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Extensions of Multivariate Dynamical Systems to Simultaneously Explain Neural and Behavioral Data

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Abstract

To examine how the brain produces behavior, new statistical methods have linked neurophysiological measures directly to mechanisms of cognitive models, modeling both modalities simultaneously. However, current simultaneous modeling efforts are largely based on either correlational methods or on functions that map one stream of data to the other. Such frameworks are limited in their ability to infer causality between brain activity and behavior, typically ignore important temporal dynamics of neural measures, or ignore large- and small-scale functional networks necessary for completing cognitive tasks. In this article, we investigate one causal framework for modeling brain dynamics as a potential alternative for explaining how behavior can be viewed as an emergent property of brain dynamics. Our proposed framework can be considered an extension of multivariate dynamical systems (MDS; Ryali et al. Neuroimage, 54(2), 807–823, 2011), as it is constructed in a way such that the temporal dynamics and brain functional connectivities are explicitly contained in the model structures. To test the potential usefulness of the MDS framework, we formulate a concrete model within it, demonstrate that it generates reasonable predictions about both behavioral and fMRI data, and conduct a parameter recovery study. Specifically, we develop a generative model of perceptual decision-making in a visual motion-direction discrimination task. Two simulation studies under different experimental protocols illustrate that the MDS model can capture key characteristics of both behavioral and neural measures that typically occur in experimental data. We also examine whether or not such a complex system can be inferred from experimental data by evaluating whether current algorithms for fitting models to data can recover sensible parameter estimates. Our parameter recovery study suggests that the MDS parameters can be recovered using likelihood-free estimation techniques. Together, these results suggest that our MDS-based framework shows great promise for developing fully integrative models of brain-behavior relationships.

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References

  • Albright, T. D. (1984). Direction and orientation selectivity of neurons in visual area MT of the macaque. Journal of Neurophysiology, 52(6), 1106–1130.

    PubMed  Google Scholar 

  • Anderson, J. R. (2007). How can the human mind occur in the physical universe?. New York: Oxford University Press.

    Google Scholar 

  • Andersen, R. A., Brotchie, P. R., Mazzoni, P. (1992). Evidence for the lateral intraparietal area as the parietal eye field. Current Opinion in Neurobiology, 2(6), 840–846.

    PubMed  Google Scholar 

  • Anderson, J. R., Byrne, D., Fincham, J. M., Gunn, P. (2008). Role of prefrontal and parietal cortices in associative learning. Cerebral Cortex, 18, 904–914.

    PubMed  Google Scholar 

  • Ashby, F. G., Ennis, J. M., Spiering, B. J. (2007). A neurobiological theory of automaticity in perceptual categorization. Psychological Review, 114(3), 632.

    PubMed  Google Scholar 

  • Ball, K., & Sekuler, R. (1982). A specific and enduring improvement in visual motion discrimination. Science, 218(4573), 697–698.

    PubMed  Google Scholar 

  • Bamber, D., & Van Santen, J. P. (2000). How to assess a model’s testability and identifiability. Journal of Mathematical Psychology, 44(1), 20–40.

    PubMed  Google Scholar 

  • Beaumont, M. A. (2010). Approximate Bayesian computation in evolution and ecology. Annual Review of Ecology, Evolution, and Systematics, 41, 379–406.

    Google Scholar 

  • Birn, R. M., Cox, R. W., Bandettini, P. A. (2002). Detection versus estimation in event-related fMRI: choosing the optimal stimulus timing. Neuroimage, 15(1), 252–264.

    PubMed  Google Scholar 

  • Bogacz, R., Wagenmakers, E. J., Forstmann, B. U., Nieuwenhuis, S. (2010). The neural basis of the speed-accuracy tradeoff. Trends in Neuroscience, 33, 10–16.

    Google Scholar 

  • Borst, J. P., & Anderson, J. R. (2013). Using model-based functional MRI to locate working memory updates and declarative memory retrievals in the fronto-parietal network. Proceedings of the National Academy of Sciences of the United States, 110, 1628–1633.

    Google Scholar 

  • Borst, J. P., Taatgen, N. A., Stocco, A., Van Rijn, H. (2010a). The neural correlates of problem states: testing fMRI predictions of a computational model of multitasking. PLoS ONE, 5, e12966.

    PubMed  PubMed Central  Google Scholar 

  • Borst, J. P., Taatgen, N. A., Van Rijn, H. (2010b). The problem state: a cognitive bottleneck in multitasking. Journal of Experimental Psychology: Learning, Memory, & Cognition, 36, 363–382.

    Google Scholar 

  • Boucher, L., Palmeri, T. J., Logan, G. D., Schall, J. D. (2007). Inhibitory control in mind and brain: an interactive race model of countermanding saccades. Psychological Review, 114(2), 376.

    PubMed  Google Scholar 

  • Britten, K. H., Shadlen, M. N., Newsome, W. T., Movshon, J. A. (1992). The analysis of visual motion: a comparison of neuronal and psychophysical performance. The Journal of Neuroscience, 12(12), 4745–4765.

    PubMed  PubMed Central  Google Scholar 

  • Britten, K. H., Newsome, W. T., Shadlen, M. N., Celebrini, S., Movshon, J. A. (1996). A relationship between behavioral choice and the visual responses of neurons in macaque MT. Visual Neuroscience, 13(1), 87–100.

    PubMed  Google Scholar 

  • Brown, S., & Heathcote, A. (2005). A ballistic model of choice response time. Psychological Review, 112, 117–128.

    PubMed  Google Scholar 

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

    PubMed  Google Scholar 

  • Brown, J. W., Hanes, D. P., Schall, J. D., Stuphorn, V. (2008). Relation of frontal eye field activity to saccade initiation during a countermanding task. Experimental Brain Research, 190(2), 135.

    PubMed  PubMed Central  Google Scholar 

  • Buxton, R. B., Wong, E. C., Frank, L. R. (1998). Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magnetic Resonance in Medicine, 39(6), 855–864.

    PubMed  Google Scholar 

  • Carpenter, R. (1999). Visual selection: neurons that make up their minds. Current Biology, 9(16), R595–R598.

    PubMed  Google Scholar 

  • Carpenter, R. H., & Williams, M. (1995). Neural computation of log likelihood in control of saccadic eye movements. Nature, 377(6544), 59.

    PubMed  Google Scholar 

  • Carpenter, R., Reddi, B., Anderson, A. (2009). A simple two-stage model predicts response time distributions. The Journal of Physiology, 587(16), 4051–4062.

    PubMed  PubMed Central  Google Scholar 

  • Cassey, P. J., Gaut, G., Steyvers, M., Brown, S. D. (2016). A generative joint model for spike trains and saccades during perceptual decision-making. Psychonomic Bulletin & Review, 23(6), 1757–1778.

    Google Scholar 

  • Celebrini, S., & Newsome, W. T. (1995). Microstimulation of extrastriate area MST influences performance on a direction discrimination task. Journal of Neurophysiology, 73(2), 437–448.

    PubMed  Google Scholar 

  • Churchland, A. K., Kiani, R., Shadlen, M. N. (2008). Decision-making with multiple alternatives. Nature Neuroscience, 11(6), 693.

    PubMed  PubMed Central  Google Scholar 

  • Colby, C. L., & Goldberg, M. E. (1999). Space and attention in parietal cortex. Annual Review of Neuroscience, 22(1), 319–349.

    PubMed  Google Scholar 

  • Croner, L. J., & Albright, T. D. (1999). Segmentation by color influences responses of motion-sensitive neurons in the cortical middle temporal visual area. Journal of Neuroscience, 19(10), 3935–3951.

    PubMed  Google Scholar 

  • Daunizeau, J., Friston, K. J., Kiebel, S. J. (2009). Variational bayesian identification and prediction of stochastic nonlinear dynamic causal models. Physica D: Nonlinear Phenomena, 238(21), 2089–2118.

    Google Scholar 

  • Daunizeau, J., Adam, V., Rigoux, L. (2014). VBA: a probabilistic treatment of nonlinear models for neurobiological and behavioural data. PLoS Computational Biology, 10(1), e1003441.

    PubMed  PubMed Central  Google Scholar 

  • David, O., Kiebel, S. J., Harrison, L. M., Mattout, J., Kilner, J. M., Friston, K. J. (2006). Dynamic causal modeling of evoked responses in EEG and MEG. NeuroImage, 30(4), 1255–1272.

    PubMed  Google Scholar 

  • de Hollander, G., Forstmann, B. U., Brown, S. D. (2016). Different ways of linking behavioral and neural data via computational cognitive models. Cognitive Neuroscience and Neuroimaging, 1, 101–109.

    Google Scholar 

  • Ding, L., & Gold, J. I. (2013). The basal ganglia’s contributions to perceptual decision making. Neuron, 79 (4), 640–649.

    PubMed  PubMed Central  Google Scholar 

  • Dorris, M. C., Pare, M., Munoz, D. P. (1997). Neuronal activity in monkey superior colliculus related to the initiation of saccadic eye movements. Journal of Neuroscience, 17(21), 8566–8579.

    PubMed  Google Scholar 

  • Forstmann, B. U., & Wagenmakers, E. -J. (2015). An introduction to model-based cognitive neuroscience. New York: Springer.

    Google Scholar 

  • Forstmann, B. U., Dutilh, G., Brown, S., Neumann, J., von Cramon, D. Y., Ridderinkhof, K. R., Wagenmakers, E. -J. (2008). Striatum and pre-SMA facilitate decision-making under time pressure. Proceedings of the National Academy of Sciences, 105(45), 17538–17542.

    Google Scholar 

  • Forstmann, B. U., Anwander, A., Schäfer, A., Neumann, J., Brown, S., Wagenmakers, E. -J., Bogacz, R., Turner, R. (2010). Cortico-striatal connections predict control over speed and accuracy in perceptual decision making. Proceedings of the National Academy of Sciences, 107(36), 15916–15920.

    Google Scholar 

  • Frigo, M., & Johnson, S. G. (2005). The design and implementation of FFTW3. Proceedings of the IEEE, 93(2), 216–231. special issue on “Program Generation, Optimization, and Platform Adaptation”.

    Google Scholar 

  • Friston, K. (2009). Causal modelling and brain connectivity in functional magnetic resonance imaging. PLoS Biology, 7(2), e1000033.

    PubMed Central  Google Scholar 

  • Friston, K. J., Mechelli, A., Turner, R., Price, C. J. (2000). Nonlinear responses in fMRI: the Balloon model, Volterra kernels, and other hemodynamics. NeuroImage, 12(4), 466–477.

    PubMed  Google Scholar 

  • Friston, K., Harisson, L., Penny, W. (2003). Dynamic causal modeling. NeuroImage, 19, 1273–1302.

    PubMed  Google Scholar 

  • Friston, K., Preller, K. H., Mathys, C., Cagnan, H., Heinzle, J., Razi, A., Zeidman, P. (2017). Dynamic causal modelling revisited. NeuroImage.

  • Galdo, M., Bahg, G., Turner, B. M. (2019). Variational bayesian methods for cognitive science, in press at Psychological Methods.

  • Georgiev, D., Rocchi, L., Tocco, P., Speekenbrink, M., Rothwell, J. C., Jahanshahi, M. (2016). Continuous theta burst stimulation over the dorsolateral prefrontal cortex and the Pre-SMA alter drift rate and response thresholds respectively during perceptual decision-making. Brain stimulation, 9(4), 601–608.

    PubMed  Google Scholar 

  • Gold, J. I., & Shadlen, M. N. (2001). Neural computations that underlie decisions about sensory stimuli. Trends in Cognitive Sciences, 5(1), 10–16.

    PubMed  Google Scholar 

  • Gold, J. I., & Shadlen, M. N. (2002). Banburismus and the brain: decoding the relationship between sensory stimuli, decisions, and reward. Neuron, 36(2), 299–308.

    PubMed  Google Scholar 

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

    PubMed  Google Scholar 

  • Graybiel, A. M. (1995). Building action repertoires: memory and learning functions of the basal ganglia. Current Opinion in Neurobiology, 5(6), 733–741.

    PubMed  Google Scholar 

  • Hikosaka, O., Takikawa, Y., Kawagoe, R. (2000a). Role of the basal ganglia in the control of purposive saccadic eye movements. Physiological Reviews, 80(3), 953–978.

    PubMed  Google Scholar 

  • Hikosaka, O., Takikawa, Y., Kawagoe, R. (2000b). Role of the basal ganglia in the control of purposive saccadic eye movements. Physiological Reviews, 80(3), 953–978.

    PubMed  Google Scholar 

  • Hikosaka, O., Nakamura, K., Nakahara, H. (2006). Basal ganglia orient eyes to reward. Journal of Neurophysiology, 95(2), 567–584.

    PubMed  Google Scholar 

  • Ho, T. C., Brown, S., Serences, J. T. (2009). Domain general mechanisms of perceptual decision making in human cortex. Journal of Neuroscience, 29(27), 8675–8687.

    PubMed  Google Scholar 

  • Holmes, W. R. (2015). A practical guide to the probability density approximation (PDA) with improved implementation and error characterization. Journal of Mathematical Psychology, 68, 13–24.

    Google Scholar 

  • Houk, J. C., Davis, J. L., Beiser, D.G. (1995). Models of information processing in the basal ganglia. Cambridge: MIT press.

    Google Scholar 

  • Kamitani, Y., & Tong, F. (2005). Decoding the visual and subjective contents of the human brain. Nature Neuroscience, 8(5), 679.

    PubMed  PubMed Central  Google Scholar 

  • Kamitani, Y., & Tong, F. (2006). Decoding seen and attended motion directions from activity in the human visual cortex. Current Biology, 16(11), 1096–1102.

    PubMed  Google Scholar 

  • Kiebel, S. J., Garrido, M. I., Moran, R. J., Friston, K. J. (2008). Dynamic causal modelling for EEG and MEG. Cognitive Neurodynamics, 2(2), 121.

    PubMed  PubMed Central  Google Scholar 

  • Kim, J. N., & Shadlen, M. N. (1999). Neural correlates of a decision in the dorsolateral prefrontal cortex of the macaque. Nature Neuroscience, 2, 176–185.

    PubMed  Google Scholar 

  • Korhonen, O., Saarimäki, H., Glerean, E., Sams, M., Saramäki, J. (2017). Consistency of regions of interest as nodes of fMRI functional brain networks. Network Neuroscience, 1(3), 254–274.

    PubMed  PubMed Central  Google Scholar 

  • Kragel, J. E., Morton, N. W., Polyn, S. M. (2015). Neural activity in the medial temporal lobe reveals the fidelity of mental time travel. Journal of Neuroscience, 35(7), 2914–2926.

    PubMed  Google Scholar 

  • Liu, T. T., Frank, L. R., Wong, E. C., Buxton, R. B. (2001). Detection power, estimation efficiency, and predictability in event-related fmri. Neuroimage, 13(4), 759–773.

    PubMed  Google Scholar 

  • Lo, C. -C., & Wang, X. -J. (2006). Cortico–basal ganglia circuit mechanism for a decision threshold in reaction time tasks. Nature Neuroscience, 9(7), 956.

    PubMed  Google Scholar 

  • Mandeville, J. B., Marota, J. J., Ayata, C., Zaharchuk, G., Moskowitz, M. A., Rosen, B. R., Weisskoff, R. M. (1999). Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. Journal of Cerebral Blood Flow & Metabolism, 19(6), 679–689.

    Google Scholar 

  • Mansfield, E. L., Karayanidis, F., Jamadar, S., Heathcote, A., Forstmann, B. U. (2011). Adjustments of response threshold during task switching: a model-based functional magnetic resonance imaging study. J Neurosci, 31(41), 14688–92.

    PubMed  PubMed Central  Google Scholar 

  • Marreiros, A. C., Kiebel, S. J., Friston, K. J. (2008). Dynamic causal modelling for fMRI: a two-state model. Neuroimage, 39(1), 269–278.

    PubMed  Google Scholar 

  • Maunsell, J. H., & Van Essen, D. C. (1983). Functional properties of neurons in middle temporal visual area of the macaque monkey. I. Selectivity for stimulus direction, speed, and orientation. Journal of Neurophysiology, 49(5), 1127–1147.

    PubMed  Google Scholar 

  • McClelland, J. L. (1993). Toward a theory of information processing in graded, random, interactive networks. In Meyer, D. E., & Kornblum, S. (Eds.) Attention and performance XIV:Synergies in experimental psychology, artificial intelligence and cognitive neuroscience (pp. 655–688). Cambridge: MIT Press.

  • Miletić, S., Turner, B. M., Forstmann, B. U., van Maanen, L. (2017). Parameter recovery for the leaky competing accumulator model. Journal of Mathematical Psychology, 76, 25–50.

    Google Scholar 

  • Molloy, M. F., Galdo, M., Bahg, G., Liu, Q., Turner, B. M. (2019). What?s in a response time?: On the importance of response time measures in constraining models of context effects. Decision, 6(2), 171.

    Google Scholar 

  • Niwa, M., & Ditterich, J. (2008). Perceptual decisions between multiple directions of visual motion. Journal of Neuroscience, 28(17), 4435–4445.

    PubMed  Google Scholar 

  • Norman, K. A., Polyn, S. M., Detre, G. J., Haxby, J. V. (2006). Beyond mind-reading: multi-voxel pattern analysis of fMRI data. Trends in Cognitive Sciences, 10(9), 424–430.

    PubMed  Google Scholar 

  • O’Reilly, R.C. (2006). Biologically based computational models of cortical cognition. Science, 314, 91–94.

    PubMed  Google Scholar 

  • Palestro, J. J., Bahg, G., Sederberg, P. B., Lu, Z.-L., Steyvers, M., Turner, B. M. (2018a). A tutorial on joint models of neural and behavioral measures of cognition. Journal of Mathematical Psychology, 84, 20–48.

    Google Scholar 

  • Palestro, J. J., Sederberg, P. B., Osth, A. F., Van Zandt, T., Turner, B. M. (2018b). Likelihood-free methods for cognitive science. Berlin: Springer.

    Google Scholar 

  • Penny, W., Ghahramani, Z., Friston, K. (2005). Bilinear dynamical systems. Philosophical Transactions of the Royal Society B: Biological Sciences, 360(1457), 983–993.

    Google Scholar 

  • Pirrone, A., Stafford, T., Marshall, J. A. (2014). When natural selection should optimize speed-accuracy trade-offs. Frontiers in Neuroscience, 8, 73.

    PubMed  PubMed Central  Google Scholar 

  • Polyn, S. M., Natu, V. S., Cohen, J. D., Norman, K. A. (2005). Category-specific cortical activity precedes retrieval during memory search. Science, 310(5756), 1963–1966.

    PubMed  Google Scholar 

  • Purcell, B., Heitz, R., Cohen, J., Schall, J., Logan, G., Palmeri, T. (2010). Neurally-constrained modeling of perceptual decision making. Psychological Review, 117, 1113–1143.

    PubMed  PubMed Central  Google Scholar 

  • Ratcliff, R., & Rouder, J. N. (1998). Modeling response times for two-choice decisions. Psychological Science, 9, 347–356.

    Google Scholar 

  • Ratcliff, R., & Smith, P. L. (2004). A comparison of sequential sampling models for two-choice reaction time. Psychological Review, 111, 333–367.

    PubMed  PubMed Central  Google Scholar 

  • Ratcliff, R., Cherian, A., Segraves, M. (2003). A comparison of macaque behavior and superior colliculus neuronal activity to predictions from models of simple two-choice decisions. Journal of Neurophysiology, 90, 1392–1407.

    PubMed  Google Scholar 

  • Ratcliff, R., Hasegawa, Y. T., Hasegawa, Y. P., Smith, P. L., Segraves, M. A. (2007). Dual diffusion model for single-cell recording data from the superior colliculus in a brightness-discrimination task. Journal of Neurophysiology, 97, 1756–1774.

    PubMed  Google Scholar 

  • Ratcliff, R., Voskuilen, C., Teodorescu, A. (2018). Modeling 2-alternative forced-choice tasks: accounting for both magnitude and difference effects. Cognitive Psychology, 103, 1–22.

    PubMed  PubMed Central  Google Scholar 

  • Redgrave, P., Prescott, T. J., Gurney, K. N. (1999). The basal ganglia: a vertebrate solution to the selection problem? Neuroscience, 89(4), 1009–1023.

    PubMed  Google Scholar 

  • Rigoux, L., & Daunizeau, J. (2015). Dynamic causal modelling of brain–behaviour relationships. Neuroimage, 117, 202–221.

    PubMed  Google Scholar 

  • Roe, R. M., Busemeyer, J. R., Townsend, J. T. (2001). Multialternative decision field theory: a dynamic connectionist model of decision making. Psychological Review, 108, 370–392.

    PubMed  Google Scholar 

  • Roitman, J., & Shadlen, M. (2002). Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task. Journal of Neuroscience, 22(21), 9475–9489.

    PubMed  Google Scholar 

  • Ryali, S., Chen, T., Supekar, K., Tu, T., Kochalka, J., Cai, W., Menon, V. (2016). Multivariate dynamical systems-based estimation of causal brain interactions in fMRI: group-level validation using benchmark data, neurophysiological models and human connectome project data. Journal of Neuroscience Methods, 268, 142–153.

    PubMed  PubMed Central  Google Scholar 

  • Ryali, S., Supekar, K., Chen, T., Menon, V. (2011). Multivariate dynamical systems models for estimating causal interactions in fmri. Neuroimage, 54(2), 807–823.

    PubMed  Google Scholar 

  • Ryyppö, E., Glerean, E., Brattico, E., Saramäki, J., Korhonen, O. (2018). Regions of interest as nodes of dynamic functional brain networks. Network Neuroscience, 2(4), 513–535.

    PubMed  PubMed Central  Google Scholar 

  • Salzman, C. D., & Newsome, W. T. (1994). Neural mechanisms for forming a perceptual decision. Science, 264(5156), 231–237.

    PubMed  Google Scholar 

  • Schall, J. D., Morel, A., King, D. J., Bullier, J. (1995). Topography of visual cortex connections with frontal eye field in macaque: convergence and segregation of processing streams. Journal of Neuroscience, 15(6), 4464–4487.

    PubMed  Google Scholar 

  • Schall, J. D. (2003). Neural correlates of decision processes: neural and mental chronometry. Current Opinion in Neurobiology, 12, 182–186.

    Google Scholar 

  • Serences, J. T., & Boynton, G. M. (2007a). Feature-based attentional modulations in the absence of direct visual stimulation. Neuron, 55(2), 301–312.

    PubMed  Google Scholar 

  • Serences, J. T., & Boynton, G. M. (2007b). The representation of behavioral choice for motion in human visual cortex. Journal of Neuroscience, 27(47), 12893–12899.

    PubMed  Google Scholar 

  • Shadlen, M. N., & Newsome, W. T. (2001). Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey. Journal of Neurophysiology, 86, 1916–1936.

    PubMed  Google Scholar 

  • Shadlen, M. N., Britten, K. H., Newsome, W. T., Movshon, J. A. (1996). A computational analysis of the relationship between neuronal and behavioral responses to visual motion. Journal of Neuroscience, 16(4), 1486–1510.

    PubMed  Google Scholar 

  • Silverman, B. W. (1986). Density estimation for statistics and data analysis. London: Chapman & Hall.

    Google Scholar 

  • Simoncelli, E. P., & Heeger, D. J. (1998). A model of neuronal responses in visual area MT. Vision Research, 38(5), 743–761.

    PubMed  Google Scholar 

  • Smith, P. L. (1995). Psychophysically principled models of visual simple reaction time. Psychological Review, 102(3), 567–593.

    Google Scholar 

  • Smith, P. L., & Vickers, D. (1988). The accumulator model of two-choice discrimination. Journal of Mathematical Psychology, 32, 135–168.

    Google Scholar 

  • Smith, J. F., Pillai, A., Chen, K., Horwitz, B. (2010). Identification and validation of effective connectivity networks in functional magnetic resonance imaging using switching linear dynamic systems. Neuroimage, 52(3), 1027–1040.

    PubMed  Google Scholar 

  • Stephan, K. E., Weiskopf, N., Drysdale, P. M., Robinson, P. A., Friston, K. J. (2007). Comparing hemodynamic models with dcm. Neuroimage, 38(3), 387–401.

    PubMed  PubMed Central  Google Scholar 

  • Stephan, K. E., Kasper, L., Harrison, L. M., Daunizeau, J., den Ouden, H. E., Breakspear, M., Friston, K. J. (2008). Nonlinear dynamic causal models for fMRI. Neuroimage, 42(2), 649–662.

    PubMed  PubMed Central  Google Scholar 

  • Stephan, K. E., Penny, W. D., Moran, R. J., den Ouden, H. E., Daunizeau, J., Friston, K. J. (2010). Ten simple rules for dynamic causal modeling. Neuroimage, 49(4), 3099–3109.

    PubMed  PubMed Central  Google Scholar 

  • Stewart, T. C., Choo, X., Eliasmith, C. (2010). Symbolic reasoning in spiking neurons: a model of the cortex/basal ganglia/thalamus loop. In Catrambone, R., & Ohlsson, S. (Eds.) Proceedings of the 32nd Annual Conference of the Cognitive Science Society (pp. 1100–1105). Austin: Cognitive Science Society.

  • Teller, D. Y. (1984). Linking propositions. Vision Research, 24, 1233–1246.

    PubMed  Google Scholar 

  • Teodorescu, A. R., & Usher, M. (2013). Disentangling decision models – from independence to competition. Psychological Review, 120, 1–38.

    PubMed  Google Scholar 

  • Teodorescu, A. R., Moran, R., Usher, M. (2016). Absolutely relative or relatively absolute: violations of value invariance in human decision making. Psychonomic Bulletin & Review, 23(1), 22–38.

    Google Scholar 

  • ter Braak, C. J. F. (2006). A Markov Chain Monte Carlo version of the genetic algorithm Differential Evolution: easy Bayesian computing for real parameter spaces. Statistics and Computing, 16, 239–249.

    Google Scholar 

  • Toni, T., Welch, D., Strelkowa, N., Ipsen, A., Stumpf, M. P. (2009). Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. Journal of the Royal Society Interface, 6, 187–202.

    Google Scholar 

  • Turner, B. M. (2019). Toward a common representational framework for adaptation. In Press at Psychological Review.

  • Turner, B. M., & Sederberg, P. B. (2012). Approximate Bayesian computation with Differential Evolution. Journal of Mathematical Psychology, 56, 375–385.

    Google Scholar 

  • Turner, B. M., & Sederberg, P. B. (2014). A generalized, likelihood-free method for parameter estimation. Psychonomic Bulletin and Review, 21, 227–250.

    PubMed  Google Scholar 

  • Turner, B. M., & Van Zandt, T. (2014). Hierarchical approximate Bayesian computation. Psychometrika, 79, 185–209.

    PubMed  Google Scholar 

  • Turner, B. M., & Van Zandt, T. (2018). Approximating bayesian inference through model simulation. Trends in Cognitive Sciences.

  • Turner, B. M., Dennis, S., Van Zandt, T. (2013a). Bayesian analysis of memory models. Psychological Review, 120, 667–678.

    PubMed  PubMed Central  Google Scholar 

  • Turner, B. M., Forstmann, B. U., Wagenmakers, E.-J., Brown, S. D., Sederberg, P. B., Steyvers, M. (2013b). A bayesian framework for simultaneously modeling neural and behavioral data. NeuroImage, 72, 193–206.

    PubMed  PubMed Central  Google Scholar 

  • Turner, B. M., Sederberg, P. B., Brown, S., Steyvers, M. (2013c). A method for efficiently sampling from distributions with correlated dimensions. Psychological Methods, 18, 368–384.

    PubMed  PubMed Central  Google Scholar 

  • Turner, B. M., Sederberg, P. B., McClelland, J. L. (2015a). Bayesian analysis of simulation-based models. In Press.

  • Turner, B. M., Van Maanen, L., Forstmann, B. U. (2015b). Informing cognitive abstractions with neurophysiology: the neural drift diffusion model. Psychological Review, 122, 312–336.

    PubMed  Google Scholar 

  • Turner, B. M., Rodriguez, C. A., Norcia, T., Steyvers, M., McClure, S. M. (2016). Why more is better: a method for simultaneously modeling EEG, fMRI, and behavior. NeuroImage, 128, 96–115.

    PubMed  Google Scholar 

  • Turner, B., Wang, T., Merkle, E. (2017a). Factor analysis linking functions for simultaneously modeling neural and behavioral data. NeuroImage, 153, 28–48.

    PubMed  Google Scholar 

  • Turner, B. M., Forstmann, B. U., Love, B. U., Palmeri, T. J., Van Maanen, L. (2017b). Approaches to analysis in model-based cognitive neuroscience. Journal of Mathematical Psychology, 76, 65–79.

    PubMed  Google Scholar 

  • Turner, B. M., Rodriguez, C. A., Liu, Q., Molloy, M. F., Hoogendijk, M., McClure, S. M. (2018). On the neural and mechanistic bases of self-control. Cerebral Cortex, 29(2), 732–750.

    Google Scholar 

  • Turner, B. M., Forstmann, B. U., Steyvers, M., et al. (2019a). Joint models of neural and behavioral data. Berlin: Springer.

    Google Scholar 

  • Turner, B. M., Palestro, J. J., Miletić, S., Forstmann, B. U. (2019b). Advances in techniques for imposing reciprocity in brain-behavior relations. Neuroscience & Biobehavioral Reviews, 102, 327– 336.

    Google Scholar 

  • Tversky, A., & Simonson, I. (1993). Context-dependent preferences. Management Science, 39(10), 1179–1189.

    Google Scholar 

  • Usher, M., & McClelland, J. L. (2001). The time course of perceptual choice: the leaky competing accumulator model. Psychological Review, 108, 550–592.

    PubMed  Google Scholar 

  • van Maanen, L., Brown, S. D., Eichele, T., Wagenmakers, E. -J., Ho, T., Serences, J. (2011). Neural correlates of trial-to-trial fluctuations in response caution. Journal of Neuroscience, 31, 17488–17495.

    PubMed  Google Scholar 

  • van Ravenzwaaij, D., Provost, A., Brown, S. D. (2017). A confirmatory approach for integrating neural and behavioral data into a single model. Journal of Mathematical Psychology, 76, 131–141.

    Google Scholar 

  • Vanduffel, W., Fize, D., Mandeville, J. B., Nelissen, K., Van Hecke, P., Rosen, B. R., Tootell, R. B., Orban, G. A. (2001). Visual motion processing investigated using contrast agent-enhanced fMRI in awake behaving monkeys. Neuron, 32(4), 565–577.

    PubMed  Google Scholar 

  • Wagenmakers, E.-J., Farrell, S., Ratcliff, R. (2004). Estimation and interpretation of 1/fα noise in human cognition. Psychonomic Bulletin and Review, 11, 579–615.

    PubMed  Google Scholar 

  • Wickens, J. (1997). Basal ganglia: structure and computations. Network: Computation in Neural Systems, 8 (4), R77–R109.

    Google Scholar 

  • Zeki, S. M. (1974). Functional organization of a visual area in the posterior bank of the superior temporal sulcus of the rhesus monkey. The Journal of Physiology, 236(3), 549–573.

    PubMed  PubMed Central  Google Scholar 

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Funding

This research was supported by NSF-SMA 1533500 and a CAREER award from the National Science Foundation (BMT).

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Authors and Affiliations

  1. Department of Psychology, The Ohio State University, Columbus, OH, USA

    Qingfang Liu, Alexander A. Petrov & Brandon M. Turner

  2. Division of Arts and Sciences, NYU Shanghai, Shanghai, China

    Zhong-Lin Lu

  3. Center for Neural Science and Department of Psychology, New York University, New York, NY, USA

    Zhong-Lin Lu

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  1. Qingfang Liu
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  2. Alexander A. Petrov
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  3. Zhong-Lin Lu
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  4. Brandon M. Turner
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Correspondence to Brandon M. Turner.

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The simulation code is available at https://github.com/MbCN-lab/MDS-Simulation.

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Liu, Q., Petrov, A.A., Lu, ZL. et al. Extensions of Multivariate Dynamical Systems to Simultaneously Explain Neural and Behavioral Data. Comput Brain Behav 3, 430–457 (2020). https://doi.org/10.1007/s42113-020-00072-0

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