible switch between simple cognitive tasks. J. Exp. Psychol. Gen.
**1995**, 124, 207–231. [Google Scholar] [CrossRef] - Schmitz, F.; Voss, A. Decomposing task-switching costs with the diffusion model. J. Exp. Psychol. Hum. Percept. Perform.
**2012**, 38, 222–250. [Google Scholar] [CrossRef] [PubMed] - Schmitz, F.; Voss, A. Components of task switching: A closer look at task switching and cue switching. Acta Psychol.
**2014**, 151, 184–196. [Google Scholar] [CrossRef] [PubMed] - Miller, J.; Ulrich, R. Mental chronometry and individual differences: Modeling reliabilities and correlations of reaction time means and effect sizes. Psychon. Bull. Rev.
**2013**, 20, 819–858. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lerche, V.; Voss, A.; Nagler, M. How many trials are required for parameter estimation in diffusion modeling? A comparison of different optimization criteria. Behav. Res. Methods
**2017**, 49, 513–537. [Google Scholar] [CrossRef] [PubMed] - Eid, M. A multitrait-multimethod model with minimal assumptions. Psychometrika
**2000**, 65, 241–261. [Google Scholar] [CrossRef] - Van Ravenzwaaij, D.; Donkin, C.; Vandekerckhove, J. The EZ diffusion model provides a powerful test of simple empirical effects. Psychon. Bull. Rev.
**2017**, 24, 547–556. [Google Scholar] [CrossRef] [PubMed] - Akaike, H. Information theory and an extension of the maximum likelihood principle. In Proceedings of the 2nd International Symposium on Information Theory, Tsahkadsor, Armenia, 2–8 September 1971; Petrov, B., Csáki, F., Eds.; Akadémiai Kiadó: Budapest, Hungary, 1973. [Google Scholar]
- Schwarz, G. Estimating the Dimension of a Model. Ann. Stat.
**1978**, 6, 461–464. [Google Scholar] [CrossRef] - Schubert, A.L.; Hagemann, D.; Voss, A.; Bergmann, K. Evaluating the model fit of diffusion models with the root mean square error of approximation. J. Math. Psychol.
**2017**, 77, 29–45. [Google Scholar] [CrossRef] - Clauset, A.; Shalizi, C.R.; Newman, M.E.J. Power-Law Distributions in Empirical Data. SIAM Rev.
**2009**, 51, 661–703. [Google Scholar] [CrossRef] [Green Version] - Voss, A.; Nagler, M.; Lerche, V. Diffusion Models in Experimental Psychology. Exp. Psychol.
**2013**, 60, 385–402. [Google Scholar] [CrossRef] [PubMed] - Jackson, D.L.; Gillaspy, J.A.J.; Purc-Stephenson, R. Reporting practices in confirmatory factor analysis: An overview and some recommendations. Psychol. Methods
**2009**, 14, 6–23. [Google Scholar] [CrossRef] [PubMed] - D’Agostino, R.B. Graphical analyses. In Goodness-of-Fit Techniques; D’Agostino, R.B., Stephens, M.A., Eds.; Marcel Dekker: New York, NY, USA, 1986; pp. 7–62. [Google Scholar]
- Skrondal, A.; Laake, P. Regression among factor scores. Psychometrika
**2001**, 66, 563–575. [Google Scholar] [CrossRef] - Frischkorn, G.T.; Schubert, A.L.; Neubauer, A.B.; Hagemann, D. The Worst Performance Rule as Moderation: New Methods for Worst Performance Analysis. J. Intell.
**2016**, 4, 9. [Google Scholar] [CrossRef] - Lee, M.D. How cognitive modeling can benefit from hierarchical Bayesian models. J. Math. Psychol.
**2011**, 55, 1–7. [Google Scholar] [CrossRef] - Lee, M.D.; Wagenmakers, E.J. Bayesian Cognitive Modeling: A Practical Course; Cambridge University Press: Cambridge, UK, 2013. [Google Scholar]
- Kruschke, J.K.; Liddell, T.M. The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective. Psychon. Bull. Rev.
**2017**, 25, 178–206. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Vandekerckhove, J.; Tuerlinckx, F.; Lee, M.D. Hierarchical diffusion models for two-choice response times. Psychol. Methods
**2011**, 16, 44–62. [Google Scholar] [CrossRef] [PubMed] - Hamaker, E.L.; Dolan, C.V.; Molenaar, P.C.M. Statistical Modeling of the Individual: Rationale and Application of Multivariate Stationary Time Series Analysis. Multivar. Behav. Res.
**2005**, 40, 207–233. [Google Scholar] [CrossRef] [PubMed] - Heck, D.W.; Arnold, N.R.; Arnold, D. TreeBUGS: An R Package for Hierarchical Multinomial-Processing-Tree Modeling. Behav. Res. Methods
**2017**, 50, 264–284. [Google Scholar] [CrossRef] [PubMed] - Bürkner, P.C. brms: An R Package for Bayesian Multilevel Models Using Stan. J. Stat. Softw.
**2017**, 80, 1–28. [Google Scholar] [CrossRef] - Nunez, M.D.; Gosai, A.; Vandekerckhove, J.; Srinivasan, R. The latency of a visual evoked potential tracks the onset of decision making. bioRxiv
**2018**. [Google Scholar] [CrossRef] - Kelly, S.P.; O’Connell, R.G. Internal and External Influences on the Rate of Sensory Evidence Accumulation in the Human Brain. J. Neurosci.
**2013**, 33, 19434–19441. [Google Scholar] [CrossRef] [PubMed] [Green Version] - O’Connell, R.G.; Dockree, P.M.; Kelly, S.P. A supramodal accumulation-to-bound signal that determines perceptual decisions in humans. Nat. Neurosci.
**2012**, 15, 1729–1735. [Google Scholar] [CrossRef] [PubMed] - Box, G.E.P. Science and Statistics. J. Am. Stat. Assoc.
**1976**, 71, 791–799. [Google Scholar] [CrossRef]

1. | Oberauer and Lewandowsky [79] are working on an alternative measurement model that is more closely connected to interference models of working memory [42,45]. For a preprint, see: osf.io/vkhmu. |

2. | These two references focus on Bayesian hierarchical modeling. While Bayesian parameter estimation might have additional advantages over frequentist estimation approaches [104], the benefits of hierarchical modeling apply to both Bayesian and frequentist methods. |

3. | Typically a Gaussian distribution with a mean and standard deviation is assumed. |

**Figure 1.**Graphical illustration of the drift-diffusion model. The decision process starts at the starting point z, and information is accumulated until the boundary a is reached. The systematic part of the accumulation process, the drift rate v, is illustrated with the black arrow. The non-decision time ${t}_{0}$ is not included in this figure.

**Figure 2.**Visualization of the time-based resource sharing (TBRS) theory as implemented in the TBRS2 model by Gauvrit and Mathy [75]. At the top, the current task is displayed. A colored box represents a to- be-encoded memory item, a black box represents a distractor task, and a white box represents free time. Below, the focus of attention is shown. During free time, participants engage in refreshing of the already encoded memory item; during distractor tasks or encoding of other items, the already encoded memory items decay over time.

**Figure 3.**Illustration of the Shrinking Spotlight model for selective attention. The attentional focus narrows to the central arrow over time (

**left part**). This results in a stronger weight of the critical information (i.e., the central stimulus) in the drift-rate of an associated diffusion process (

**right part**).

**Figure 4.**Flowchart illustrating the different planning and decision steps when using cognitive models in intelligence research.

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Frischkorn, G.T.; Schubert, A.-L.
Cognitive Models in Intelligence Research: Advantages and Recommendations for Their Application. *J. Intell.* **2018**, *6*, 34.
https://doi.org/10.3390/jintelligence6030034

**AMA Style**

Frischkorn GT, Schubert A-L.
Cognitive Models in Intelligence Research: Advantages and Recommendations for Their Application. *Journal of Intelligence*. 2018; 6(3):34.
https://doi.org/10.3390/jintelligence6030034

**Chicago/Turabian Style**

Frischkorn, Gidon T., and Anna-Lena Schubert.
2018. "Cognitive Models in Intelligence Research: Advantages and Recommendations for Their Application" *Journal of Intelligence* 6, no. 3: 34.
https://doi.org/10.3390/jintelligence6030034