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EZ-CDM: Fast, simple, robust, and accurate estimation of circular diffusion model parameters

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Abstract

The investigation of cognitive processes that form the basis of decision-making in paradigms involving continuous outcomes has gained the interest of modeling researchers who aim to develop a dynamic decision theory that accounts for both speed and accuracy. One of the most important of these continuous models is the circular diffusion model (CDM, Smith. Psychological Review, 123(4), 425. 2016), which posits a noisy accumulation process mathematically described as a stochastic two-dimensional Wiener process inside a disk. Despite the considerable benefits of this model, its mathematical intricacy has limited its utilization among scholars. Here, we propose a straightforward and user-friendly method for estimating the CDM parameters and fitting the model to continuous-scale data using simple formulas that can be readily computed and do not require theoretical knowledge of model fitting or extensive programming. Notwithstanding its simplicity, we demonstrate that the aforementioned method performs with a level of accuracy that is comparable to that of the maximum likelihood estimation method. Furthermore, a robust version of the method is presented, which maintains its simplicity while exhibiting a high degree of resistance to contaminant responses. Additionally, we show that the approach is capable of reliably measuring the key parameters of the CDM, even when these values are subject to across-trial variability. Finally, we demonstrate the practical application of the method on experimental data. Specifically, an illustrative example is presented wherein the method is employed along with estimating the probability of guessing. It is hoped that the straightforward methodology presented here will, on the one hand, help narrow the divide between theoretical constructs and empirical observations on continuous response tasks and, on the other hand, inspire cognitive psychology researchers to shift their laboratory investigations towards continuous response paradigms.

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Code Availability

The codes accompanied with a tutorial for using the simple and robust EZ-CDM, along with the mixed model with guess are available at https://github.com/HasanQD/EZ-CDM. Also, implementations for calculating the likelihood function with this method and the simulation of the data are available in https://github.com/HasanQD/CDM.

References

  • Banerjee, A., Dhillon, I. S., Ghosh, J., Sra, S., & Ridgeway, G. (2005). Clustering on the unit hypersphere using von Mises-Fisher distributions. Journal of Machine Learning Research 6(9)

  • Bays, P., Gorgoraptis, N., Wee, N., Marshall, L., & Husain, M. (2011). Temporal dynamics of encoding, storage, and reallocation of visual working memory. Journal of Vision, 11, 6.

    Article  PubMed  Google Scholar 

  • Bays, P. M., Catalao, R. F., & Husain, M. (2009). The precision of visual working memory is set by allocation of a shared resource. Journal of Vision, 9(10), 7.

    Article  Google Scholar 

  • Bishop, C. M. (2006). Pattern recognition and machine learning. Springer.

    Google Scholar 

  • Boehm, U., Annis, J., Frank, M. J., Hawkins, G. E., Heathcote, A., Kellen, D., Krypotos, A. M., Lerche, V., Logan, G. D., Palmeri, T. J., et al. (2018). Estimating across-trial variability parameters of the diffusion decision model: Expert advice and recommendations. Journal of Mathematical Psychology, 87, 46–75.

    Article  Google Scholar 

  • Bogacz, R., Brown, E., Moehlis, J., Holmes, P., & Cohen, J. D. (2006). The physics of optimal decision-making: A formal analysis of models of performance in two-alternative forced-choice tasks. Psychological Review, 113(4), 700–765.

    Article  PubMed  Google Scholar 

  • Borodin, A. N., & Salminen, P. (2002). Handbook of Brownian motion-facts and formulae, 2nd edn. Springer Science & Business Media

  • Brown, S., & Heathcote, A. (2005). A ballistic model of choice response time. Psychological Review, 112(1), 117.

    Article  PubMed  Google Scholar 

  • Brown, S. D., & Heathcote, A. (2008). The simplest complete model of choice response time: Linear ballistic accumulation. Cognitive Psychology, 57(3), 153–178.

    Article  PubMed  Google Scholar 

  • Casella, G., & Berger, R. L. (2001). Statistical inference. Cengage Learning.

    Google Scholar 

  • Dekking, F. M., Kraaikamp, C., Lopuhaä, H. P., & Meester, L. E. (2005). A Modern Introduction to Probability and Statistics: Understanding why and how, (vol. 488). Springer.

  • Drugowitsch, J., Moreno-Bote, R., Churchland, A. K., Shadlen, M. N., & Pouget, A. (2012). The cost of accumulating evidence in perceptual decision making. Journal of Neuroscience, 32(11), 3612–3628. https://doi.org/10.1523/JNEUROSCI.4010-11.2012

    Article  PubMed  Google Scholar 

  • Evans, N. J., & Brown, S. D. (2017). People adopt optimal policies in simple decision-making, after practice and guidance. Psychonomic Bulletin & Review, 24(2), 597–606.

    Article  Google Scholar 

  • Evans, N. J., Bennett, A. J., & Brown, S. D. (2018). Optimal or not; depends on the task. Psychonomic Bulletin & Review, 26, 1027–1034.

    Article  Google Scholar 

  • Evans, N. J., Hawkins, G. E., & Brown, S. D. (2020). The role of passing time in decision-making. Journal of Experimental Psychology: Learning, Memory, and Cognition, 46(2), 316.

    PubMed  Google Scholar 

  • Fan, J. E., & Turk-Brown, N. B. (2013). Internal attention to features in visual short-term memory guides object learning. Cognition, 129, 292–308.

    Article  PubMed  PubMed Central  Google Scholar 

  • Fontanesi, L., Gluth, S., Spektor, M. S., & Rieskamp, J. (2019). A reinforcement learning diffusion decision model for value-based decisions. Psychonomic Bulletin & Review, 26, 1099–1121.

    Article  Google Scholar 

  • Forstmann, B. U., Ratcliff, R., & Wagenmakers, E. J. (2016). Sequential sampling models in cognitive neuroscience: Advantages, applications, and extensions. Annual Review of Psychology, 67, 641–666.

    Article  PubMed  Google Scholar 

  • Fougnie, D., & Alvarez, G. A. (2011). Object features fail independently in visual working memory: Evidence for a probabilistic feature-store model. Journal of Vision, 11, 3.

    Article  PubMed  Google Scholar 

  • Fougnie, D., Suchow, J. W., & Alvarez, G. A. (2012). Variability in the quality of visual working memory. Nature Communications, 3, 1229.

    Article  PubMed  Google Scholar 

  • Gold, J. I., & Shadlen, M. N. (2007). The neural basis of decision-making. Annual Review of Neuroscience, 30, 535–574.

    Article  PubMed  Google Scholar 

  • Gomez, P., Ratcliff, R., & Perea, M. (2007). A model of the go/no-go task. Journal of Experimental Psychology: General, 136(3), 389.

    Article  PubMed  Google Scholar 

  • Green, M. L., & Pratte, M. S. (2022). Local motion pooling is continuous, global motion perception is discrete. Journal of Experimental Psychology: Human Perception and Performance, 48(1), 52.

    PubMed  Google Scholar 

  • Gunseli, E., van Moorselaar, D., Meeter, M., & Olivers, C. N. L. (2015). The reliability of retro-cues determine working memory representations. Psychonomic Bulletin & Review, 22, 1334–1341.

    Article  Google Scholar 

  • Harris, C. R., Millman, K. J., van der Walt, S. J., Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., Taylor, J., Berg, S., Smith, N. J., Kern, R., Picus, M., Hoyer, S., van Kerkwijk, M. H., Brett, M., Haldane, A., del Río, J. F., Wiebe, M., Peterson, P., ..., & Oliphant, T. E. (2020). Array programming with numpy. Nature, 585(7825), 357–362.

  • Hawkins, G. E., & Heathcote, A. (2021). Racing against the clock: Evidence-based versus time-based decisions. Psychological Review, 128(2), 222. https://doi.org/10.1037/rev0000259

    Article  PubMed  Google Scholar 

  • Hawkins, G. E., Forstmann, B. U., Wagenmakers, E. J., Ratcliff, R., & Brown, S. D. (2015). Revisiting the evidence for collapsing boundaries and urgency signals in perceptual decision-making. Journal of Neuroscience, 35(6), 2476–2484. https://doi.org/10.1523/JNEUROSCI.2410-14.2015

    Article  PubMed  Google Scholar 

  • Heath, R. A. (2000). The Ornstein-Uhlenbeck model for decision time in cognitive tasks: An example of control of nonlinear network dynamics. Psychological Research, 63(2), 183–191. https://doi.org/10.1007/PL00008177

    Article  PubMed  Google Scholar 

  • Huang-Pollock, C., Ratcliff, R., McKoon, G., Roule, A., Warner, T., Feldman, J., & Wise, S. (2020). A diffusion model analysis of sustained attention in children with attention deficit hyperactivity disorder. Neuropsychology, 34, 641–653. https://doi.org/10.1037/neu0000636

    Article  PubMed  PubMed Central  Google Scholar 

  • Kato, S., & Eguchi, S. (2016). Robust estimation of location and concentration parameters for the von Mises-Fisher distribution. Statistical Papers, 57(1), 205–234.

    Article  Google Scholar 

  • Kool, W., Conway, A. R. A., & Turk-Browne, N. B. (2014). Sequential dynamics in visual short-term memory. Attention, Perception, & Psychophysics, 76, 1885–1901.

    Article  Google Scholar 

  • Krajbich, I., Armel, C., & Rangel, A. (2010). Visual fixations and the computation and comparison of value in simple choice. Nature Neuroscience, 13(10), 1292–1298.

    Article  PubMed  Google Scholar 

  • Krajbich, I., Lu, D., Camerer, C., & Rangel, A. (2012). The attentional drift-diffusion model extends to simple purchasing decisions. Frontiers in Psychology, 3, 193.

    Article  PubMed  PubMed Central  Google Scholar 

  • Kvam, P. D. (2019). A geometric framework for modeling dynamic decisions among arbitrarily many alternatives. Journal of Mathematical Psychology, 91, 14–37.

    Article  Google Scholar 

  • Kvam, P. D. (2019). Modeling accuracy, response time, and bias in continuous orientation judgments. Journal of Experimental Psychology: Human Perception and Performance, 45(3), 301.

    PubMed  Google Scholar 

  • Kvam, P. D., & Turner, B. M. (2021). Reconciling similarity across models of continuous selections. Psychological Review.

  • Kvam, P. D., Marley, A., & Heathcote, A. (2021). A unified theory of discrete and continuous responding. Psychological Review. https://doi.org/10.1037/rev0000378

    Article  PubMed  Google Scholar 

  • Laming, D. R. J. (1968). Information theory of choice-reaction times. Academic Press.

    Google Scholar 

  • Lerche, V., & Voss, A. (2016). Model complexity in diffusion modeling: Benefits of making the model more parsimonious. Frontiers in Psychology, 1324

  • Lerche, V., & Voss, A. (2017). Retest reliability of the parameters of the ratcliff diffusion model. Psychological Research, 81, 629–652.

    Article  PubMed  Google Scholar 

  • Lerche, V., Voss, A., & Nagler, M. (2017). How many trials are required for parameter estimation in diffusion modeling? a comparison of different optimization criteria. Behavior Research Methods, 49, 513–537.

    Article  PubMed  Google Scholar 

  • Ma, W. J., Husain, M., & Bays, P. M. (2014). Changing concepts of working memory. Nature Neuroscience, 17, 347–356.

    Article  PubMed  PubMed Central  Google Scholar 

  • Manning, C., Hassall, C. D., Hunt, L. T., Norcia, A. M., Wagenmakers, E. J., Evans, N. J., & Scerif, G. (2022). Behavioural and neural indices of perceptual decision-making in autistic children during visual motion tasks. Scientific Reports, 12(1), 1–19. https://doi.org/10.1038/s41598-022-09885-4

    Article  Google Scholar 

  • Manning, C., Hassall, C. D., Hunt, L. T., Norcia, A. M., Wagenmakers, E. J., Margaret, Snowling G., & J adn Scerif, Evans NJ,. (2022). Visual motion and decision-making in dyslexia: Reduced accumulation of sensory evidence and related neural dynamics. Journal of Neuroscience, 42(1), 121–134. https://doi.org/10.1523/JNEUROSCI.1232-21.2021

  • Mardia, K. V., & Jupp, P. E. (1999). Directional statistics. Wiley Online Library

  • Marshall, L., & Bays, P. M. (2013). Obligatory encoding of task-irrelevant features depletes working memory resources. Journal of Vision, 13, 21.

    Article  PubMed  PubMed Central  Google Scholar 

  • Matzke, D., Dolan, C. V., Logan, G. D., Brown, S. D., & Wagenmakers, E. J. (2013). Bayesian parametric estimation of stop-signal reaction time distributions. Journal of Experimental Psychology General, 142(4), 1047.

    Article  PubMed  Google Scholar 

  • Matzke, D., Hughes, M., Badcock, J. C., Michie, P., & Heathcote, A. (2017). Failures of cognitive control or attention? the case of stop-signal deficits in Schizophrenia. Attention, Perception, & Psychophysics, 79, 1078–1086.

    Article  Google Scholar 

  • Matzke, D., Love, J., & Heathcote, A. (2017). A bayesian approach for estimating the probability of trigger failures in the stop-signal paradigm. Behavior Research Methods, 49, 267–281.

    Article  PubMed  Google Scholar 

  • Miletić, S., Boag, R. J., Trutti, A. C., Stevenson, N., Forstmann, B. U., & Heathcote, A. (2021). A new model of decision processing in instrumental learning tasks. Elife, 10, e63055. https://doi.org/10.7554/eLife.63055

    Article  PubMed  PubMed Central  Google Scholar 

  • mpmath development team, T. (2023). mpmath: A Python library for arbitrary-precision floating-point arithmetic (version 1.3.0). http://mpmath.org/

  • Nejati, V., Hadian-Rasanan, A. H., Rad, J. A., Alavi, M. M., Haghie, S., & Nitsche, M. A. (2022). Transcranial direct current stimulation (tDCS) alters the pattern of information processing in children with ADHD: Evidence from drift diffusion modeling. Neurophysiologie Clinique, 52, 17–21. https://doi.org/10.1016/j.neucli.2021.11.005

    Article  PubMed  Google Scholar 

  • Nelder, J. A., & Mead, R. (1965). A simplex method for function minimization. The Computer Journal, 7(4), 308–313.

    Article  Google Scholar 

  • Pearson, K. (1894). Contributions to the mathematical theory of evolution. Philosophical Transactions of the Royal Society of London A, 185, 71–110.

    Article  Google Scholar 

  • Pedersen, M. L., Frank, M. J., & Biele, G. (2017). The drift diffusion model as the choice rule in reinforcement learning. Psychonomic Bulletin & Review, 24, 1234–1251.

    Article  Google Scholar 

  • Ratcliff, R. (1978). A theory of memory retrieval. Psychological Review, 85(2), 59.

    Article  Google Scholar 

  • Ratcliff, R. (2008). The EZ diffusion method: Too EZ? Psychonomic Bulletin & Review, 15(6), 1218–1228.

    Article  Google Scholar 

  • Ratcliff, R. (2013). Parameter variability and distributional assumptions in the diffusion model. Psychological Review, 120(1), 281.

    Article  PubMed  Google Scholar 

  • Ratcliff, R. (2018). Decision making on spatially continuous scales. Psychological Review, 125(6), 888.

    Article  PubMed  PubMed Central  Google Scholar 

  • Ratcliff, R., & Childers, R. (2015). Individual differences and fitting methods for the two-choice diffusion model of decision making. Decision, 2(4), 237.

    Article  Google Scholar 

  • Ratcliff, R., & McKoon, G. (2020). Decision making in numeracy tasks with spatially continuous scales. Cognitive Psychology, 116, 101259.

    Article  PubMed  Google Scholar 

  • Ratcliff, R., & Smith, P. L. (2004). A comparison of sequential sampling models for two-choice reaction time. Psychological Review, 111(2), 333.

    Article  PubMed  PubMed Central  Google Scholar 

  • 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(3), 438–481.

    Article  Google Scholar 

  • Ratcliff, R., Smith, P. L., Brown, S. D., & McKoon, G. (2016). Diffusion decision model: Current issues and history. Trends in Cognitive Sciences, 20(4), 260–281.

    Article  PubMed  PubMed Central  Google Scholar 

  • Ratcliff, R., Huang-Pollock, C., & McKoon, G. (2018). Modeling individual differences in the go/no-go task with a diffusion model. Decision, 5(1), 42–62.

    Article  PubMed  Google Scholar 

  • Ross SM (2007) Introduction to probability models, 9th edn. Academic press

  • Sewell, D. K., Jach, H. K., Boag, R. J., & Heer, C. A. V. (2019). Combining error-driven models of associative learning with evidence accumulation models of decision-making. Psychonomic Bulletin & Review, 26, 868–893.

    Article  Google Scholar 

  • Sheskin, D. J. (2003). Handbook of parametric and nonparametric statistical procedures. Chapman and hall/CRC

  • Shinn, M., Lam, N. H., & Murray, J. D. (2020). A flexible framework for simulating and fitting generalized drift-diffusion models. ELife, 9, e56938. https://doi.org/10.7554/eLife.56938

    Article  PubMed  PubMed Central  Google Scholar 

  • Smith, P., Garrett, P., & Zhou, J. (2023). Obtaining stable predicted distributions of response times and decision outcomes for the circular diffusion model

  • Smith, P. L. (2016). Diffusion theory of decision making in continuous report. Psychological Review, 123(4), 425.

    Article  PubMed  Google Scholar 

  • Smith, P. L. (2019). Linking the diffusion model and general recognition theory: Circular diffusion with bivariate-normally distributed drift rates. Journal of Mathematical Psychology, 91, 145–158.

    Article  Google Scholar 

  • Smith, P. L., & Corbett, E. A. (2019). Speeded multielement decision-making as diffusion in a hypersphere: Theory and application to double-target detection. Psychonomic Bulletin & Review, 26(1), 127–162.

    Article  Google Scholar 

  • Smith, P. L., Saber, S., Corbett, E. A., & Lilburn, S. D. (2020). Modeling continuous outcome color decisions with the circular diffusion model: Metric and categorical properties. Psychological Review, 127(4), 562.

    Article  PubMed  Google Scholar 

  • Starns, J. J., & Ratcliff, R. (2012). Age-related differences in diffusion model boundary optimality with both trial-limited and time-limited tasks. Psychonomic Bulletin & Review, 19(1), 139–145.

    Article  Google Scholar 

  • Stigler, S. M. (2007). The epic story of maximum likelihood. Statistical Science, 598–620.

  • Stone, M. (1960). Models for choice-reaction time. Psychometrika, 25(3), 251–260. https://doi.org/10.1007/BF02289729

    Article  Google Scholar 

  • Storn, R., & Price, K. (1997). Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4), 341.

    Article  Google Scholar 

  • Swan, G., & Wyble, B. (2014). The binding pool: A model of shared neural resources for distinct items in visual working memory. Attention, Perception, & Psychophysics, 76, 2136–2157.

    Article  Google Scholar 

  • Tillman, G., Van Zandt, T., & Logan, G. D. (2020). Sequential sampling models without random between-trial variability: The racing diffusion model of speeded decision making. Psychonomic Bulletin & Review, 27(5), 911–936.

    Article  Google Scholar 

  • Unsworth, N., Fukuda, K., Awh, E., & Vogel, E. K. (2014). Working memory and fluid intelligence: Capacity, attention control, and secondary memory retrieval. Cognitive Psychology, 71, 1–26.

    Article  PubMed  PubMed Central  Google Scholar 

  • Usher, M., & McClelland, J. L. (2001). The time course of perceptual choice: The leaky, competing accumulator model. Psychological Review, 108(3), 550.

    Article  PubMed  Google Scholar 

  • van den Berg, R., Shin, H., Chou, W. C., George, R., & Ma, W. J. (2012). Variability in encoding precision accounts for visual short-term memory limitations. Proceedings of the National Academy of Sciences, 109, 8780–8785.

    Article  Google Scholar 

  • van den Berg, R., Awh, E., & Ma, W. J. (2014). Factorial comparison of working memory models. Psychological Review, 121, 124–149.

    Article  PubMed  PubMed Central  Google Scholar 

  • vanRossum, G. (1995) Python reference manual. Department of Computer Science [CS] (R 9525)

  • van Ravenzwaaij, D., & Oberauer, K. (2009). How to use the diffusion model: Parameter recovery of three methods: EZ, fast-dm, and DMAT. Journal of Mathematical Psychology, 53(6), 463–473.

    Article  Google Scholar 

  • van Ravenzwaaij, D., Donkin, C., & Vandekerckhove, J. (2017). The EZ diffusion model provides a powerful test of simple empirical effects. Psychonomic Bulletin & Review, 24(2), 547–556.

    Article  Google Scholar 

  • van Ravenzwaaij, D., Brown, S. D., Marley, A., & Heathcote, A. (2020). Accumulating advantages: A new conceptualization of rapid multiple choice. Psychological Review, 127(2), 186–215. https://doi.org/10.1037/rev0000166

  • Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S. J., Brett, M., Wilson, J., Millman, K. J., Mayorov, N., Nelson, A. R. J., Jones, E., Kern, R., Larson, E., Carey, C. J., Polat, I., Feng, Y., Moore, E. W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E. A., Harris, C. R., Archibald, A. M., Ribeiro, A. H., Pedregosa, F., van Mulbregt, P., SciPy 10 Contributors. (2020). Scipy 1.0: Fundamental algorithms for scientific computing in python. Nature Methods, 17(3), 261–272

  • Voss, A., Lerche, V., Mertens, U., & Voss, J. (2019). Sequential sampling models with variable boundaries and non-normal noise: A comparison of six models. Psychonomic Bulletin & Review, 26(3), 813–832. https://doi.org/10.3758/s13423-018-1560-4

    Article  Google Scholar 

  • Wagenmakers, E. J. (2009). Methodological and empirical developments for the Ratcliff diffusion model of response times and accuracy. European Journal of Cognitive Psychology, 21(5), 641–671.

    Article  Google Scholar 

  • Wagenmakers, E. J., Van Der Maas, H. L., & Grasman, R. P. (2007). An EZ-diffusion model for response time and accuracy. Psychonomic Bulletin & Review, 14(1), 3–22.

    Article  Google Scholar 

  • Wagenmakers, E. J., van der Maas, H. L. J., Dolan, C. V., & Grasman, R. P. P. P. (2008). Ez does it! extensions of the EZ-diffusion model. Psychonomic Bulletin & Review, 15(6), 1229–1235.

    Article  Google Scholar 

  • Weigard, A., & Huang-Pollock, C. (2017). The role of speed in ADHD-related working memory deficits: A time-based resource-sharing and diffusion model account. Clinical Psychological Science, 5, 195–211. https://doi.org/10.1177/2167702616668320

    Article  PubMed  Google Scholar 

  • Yap, M. J., Balota, D. A., Sibley, D. E., & Ratcliff, R. (2012). Individual differences in visual word recognition: Insights from the english lexicon project. Journal of Experimental Psychology: Human Perception and Performance, 38(1), 53.

    PubMed  Google Scholar 

  • Zhang, W., & Luck, S. J. (2008). Discrete fixed-resolution representations in visual working memory. Nature, 453(7192), 233–235.

    Article  PubMed  PubMed Central  Google Scholar 

  • Zhou, J., Osth, A. F., Lilburn, S. D., & Smith, P. L. (2021). A circular diffusion model of continuous-outcome source memory retrieval: Contrasting continuous and threshold accounts. Psychonomic Bulletin & Review, 28(4), 1112–1130.

    Article  Google Scholar 

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Acknowledgements

The authors express gratitude towards P.L. Smith and co-authors in Smith et al. (2020) for providing open-access data, which was utilized in this study. We also thank P.L. Smith for carefully reading the manuscript and providing his insightful remarks. Also, HQ thanks all friends at the CMPLab, with special recognition to Mehdi Ebrahimi Mehr, for their support.

Funding

JAR was supported by the IRAN Cognitive Sciences & Technologies Council (Grant No. 9311), and Iran National Science Foundation, INSF (Grant No. 99010447 and 4001703).

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  1. Institute for Cognitive and Brain Sciences, Shahid Beheshti University, Tehran, Iran

    Hasan Qarehdaghi & Jamal Amani Rad

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Correspondence to Jamal Amani Rad.

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The early idea of this work was presented as a talk at the 44th Annual Conference of the Cognitive Science Society (CogSci 2022) as well as the MathPsych/ICCM 2022 in July 2022 and published as a short paper in the CogSci Proceedings.

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Qarehdaghi, H., Rad, J.A. EZ-CDM: Fast, simple, robust, and accurate estimation of circular diffusion model parameters. Psychon Bull Rev (2024). https://doi.org/10.3758/s13423-024-02483-7

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