The Lognormal Race: A Cognitive-Process Model of Choice and Latency with Desirable Psychometric Properties

Psychometrika

Volumn 80, Issue 2, 2015, Pages 491-513

  Rouder, Jeffrey N ^a   Province, Jordan M ^a   Morey, Richard D ^b   Gomez, Pablo ^c   Heathcote, Andrew ^d  

^a UNIVERSITY OF MISSOURI   (United States)

^b UNIVERSITY OF GRONINGEN   (Netherlands)

^c DEPAUL UNIVERSITY   (United States)

^d UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

cognitive psychometrics; race models; response times models

Indexed keywords

BAYES THEOREM; DECISION MAKING; DECISION THEORY; HUMAN; MATHEMATICAL PHENOMENA; PHYSIOLOGY; PSYCHOMETRY; REACTION TIME; STATISTICAL MODEL;

BAYES THEOREM; CHOICE BEHAVIOR; DECISION THEORY; HUMANS; LINEAR MODELS; MATHEMATICAL CONCEPTS; PSYCHOMETRICS; REACTION TIME;

EID: 84930573580     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11336-013-9396-3     Document Type: Article

References (64)

1. Anderson, J.R., & Lebiere, C. (1998). The atomic component of thought. Mahwah: Lawrence Erlbaum Associates.
2. Audley, R.J., & Pike, A.R. (1965). Some alternative stochastic models of choice. British Journal of Mathematical and Statistical Psychology, 18, 207–225.
3. Bertelson, P. (1961). Sequential redundancy and speed in a serial two choice responding task. Quarterly Journal of Experimental Psychology, 13, 290–292.
4. Brown, S.D., & Heathcote, A. (2008). The simplest complete model of choice reaction time: linear ballistic accumulation. Cognitive Psychology, 57, 153–178.
5. Craigmile, P.F., Peruggia, M., & Van Zandt, T. (2010). Hierarchical Bayes models for response time. Psychometrika, 75, 613–632.
6. Davis, C. (2010). The spatial coding model of visual word identification. Psychological Review, 117(3), 713.
7. Diederich, A., & Busemeyer, J.R. (2003). Simple matrix methods for analyzing diffusion models of choice probability, choice response time and simple response time. Journal of Mathematical Psychology, 47, 304–322.
8. Dufau, S., Grainger, J., & Ziegler, J.C. (2012). How to say “no” to a nonword: a leaky competing accumulator model of lexical decision. Journal of Experimental Psychology: Learning, Memory, and Cognition, 38, 1117–1128.
9. Dzhafarov, E.N. (1992). The structure of simple reaction time to step-function signals. Journal of Mathematical Psychology, 36, 235–268.
10. Embretson, S.E. (1991). A multidimensional latent trait model for measuring learning and change. Psychometrika, 56, 495–516.
11. Falmagne, J.C., Cohen, S.P., & Dwivedi, A. (1975). Two choice reactions as an ordered memory scanning process. In P.M.A. Rabbit & S. Dornic (Eds.), Attention and performance V (pp. 296–344). New York: Academic Press.
12. Gelfand, A., & Smith, A.F.M. (1990). Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398–409.
13. Gelman, A., Carlin, J.B., Stern, H.S., & Rubin, D.B. (2004). Bayesian data analysis (2nd ed.). London: Chapman and Hall
14. Gold, J.I., & Shadlen, M.N. (2007). The neural basis of decision making. Annual Review of Neuroscience, 30, 535–574.
15. Gomez, P., Ratcliff, R., & Perea, M. (2008). The overlap model: a model of letter position coding. Psychological Review, 115(3), 577.
16. Greenwald, A.G., Draine, S.C., & Abrams, R.L. (1996). Three cognitive markers of unconscious semantic activation. Science, 273(5282), 1699–1702.
17. Grice, G.R. (1968). Stimulus intensity and response evocation. Psychological Review, 75, 359–373.
18. Hanes, D.P., & Schall, J.D. (1996). Neural control of voluntary movement initiation. Science, 274(5286), 427–430.
19. Heathcote, A., & Love, J. (2012). Linear deterministic accumulator models of simple choice. Frontiers in Cognitive Science, 3, 292. http://www.frontiersin.org/Cognitive_Science/10.3389/fpsyg.2012.0029.
20. Huk, A., & Shadlen, M.N. (2005). Neural activity in macaque parietal cortex reflects temporal integration of visual motion signals during perceptual decision making. Journal of Neuroscience, 25, 10420–10436.
21. Jackman, S. (2009). Bayesian analysis for the social sciences. Chichester: Wiley.
22. Kass, R.E. (1993). Bayes factors in practice. The Statistician, 42, 551–560.
23. Kass, R.E., & Raftery, A.E. (1995). Bayes factors. Journal of the American Statistical Association, 90, 773–795.
24. Kucera, H., & Francis, W.N. (1967). Computational analysis of present-day American English. Providence: Brown University Press.
25. Lee, S.-Y. (2007). Structural equation modelling: a Bayesian approach. New York: Wiley.
26. Link, S.W. (1992). Wave theory of difference and similarity. Hillsdale: Erlbaum.
27. Luce, R.D. (1986). Response times. New York: Oxford University Press.
28. McClelland, J.L. (1993). Toward a theory of information processing in graded, random, and interactive networks. In D.E. Meyer & S. Kornblum (Eds.), Attention & performance XIV: synergies in experimental psychology, artificial intelligence and cognitive neuroscience. Cambridge: MIT Press.
29. McClelland, J.L., & Rumelhart, D.E. (1981). An interactive activation model of context effects in letter perception: I. An account of basic findings. Psychological Review, 88, 375–407.
30. McGill, W. (1963). Stochastic latency mechanism. In R.D. Luce & E. Galanter (Eds.), Handbook of mathematical psychology (Vol. 1, pp. 309–360). New York: Wiley.
31. Morey, R.D., Rouder, J.N., Pratte, M.S., & Speckman, P.L. (2011). Using MCMC chain outputs to efficiently estimate Bayes factors. Journal of Mathematical Psychology, 55, 368–378. http://dx.doi.org/10.1016/j.jmp.2011.06.004.
32. Peruggia, M., Van Zandt, T., & Chen, M. (2002). Was it a car or a cat I saw? An analysis of response times for word recognition. Case Studies in Bayesian Statistics, 6, 319–334.
33. Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.
34. Ratcliff, R. (1978). A theory of memory retrieval. Psychological Review, 85, 59–108.
35. Ratcliff, R., & McKoon, G.M. (2008). The diffusion decision model: theory and data for two-choice decision tasks. Neural Computation, 20, 873–922.
36. Ratcliff, R., & Rouder, J.N. (1998). Modeling response times for decisions between two choices. Psychological Science, 9, 347–356.
37. Ratcliff, R., Thapar, A., & McKoon, G. (2003). A diffusion model analysis of the effects of aging on brightness discrimination. Perception and Psychophysics, 65, 523–535.
38. Ratcliff, R., Gomez, P., & McKoon, G.M. (2004). A diffusion model account of the lexical decision task. Psychological Review, 111, 159–182.
39. Reddi, B., & Carpenter, R. (2003). Accuracy, information and response time in a saccadic decision task. Journal of Neurophysiology, 90, 3538–3546.
40. Riefer, D.M., Knapp, B.R., Batchelder, W.H., Bamber, D., & Manifold, V. (2002). Cognitive psychometrics: assessing storage and retrieval deficits in special populations with multinomial processing tree models. Psychological Assessment, 14, 184–201.
41. Roberts, G.O., & Sahu, S.K. (1997). Updating schemes, correlation structure, blocking and parameterization for the Gibbs sampler. Journal of the Royal Statistical Society, Series B, Methodological, 59, 291–317.
42. Roberts, S., & Pashler, H. (2000). How persuasive is a good fit? A comment on theory testing. Psychological Review, 107, 358–367.
43. Roitman, J.D., & Shadlen, M.N. (2002). Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task. Journal of Neuroscience, 22, 9475–9489.
44. Rouder, J.N. (2005). Are unshifted distributional models appropriate for response time? Psychometrika, 70, 377–381.
45. Rouder, J.N., Sun, D., Speckman, P.L., Lu, J., & Zhou, D. (2003). A hierarchical Bayesian statistical framework for response time distributions. Psychometrika, 68, 587–604.
46. Rumelhart, D.E., & McClelland, J.L. (1982). An interactive activation model of context effects in letter perception: II. The contextual enhancement effect and some tests and extensions of the model. Psychological Review, 89, 60–94.
47. Schall, J.D. (2003). Neural correlates of decision processes: neural and mental chronometry. Current Opinion in Neurobiology, 13, 182–186.
48. Skrondal, A., & Rabe-Hesketh, S. (2004). Generalized latent variable modeling: multilevel, longitudinal, and structural equation models. Boca Raton: CRC Press.
49. Smith, P.L. (2000). Stochastic dynamic models of response time and accuracy: a foundational primer. Journal of Mathematical Psychology, 44, 408–463.
50. Spiegelhalter, D.J., Best, N.G., Carlin, B.P., & van der Linde, A. (2002). Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society, Series B, Statistical Methodology, 64, 583–639.
51. Thissen, D. (1983). Timed testing: an approach using item response theory. In D.J. Weiss (Ed.), New horizons in testing: latent trait test theory and computerized adaptive testing (pp. 179–203). New York: Academic Press.
52. Tuerlickx, F., & De Boek, P. (2005). Two interpretations of the discrimination parameter. Psychometrika, 70, 629–650.
53. Ulrich, R., & Miller, J.O. (1993). Information processing models generating lognormally distributed reaction times. Journal of Mathematical Psychology, 37, 513–525.
54. Usher, M., & McClelland, J.L. (2001). On the time course of perceptual choice: the leaky competing accumulator model. Psychological Review, 108, 550–592.
55. van Breukelen, G.J.P. (2005). Psychometric modeling of response time and accuracy with mixed and conditional regression. Psychometrika.
56. Vandekerckhove, J., Tuerlinckx, F., & Lee, M.D. (2011). Hierarchical diffusion models for two-choice response time. Psychological Methods, 16, 44–62.
57. Vandekerckhove, J., Verheyen, S., & Tuerlinckx, F. (2010). A cross random effects diffusion model for speeded semantic categorization decisions. Acta Psychologica, 133, 269–282.
58. van der Linden, W.J. (2007). A hierarchical framework for modeling speed and accuracy on test items. Psychometrika, 72, 287–308.
59. van der Linden, W.J. (2009). Conceptual issues in response-time modeling. Journal of Educational Measurement, 14, 247–272.
60. van der Linden, W.J., Scrams, D.J., & Schnipke, D.L. (1999). Using response-time constraints to control for differential speededness in computerized adaptive testing. Applied Psychological Measurement, 23, 195–210.
61. van der Maas, H.L.J., Molenaar, D., Maris, G., Kievit, R.A., & Borsboom, D. (2001). Cognitive psychology meets psychometric theory: on the relation between process models for decision making and latent variable models for individual differences. Psychological Review, 118, 339–356.
62. Wagenmakers, E.-J., van der Maas, H.L.J., & Grasman, R.P.P.P. (2007). An EZ-diffusion model for response time and accuracy. Psychonomic Bulletin & Review, 14, 3–22.
63. Whitney, C., Bertrand, D., & Grainger, J. (2011). On coding the position of letters in words. Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie), 1–6.
64. Wild, P., & Gilks, W.R. (1993). Adaptive rejection sampling from log-concave density functions. Applied Statistics, 42, 701–708.