References

Bates, Douglas, Martin Mächler, Ben Bolker, and Steve Walker. 2015. “Fitting Linear Mixed-Effects Models Using lme4.” Journal of Statistical Software 67 (1): 1–48. https://doi.org/10.18637/jss.v067.i01.

Box, George EP. 1976. “Science and Statistics.” Journal of the American Statistical Association 71 (356): 791–99. https://doi.org/10.1080/01621459.1976.10480949.

Braak, Cajo ter. 2006. “A Markov Chain Monte Carlo Version of the Genetic Algorithm Differential Evolution: Easy Bayesian Computing for Real Parameter Spaces.” Statistics and Computing 16: 239–49. https://doi.org/10.1007/s11222-006-8769-1.

Cohen, Andrew L, Adam N Sanborn, and Richard M Shiffrin. 2008. “Model Evaluation Using Grouped or Individual Data.” Psychonomic Bulletin & Review 15 (4): 692–712. https://doi.org/10.3758/PBR.15.4.692.

Cox, D. R., and H. D. Miller. 1965. The Theory of Stochastic Processes. CRC Press.

Crossman, Edward RFW. 1959. “A Theory of the Acquisition of Speed-Skill.” Ergonomics 2 (2): 153–66. https://doi.org/10.1080/00140135908930419.

De Jong, Ritske, Chia-Chin Liang, and Erick Lauber. 1994. “Conditional and Unconditional Automaticity: A Dual-Process Model of Effects of Spatial Stimulus-Response Correspondence.” Journal of Experimental Psychology: Human Perception and Performance 20 (4): 731–50. https://doi.org/10.1037/0096-1523.20.4.731.

Diederich, Adele, and Jerome R Busemeyer. 2003. “Simple Matrix Methods for Analyzing Diffusion Models of Choice Probability, Choice Response Time, and Simple Response Time.” Journal of Mathematical Psychology 47 (3): 304–22. https://doi.org/10.1016/S0022-2496(03)00003-8.

Diederich, Adele, and K. Mallahi-Karai. 2018. “Stochastic Methods for Modeling Decision-Making.” In New Handbook of Mathematical Psychology, edited by W. H. Batchelder, H. Colonius, and E. N. Dzhafarov, 1–70. Cambridge University Press.

Diederich, Adele, and Peter Oswald. 2014. “Sequential Sampling Model for Multiattribute Choice Alternatives with Random Attention Time and Processing Order.” Frontiers in Human Neuroscience 8: 697. https://doi.org/10.3389/fnhum.2014.00697.

Ditterich, Jochen. 2006. “Evidence for Time-Variant Decision Making.” European Journal of Neuroscience 24 (12): 3628–41. https://doi.org/10.1111/j.1460-9568.2006.05221.x.

Donders, Franciscus Cornelis. 1868. “Over de Snelheid van Psychische Processen.” Onderzoekingen Gedaan in Het Physiologisch Laboratorium Der Utrechtsche Hoogeschool (1968–1869) 2: 92–120.

Ellinghaus, Ruben, Roman Liepelt, Ian G Mackenzie, and Victor Mittelstädt. 2024. “Perceptual Target Discriminability Modulates the Simon Effect Beyond the Fading of Distractor-Based Activation: Insights from Delta Plots and Diffusion Model Analyses.” Journal of Experimental Psychology: Human Perception and Performance 50 (8): 842–58. https://doi.org/10.1037/xhp0001211.

Eriksen, Barbara A, and Charles W Eriksen. 1974. “Effects of Noise Letters Upon the Identification of a Target Letter in a Nonsearch Task.” Perception & Psychophysics 16 (1): 143–49. https://doi.org/10.3758/BF03203267.

Eriksen, Charles W, and James D St. James. 1986. “Visual Attention Within and Around the Field of Focal Attention: A Zoom Lens Model.” Perception & Psychophysics 40 (4): 225–40. https://doi.org/10.3758/BF03211502.

Evans, Nathan J, and Mathieu Servant. 2020. “A Comparison of Conflict Diffusion Models in the Flanker Task Through Pseudolikelihood Bayes Factors.” Psychological Review 127 (1): 114–35. https://doi.org/10.1037/rev0000165.

———. 2022. “A Model-Based Approach to Disentangling Facilitation and Interference Effects in Conflict Tasks.” Psychological Review 129 (5): 1183–1209. https://doi.org/10.1037/rev0000357.

Farrell, Simon, and Stephan Lewandowsky. 2018. Computational Modeling of Cognition and Behavior. Cambridge University Press. https://doi.org/10.1017/CBO9781316272503.

Hawkins, Guy E, Birte U Forstmann, Eric-Jan Wagenmakers, Roger Ratcliff, and Scott D Brown. 2015. “Revisiting the Evidence for Collapsing Boundaries and Urgency Signals in Perceptual Decision-Making.” Journal of Neuroscience 35 (6): 2476–84. https://doi.org/10.1523/JNEUROSCI.2410-14.2015.

Heath, Richard A. 1992. “A General Nonstationary Diffusion Model for Two-Choice Decision-Making.” Mathematical Social Sciences 23: 283–309. https://doi.org/https://doi.org/10.1016/0165-4896(92)90044-6.

Heathcote, Andrew, Scott Brown, and Douglas JK Mewhort. 2000. “The Power Law Repealed: The Case for an Exponential Law of Practice.” Psychonomic Bulletin & Review 7 (2): 185–207. https://doi.org/10.3758/BF03212979.

Heathcote, Andrew, Yi-Shin Lin, Angus Reynolds, Luke Strickland, Matthew Gretton, and Dora Matzke. 2019. “Dynamic Models of Choice.” Behavior Research Methods 51: 961–85. https://doi.org/10.3758/s13428-018-1067-y.

Held, Leonhard. 2008. Methoden Der Statistischen Inferenz. Likelihood Und Bayes. Spektrum Akademischer Verlag.

Held, Leonhard, and Daniel Sabanés Bové. 2008. Applied Statistical Inference. Likelihood and Bayes. Spektrum Akademischer Verlag.

Henze, Norbert. 2024. Asymptotic Stochastics: An Introduction with a View Towards Statistics. Springer.

Hommel, Bernhard. 1994. “Spontaneous Decay of Response-Code Activation.” Psychological Research 56 (4): 261–68. https://doi.org/10.1007/BF00419656.

Hoyle, Fred. 1974. “The Work of Nicolaus Copernicus.” Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 336 (1604): 105–14. https://doi.org/10.1098/rspa.1974.0009.

Hübner, Ronald, and Lisa Töbel. 2019. “Conflict Resolution in the Eriksen Flanker Task: Similarities and Differences to the Simon Task.” PloS One 14 (3): e0214203. https://doi.org/https://doi.org/10.1371/journal.pone.0214203.

Janczyk, Markus, Ian Grant Mackenzie, and Valentin Koob. 2025. “A Comment on the Revised Diffusion Model for Conflict Tasks (RDMC).” Psychonomic Bulletin & Review 32: 690–704. https://doi.org/10.3758/s13423-024-02574-5.

Kelber, Paul, Victor Mittelstädt, and Rolf Ulrich. 2025. “Interplay of Aging and Practice in Conflict Processing: A Big-Data Diffusion-Model Analysis.” Psychology and Aging 40 (1): 66–85. https://doi.org/10.1037/pag0000848.

Koob, Valentin, Ian Mackenzie, Rolf Ulrich, Hartmut Leuthold, and Markus Janczyk. 2023. “The Role of Task-Relevant and Task-Irrelevant Information in Congruency Sequence Effects: Applying the Diffusion Model for Conflict Tasks.” Cognitive Psychology 140: 101528. https://doi.org/10.1016/j.cogpsych.2022.101528.

Koob, Valentin, Carlotta Sauerbier, Hannes Schröter, Rolf Ulrich, and Markus Janczyk. 2024. “Separating Facilitation and Interference in Backward Crosstalk.” Journal of Experimental Psychology: Human Perception and Performance 50 (3): 295–312. https://doi.org/10.1037/rev0000326.

Kornblum, Sylvan, Thierry Hasbroucq, and Allen Osman. 1990. “Dimensional Overlap: Cognitive Basis for Stimulus-Response Compatibility–A Model and Taxonomy.” Psychological Review 97 (2): 253–70.

Lee, Ping-Shien, and David K Sewell. 2024. “A Revised Diffusion Model for Conflict Tasks.” Psychonomic Bulletin & Review 1: 1–31. https://doi.org/10.3758/s13423-023-02288-0.

Lerche, Veronika, and Andreas Voss. 2016. “Model Complexity in Diffusion Modeling: Benefits of Making the Model More Parsimonious.” Frontiers in Psychology 7: 1324. https://doi.org/10.3389/fpsyg.2016.01324.

———. 2018. “Speed–Accuracy Manipulations and Diffusion Modeling: Lack of Discriminant Validity of the Manipulation or of the Parameter Estimates?” Behavior Research Methods 50: 2568–85. https://doi.org/10.3758/s13428-018-1034-7.

Lewandowsky, Stephan, and Simon Farrell. 2013. Computational Modeling of Cognition: Principles and Practice. Sage Publications Inc. https://doi.org/10.4135/9781483349428.

Liesefeld, Heinrich R, and Markus Janczyk. 2019. “Combining Speed and Accuracy to Control for Speed-Accuracy Trade-Offs (?).” Behavior Research Methods 51: 40–60. https://doi.org/10.3758/s13428-018-1076-x.

———. 2023. “Same Same but Different: Subtle but Consequential Differences Between Two Measures to Linearly Integrate Speed and Accuracy (LISAS Vs. BIS).” Behavior Research Methods 55 (3): 1175–92. https://doi.org/10.3758/s13428-022-01843-2.

Luce, R Duncan. 1986. Response Times: Their Role in Inferring Elementary Mental Organization. 8. Oxford University Press.

———. 1995. “Four Tensions Concerning Mathematical Modeling in Psychology.” Annual Review of Psychology 46: 1. https://doi.org/10.1146/annurev.ps.46.020195.000245 .

MacCallum, Robert C. 2003. “Working with Imperfect Models.” Multivariate Behavioral Research 38 (1): 113–39. https://doi.org/10.1207/S15327906MBR3801_5.

Mackenzie, Ian G, and Carolin Dudschig. 2021. “DMCfun: An R Package for Fitting Diffusion Model of Conflict (DMC) to Reaction Time and Error Rate Data.” Methods in Psychology 5: 100074. https://doi.org/10.1016/j.metip.2021.100074.

Mahani, Mohammad-Ali Nikouei, Karin Maria Bausenhart, Majid Nili Ahmadabadi, and Rolf Ulrich. 2019. “Multimodal Simon Effect: A Multimodal Extension of the Diffusion Model for Conflict Tasks.” Frontiers in Human Neuroscience 12: 507. https://doi.org/10.3389/fnhum.2018.00507.

Meyer, David E, Allen M Osman, David E Irwin, and Steven Yantis. 1988. “Modern Mental Chronometry.” Biological Psychology 26 (1-3): 3–67. https://doi.org/10.1016/0301-0511(88)90013-0.

Mosteller, Frederick, Stephen E Fienberg, and Robert EK Rourke. 1983. Beginning Statistics with Data Analysis. Courier Corporation.

Nelder, J. A., and R. Mead. 1965. “A Simplex Method for Function Minimization.” The Computer Journal 7 (4): 308–13. https://doi.org/10.1093/comjnl/8.1.27.

Oberauer, Klaus, and S. Lewandowsky. 2019. “Addressing the Theory Crisis in Psychology.” Psychonomic Bulletin & Review 26: 1596–1618. https://doi.org/10.3758/s13423-019-01645-2.

Price, Kenneth, Rainer M Storn, and Jouni A Lampinen. 2006. Differential Evolution: A Practical Approach to Global Optimization. Springer Science & Business Media.

Ratcliff, Roger. 1978. “A Theory of Memory Retrieval.” Psychological Review 85 (2): 59–108. https://doi.org/10.1037/0033-295X.85.2.59.

———. 2013. “Parameter Variability and Distributional Assumptions in the Diffusion Model.” Psychological Review 120 (1): 281–92. https://doi.org/10.1037/a0030775.

Ratcliff, Roger, and Jeffrey N Rouder. 1998. “Modeling Response Times for Two-Choice Decisions.” Psychological Science 9 (5): 347–56.

Ratcliff, Roger, Philip L Smith, Scott D Brown, and Gail McKoon. 2016. “Diffusion Decision Model: Current Issues and History.” Trends in Cognitive Sciences 20 (4): 260–81. https://doi.org/10.1016/j.tics.2016.01.007.

Richter, Thomas, Rolf Ulrich, and Markus Janczyk. 2023. “Diffusion Models with Time-Dependent Parameters: An Analysis of Computational Effort and Accuracy of Different Numerical Methods.” Journal of Mathematical Psychology 114: 102756. https://doi.org/10.1016/j.jmp.2023.102756.

Ridderinkhof, K. R. 2002. “Activation and Suppression in Conflict Tasks: Empirical Clarification Through Distributional Analyses.” In Common Mechanisms in Perception and Action, Attention and Performance XIX, edited by Wolfgang Prinz and Bernhard Hommel, 494–519. Oxford University Press.

Roberts, Seth, and Harold Pashler. 2000. “How Persuasive Is a Good Fit? A Comment on Theory Testing.” Psychological Review 107 (2): 358–67. https://doi.org/10.1037/0033-295X.107.2.358.

Rosenbaum, David A, and Markus Janczyk. 2019. “Who Is or Was ERFW Crossman, the Champion of the Power Law of Learning and the Developer of an Influential Model of Aiming?” Psychonomic Bulletin & Review 26 (4): 1449–63. https://doi.org/10.3758/s13423-019-01583-z.

Schwarz, W. 2022. Random Walk and Diffusion Models: An Introduction for Life and Behavioral Scientists. Springer.

Servant, Mathieu, and Gordon D Logan. 2019. “Dynamics of Attentional Focusing in the Eriksen Flanker Task.” Attention, Perception, & Psychophysics 81: 2710–21. https://doi.org/10.3758/s13414-019-01796-3.

Shiffrin, Richard M, Michael D Lee, Woojae Kim, and Eric-Jan Wagenmakers. 2008. “A Survey of Model Evaluation Approaches with a Tutorial on Hierarchical Bayesian Methods.” Cognitive Science 32 (8): 1248–84. https://doi.org/10.1080/03640210802414826.

Simon, J Richard. 1969. “Reactions Toward the Source of Stimulation.” Journal of Experimental Psychology 81 (1): 174–76. https://doi.org/10.1037/h0027448.

Simon, J Richard, and AM Small Jr. 1969. “Processing Auditory Information: Interference from an Irrelevant Cue.” Journal of Applied Psychology 53 (5): 433–35. https://doi.org/10.1037/h0028034.

Smith, Parker, and Rolf Ulrich. 2024. “The Neutral Condition in Conflict Tasks: On the Violation of the Midpoint Assumption in Reaction Time Trends.” Quarterly Journal of Experimental Psychology 77 (5): 1023–43.

Smith, Philip L. 2000. “Stochastic Dynamic Models of Response Time and Accuracy: A Foundational Primer.” Journal of Mathematical Psychology 44: 408–63. https://doi.org/10.1006/jmps.1999.1260.

Speckman, Paul L, Jeffrey N Rouder, Richard D Morey, and Michael S Pratte. 2008. “Delta Plots and Coherent Distribution Ordering.” The American Statistician 62 (3): 262–66. https://doi.org/10.1198/000313008X333493.

Sternberg, Saul. 1969. “The Discovery of Processing Stages: Extensions of Donders’ Method.” Acta Psychologica 30: 276–315.

Stins, John F, JC Tinca Polderman, Dorret I Boomsma, and Eco JC de Geus. 2007. “Conditional Accuracy in Response Interference Tasks: Evidence from the Eriksen Flanker Task and the Spatial Conflict Task.” Advances in Cognitive Psychology 3 (3): 409–17. https://doi.org/10.2478/v10053-008-0005-4.

Storn, Rainer, and Kenneth Price. 1997. “Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces.” Journal of Global Optimization 11 (4): 341–59. https://doi.org/10.1023/A:1008202821328.

Stroop, J Ridley. 1935. “Studies of Interference in Serial Verbal Reactions.” Journal of Experimental Psychology 18 (6): 643–62. https://doi.org/10.1037/h0054651.

Teschl, Gerald, and Susanne Teschl. 2013. Mathematik für Informatiker: Band 1: Diskrete Mathematik und Lineare Algebra. Springer.

Turner, Brandon M, and Per B Sederberg. 2014. “A Generalized, Likelihood-Free Method for Posterior Estimation.” Psychonomic Bulletin & Review 21: 227–50. https://doi.org/10.3758/s13423-013-0530-0.

Turner, Brandon M, Per B Sederberg, Scott D Brown, and Mark Steyvers. 2013. “A Method for Efficiently Sampling from Distributions with Correlated Dimensions.” Psychological Methods 18 (3): 368–84. https://doi.org/10.1037/a0032222.

Turner, Brandon M, and Trisha Van Zandt. 2012. “A Tutorial on Approximate Bayesian Computation.” Journal of Mathematical Psychology 56 (2): 69–85. https://doi.org/10.1016/j.jmp.2012.02.005.

Ulrich, Rolf. 2009. “Uncovering Unobservable Cognitive Mechanisms: The Contribution of Mathematical Models.” In Neuroimaging of Human Memory: Linking Cognitive Processes to Neural Systems, edited by F. Rösler, C. Ranganath, B. Röder, and R. H. Kluwe, 25–41. Oxford University Press.

Ulrich, Rolf, Hannes Schröter, Hartmut Leuthold, and Teresa Birngruber. 2015. “Automatic and Controlled Stimulus Processing in Conflict Tasks: Superimposed Diffusion Processes and Delta Functions.” Cognitive Psychology 78: 148–74. https://doi.org/10.1016/j.cogpsych.2015.02.005.

———. 2016. “Corrigendum to Automatic and Controlled Stimulus Processing in Conflict Tasks: Superimposed Diffusion Processes and Delta Functions [Cogn. Psychol. 78 (2015) 148–174].” Cognitive Psychology 91: 150. https://doi.org/10.1016/j.cogpsych.2016.11.003.

Van Zandt, Trisha. 2000. “How to Fit a Response Time Distribution.” Psychonomic Bulletin & Review 7: 424–65. https://doi.org/10.3758/BF03214357.

Voskuilen, Chelsea, Roger Ratcliff, and Philip L. Smith. 2016. “Comparing fixed and collapsing boundary versions of the diffusion model.” Journal of Mathematical Psychology 73: 59–79. https://doi.org/10.1016/j.jmp.2016.04.008.

White, Corey N., Roger Ratcliff, and Jeffrey J. Starns. 2011. “Diffusion Models of the Flanker Task: Discrete Versus Gradual Attentional Selection.” Cognitive Psychology 63 (4): 210–38. https://doi.org/10.1016/j.cogpsych.2011.08.001.

White, Corey N., Mathieu Servant, and Gordon D. Logan. 2018. “Testing the Validity of Conflict Drift-Diffusion Models for Use in Estimating Cognitive Processes: A Parameter-Recovery Study.” Psychonomic Bulletin & Review 25 (1): 286–301. https://doi.org/10.3758/s13423-017-1271-2.

Wickelgren, Wayne A. 1977. “Speed-Accuracy Tradeoff and Information Processing Dynamics.” Acta Psychologica 41 (1): 67–85. https://doi.org/10.1016/0001-6918(77)90012-9.