A hierarchical model for estimating response time distributions

Psychonomic Bulletin and Review

Volumn 12, Issue 2, 2005, Pages 195-223

  Rouder, Jeffrey N ^a   Lu, Jun ^a   Speckman, Paul ^a   Sun, Dongchu ^a   Jiang, Yi ^a  

^a UNIVERSITY OF MISSOURI   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23744457858     PISSN: 10699384     EISSN: None     Source Type: Journal    
DOI: 10.3758/BF03257252     Document Type: Review

References (103)

1. ANDREWS, S., & HEATHCOTE, A. (2001). Distinguishing common and task-specific processes in word identification: A matter of some moment. Journal of Experimental Psychology: Learning, Memory, & Cognition, 27, 514-544.
2. ASHBY, F. G., MADDOX, W. T., & LEE, W. W. (1994). On the dangers of averaging across subjects when using multidimensional scaling or the similarity-choice model. Psychological Science, 5, 144-151.
3. ASHBY, F. G., TIEN, J.-Y., & BALAKRISHNAN, J. D. (1993). Response time distributions in memory scanning. Journal of Mathematical Psychology, 37, 526-555.
4. ASHBY, F. G., & TOWNSEND, J. T. (1980). Decomposing the reaction time distribution: Pure insertion and selective influences revisited. Journal of Mathematical Psychology, 21, 93-123.
5. ATKINSON, R. C., HOLMGREN, J. E., & JUOLA, J. F. (1969). Processing time as influenced by the number of elements in a visual display. Perception & Psychophysics, 6, 321-326.
6. BALOTA, D. A., & CHUMBLEY, J. I. (1984). Are lexical decisions a good measure of lexical access? The role of word frequency in the neglected decision stage. Journal of Experimental Psychology: Human Perception & Performance, 10, 340-357.
7. BALOTA, D. A., & SPIELER, D. H. (1999). Word frequency, repetition, and lexicality effects in word recognition tasks: Beyond measures of central tendency. Journal of Experimental Psychology: General, 128, 32-55.
8. BATCHELDER, W. H., & RIEFER, D. M. (1999). Theoretical and empirical review of multinomial process tree modeling. Psychonomic Bulletin & Review, 6, 57-86.
9. BROWN, S., & HEATHCOTE, A. (2003). Averaging learning curves across and within participants. Behavior Research Methods, Instruments, & Computers, 35, 11-21.
10. BUSEMEYER, J. R., & TOWNSEND, J. T. (1993). Decision field theory: A dynamic-cognitive approach to decision making in an uncertain environment. Psychological Review, 100, 432-459.
11. CHENG, R. C. H., & AMIN, N. A. K. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society: Series B, 45, 394-403.
12. CLARK, H. H. (1973). The language-as-fixed-effect fallacy: A critique of language statistics in psychological research. Journal of Verbal Learning & Verbal Behavior, 12, 335-359.
13. COLONIUS, H. (1995). The instance theory of automaticity: Why the Weibull? Psychological Review, 102, 744-750.
14. COUSINEAU, D., GOODMAN, V. W., & SHIFFRIN, R. M. (2002). Extending statistics of extremes to distributions varying in position and scale and the implications for race models. Journal of Mathematical Psychology, 46, 431-454.
15. CURRAN, T. C., & HINTZMAN, D. G. (1995). Violations of the independence assumption in process dissociation. Journal of Experimental Psychology: Learning, Memory, & Cognition, 21, 531-547.
16. DEY, D., GHOSH, S., & MALLICK, B. (2000). Generalized linear models: A Bayesian perspective. New York: Dekker.
17. DOLAN, C. V., VAN DER MAAS, H. L. J., & MOLENAAR, P. C. M. (2002). A framework for ML estimation of parameters of (mixtures of) common reaction time distributions given optional truncation or censoring. Behavior Research Methods, Instruments, & Computers, 34, 304-323.
18. DZHAFAROV, E. N. (1992). The structure of simple reaction time to step-function signals. Journal of Mathematical Psychology, 36, 235-268.
19. EDWARDS, W. (1965). Optimal strategies for seeking information: Models for statistics, choice reaction times, and human information processing. Journal of Mathematical Psychology, 2, 312-329.
20. EDWARDS, W., LINDMAN, H., & SAVAGE, L. J. (1963). Bayesian statistical inference for psychological research. Psychological Review, 70, 193-242.
21. ESTES, W. K. (1956). The problem of inference from curves based on grouped data. Psychological Bulletin, 53, 134-140.
22. Fox, J.-P., & GLAS, C. A. W. (2001). Bayesian estimation of a multilevel IRT model using Gibbs sampling. Psychometrika, 66, 271-288.
23. GELFAND, A., & SMITH, A. F. M. (1990). Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398-409.
24. GELMAN, A., CARLIN, J. B., STERN, H. S., & RUBIN, D. B. (1995). Bayesian data analysis. London: Chapman & Hall.
25. GREEN, D. M., SMITH, A. F., & VON GIERKE, S. M. (1983). Choice reaction time with a random foreperiod. Perception & Psychophysics, 34, 195-208.
26. HAIDER, H., & FRENSCH, P. A. (2002). Why aggregated learning follows the power law of practice when individual learning does not: Comment on Rickard (1997, 1999), Delaney et al. (1998), and Palmeri (1999). Journal of Experimental Psychology: Learning, Memory, & Cognition, 28, 392-406.
27. HASHER, L., & ZACKS, R. T. (1979). Automatic and effortful processes in memory. Journal of Experimental Psychology: General, 108, 356-388.
28. HEATHCOTE, A. (1996). RTSYS: A DOS application for the analysis of reaction time data. Behavior Research Methods, Instruments, & Computers, 28, 427-445.
29. HEATHCOTE, A., BROWN, S., & MEWHORT, D. J. K. (2000). The power law repealed: The case for an exponential law of practice. Psychonomic Bulletin & Review, 7, 185-207.
30. HEATHCOTE, A., BROWN, S., & MEWHORT, D. J. K. (2002). Quantile maximum likelihood estimation of response time distributions. Psychonomic Bulletin & Review, 9, 394-401.
31. HEATHCOTE, A., POPIEL, S. J., & MEWHORT, D. J. (1991). Analysis of response time distributions: An example using the Stroop task. Psychological Bulletin, 109, 340-347.
32. HOCKLEY, W. E. (1984). Analysis of reaction time distributions in the study of cognitive processes. Journal of Experimental Psychology: Learning, Memory, & Cognition, 10, 598-615.
33. HOGG, R. V., & CRAIG, A. T. (1978). Introduction to mathematical statistics. New York: Macmillan.
34. HOHLE, R. H. (1965). Inferred components of reaction time as a function of foreperiod duration. Journal of Experimental Psychology, 69, 382-386.
35. HSU, Y. F. (1999). Two studies on simple reaction times: I. On the psychophysics of the generalized Pieron's law. II. On estimating minimum detection times using the time estimation paradigm. Unpublished doctoral dissertation, University of California, Irvine.
36. JACOBY, L. L. (1991). A process dissociation framework: Separating automatic from intentional uses of memory. Journal of Memory & Language, 30, 513-541.
37. JIANG, Y. (2002). Statistical approaches to forming group RT distributions. Unpublished master's thesis, University of Missouri, Columbia.
38. JIANG, Y., ROUDER, J. N., & SPECKMAN, P. L. (2004). A note on the sampling properties of the Vincentizing (quantile averaging) procedure. Journal of Mathematical Psychology, 48, 186-195.
39. JOHNSON, N. L., KOTZ, S., & BALAKRISHNAN, N. (1994). Continuous univariate distributions (2nd ed., Vol. 2). New York: Wiley.
40. KASS, R., & RAFTERY, A. (1995). Bayes factors. Journal of the American Statistical Association, 90, 773-795.
41. KOSSLYN, S. M. (1975). Information representation in visual images. Cognitive Psychology, 7, 341-370.
42. KREFT, I. G. G., & DE LEEUW, J. (1998). Introducing multilevel modeling. London: Sage.
43. LEE, P. M. (1997). Bayesian statistics: An introduction. New York: Wiley.
44. LEHMANN, E. L. (1991 ). Theory of point estimation. Pacific Grove, CA: Wadsworth & Brooks.
45. LINK, S. W. (1975). The relative judgement theory of two choice response time. Journal of Mathematical Psychology, 12, 114-135.
46. LINK, S. W. (1990). Modeling imageless thought: The relative judgment theory of numerical comparisons. Journal of Mathematical Psychology, 34, 2-41.
47. LOGAN, G. D. (1988). Toward an instance theory of automatization. Psychological Review, 95, 492-527.
48. LOGAN, G. D. (1992). Shapes of reaction time distributions and shapes of learning curves: A test of the instance theory of automaticity. Journal of Experimental Psychology: Learning, Memory, & Cognition, 18, 883-914.
49. LU, J. (2004). Bayesian hierarchical models and applications in psychological research. Unpublished doctoral dissertation, University of Missouri, Columbia.
50. LU, J., SUN, D., SPECKMAN, P. L., & ROUDER, J. N. (2005). Hierarchical models for practice-effects in response time. Manuscript submitted for publication.
51. LUCE, R. D. (1959). Individual choice behavior. New York: Wiley.
52. LUCE, R. D. (1986). Response times. New York: Oxford University Press.
53. MASSON, M. E. J., & LOFTUS, G. R. (2003). Using confidence intervals for graphically based data interpretation. Canadian Journal of Experimental Psychology, 57, 203-220.
54. 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.
55. MENG, X., & WONG, W. (1996). Simulating ratios of normalizing constants via a simple identity: A theoretical exploration. Statistica Sinica, 6, 831-860.
56. MOYER, R. S. (1973). Comparing objects in memory: Evidence suggesting an internal psychophysics. Perception & Psychophysics, 13, 1080-1084.
57. MOYER, R. S., & LANDAUER, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215, 1519-1520.
58. MYUNG, I. J. (2003). Tutorial on maximum likelihood estimation. Journal of Mathematical Psychology, 47, 90-100.
59. MYUNG, I. J., KIM, C., & PITT, M. A. (2002). Toward an explanation of the power law artifact: Insights from response surface analysis. Memory & Cognition, 28, 832-840.
60. MYUNG, I. J., & PITT, M. A. (1997). Applying Occam's razor in modeling cognition: A Bayesian approach. Psychonomic Bulletin & Review, 4, 79-95.
61. NELDER, J. A., & MEAD, R. (1965). A simplex method for function minimization. Computer Journal, 7, 308-313.
62. 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. In C. Gatsonis, R. E. Kass, A. Carriquiry, A. Gelman, D. Higdon, D. K. Pauler, & I. Verdinelli (Eds.), Case studies in Bayesian statistics (Vol. 6, pp. 319-334). New York: Springer-Verlag.
63. PHILLIPS, L. D., & EDWARDS, W. (1966). Conservatism in a simple probability inference task. Journal of Experimental Psychology, 72, 346-354.
64. PITT, M. A., MYUNG, I. J., & ZHANG, S. (2002). Toward a method of selecting among computational models of cognition. Psychological Review, 109, 472-491.
65. POLTROCK, S. E. (1989). A random walk model of digit comparison. Journal of Mathematical Psychology, 33, 131-162.
66. RATCLIFF, R. (1978). A theory of memory retrieval. Psychological Review, 85, 59-108.
67. RATCLIFF, R. (1979). Group reaction time distributions and an analysis of distribution statistics. Psychological Bulletin, 86, 446-461.
68. RATCLIFF, R., & ROUDER, J. N. (1998). Modeling response times for decisions between two choices. Psychological Science, 9, 347-356.
69. RATCLIFF, R., & ROUDER, J. N. (2000). A diffusion model analysis of letter masking. Journal of Experimental Psychology: Human Perception & Performance, 26, 127-140.
70. RICKARD, T. C. (1997). Bending the power law: A CMPL theory of strategy shifts and the automatization of cognitive skills. Journal of Experimental Psychology: General, 126, 288-311.
71. RIEFER, D. M., & BATCHELDER, W. H. (1988). Multinomial modeling and the measure of cognitive processes. Psychological Review, 95, 318-339.
72. ROUDER, J. N. (2000). Assessing the roles of change discrimination and luminance integration: Evidence for a hybrid race model of perceptual decision making in luminance discrimination. Journal of Experimental Psychology: Human Perception & Performance, 26, 359-378.
73. ROUDER, J. N. (2001). Testing evidence accrual models by manipulating stimulus onset. Journal of Mathematical Psychology, 45, 334-354.
74. ROUDER, J. N. (2004). Modeling the effects of choice-set size on the processing of letters and words. Psychological Review, 111, 80-93.
75. ROUDER, J. N., & BATCHELDER, W. H. (1998). Multinomial models for measuring storage and retrieval processes in paired-associate learning. In C. Dowling, F. Roberts, & P. Theuns (Eds.), Recent progress in mathematical psychology (pp. 195-225). Hillsdale, NJ: Erlbaum.
76. ROUDER, J. N., Lu, J., SUN, D., SPECKMAN, P. L., & MOREY, R. D. (2003, November). A statistical model of skill acquisition. Poster presented at the 20th Annual Meeting of the Psychonomic Society, Vancouver.
77. ROUDER, J. N., RATCLIFF, R., & MCKOON, G. M. (2000). A neural network model of priming in object recognition. Psychological Science, 11, 13-19.
78. ROUDER, J. N., & SPECKMAN, P. L. (2004). An evaluation of the Vincentizing method of forming group-level response time distributions. Psychonomic Bulletin & Review, 11, 419-427.
79. ROUDER, J. N., SUN, D., SPECKMAN, P. L., Lu, J., & ZHOU, D. (2003). A hierarchical Bayesian statistical framework for response time distributions. Psychometrika, 68, 589-606.
80. SCHNEIDER, W., & SHIFFRIN, R. M. (1977). Controlled and automatic human information processing: I. Detection, search, and attention. Psychological Review, 84, 1-66.
81. SCHWARZ, W. (2001). The ex-Wald distribution as a descriptive model of response times. Behavior Research Methods, Instruments, & Computers, 33, 457-469.
82. SHEU, C.-F., & O'CURRY, S. L. (1998). Simulation-based Bayesian inference using BUGS. Behavior Research Methods, Instruments, & Computers, 30, 232-237.
83. SMITH, D. G., & MEWHORT, D. J. K. (1998). The distribution of latencies constrains theories of decision time: A test of the random-walk model using numeric comparison. Australian Journal of Psychology, 50, 149-156.
84. SPECKMAN, P. L., & ROUDER, J. N. (2004). A comment on Heathcote, Brown, and Mewhort's QMLE method for response time distributions. Psychonomic Bulletin & Review, 11, 574-576.
85. SPIELER, D. H., BALOTA, D. A., & FAUST, M. E. (1996). Stroop performance in healthy younger and older adults and in individuals with dementia of the Alzheimer's type. Journal of Experimental Psychology: Human Perception & Performance, 22, 461-479.
86. STERNBERG, S. (1966). High-speed scanning in human memory. Science, 153, 652-654.
87. TANNER, M. A. (1993). Tools for statistical inference: Methods for the exploration of posterior distributions and likelihood functions. Berlin: Springer-Verlag.
88. THEEUWES, J. (1992). Perceptual selectivity for color and form. Perception & Psychophysics, 51, 599-606.
89. THEEUWES, J. (1994). Stimulus-driven capture and attentional set: Selective search for color and visual abrupt onsets. Journal of Experimental Psychology: Human Perception & Performance, 20, 799-806.
90. THOMAS, E. A. C., & Ross, B. (1980). On appropriate procedures for combining probability distributions within the same family. Journal of Mathematical Psychology, 21, 136-152.
91. TOWNSEND, J. T., & ASHBY, F. G. (1983). The stochastic modeling of elementary psychological processes. Cambridge: Cambridge University Press.
92. TOWNSEND, J. T., & NOZAWA, G. (1995). On the spatio-temporal properties of elementary perception: An investigation on parallel, serial, and coactive theories. Journal of Mathematical Psychology, 39, 321-359.
93. TREISMAN, A. M., & GELADE, G. (1980). A feature-integration theory of attention. Cognitive Psychology, 12, 97-136.
94. TVERSKY, A., & KAHNEMAN, D. (1990). Judgements under uncertainty: Heuristics and biases. In P. K. Moser (Ed.), Rationality in action: Contemporary approaches (pp. 171-188). New York: Cambridge University Press.
95. ULRICH, R., & MILLER, J. (1994). Effects of truncation of reaction time analysis. Journal of Experimental Psychology: General, 123, 34-80.
96. VAN ZANDT, T. (2000). How to fit a response time distribution. Psychonomic Bulletin & Review, 7, 424-465.
97. VAN ZANDT, T., COLONIUS, H., & PROCTOR, R. W. (2000). A comparison of two response time models applied to perceptual matching. Psychonomic Bulletin & Review, 7, 208-256.
98. VICKERS, D. (1980). Discrimination. In A. Welford (Ed.), Reaction times (pp. 25-72). London: Academic Press.
99. VINCENT, S. B. (1912). The function of vibrissae in the behavior of the white rat. Behavioral Monographs, 1(Whole No. 5).
100. WANG, X. H., BRADLOW, E. T., & WAINER, H. (2002). A general Bayesian model for testlets: Theory and applications. Applied Psychological Measurement, 26, 109-128.
101. WICKENS, T. D., & KEPPEL, G. (1983). On the choice of design and test statistic in the analysis of experiments with sampled materials. Journal of Verbal Learning & Verbal Behavior, 22, 296-309.
102. YELLOTT, J. I. (1969). Probability learning with noncontingent success. Journal of Mathematical Psychology, 6, 541-575.
103. YELLOTT, J. I. (1971). Correction for fast guessing and the speed-accuracy tradeoff in choice reaction time. Journal of Mathematical Psychology, 8, 159-199.