Download PDF

Theoretical and empirical review of multinomial process tree modeling

Psychonomic Bulletin & Review volume 6, pages57–86(1999)Cite this article

Abstract

We review a current and popular class of cognitive models calledmultinomial processing tree (MPT) models. MPT models are simple, substantively motivated statistical models that can be applied to categorical data. They are useful as data-analysis tools for measuring underlying or latent cognitive capacities and as simple models for representing and testing competing psychological theories. We formally describe the cognitive structure and parametric properties of the class of MPT models and provide an inferential statistical analysis for the entire class. Following this, we provide a comprehensive review of over 80 applications of MPT models to a variety of substantive areas in cognitive psychology, including various types of human memory, visual and auditory perception, and logical reasoning. We then address a number of theoretical issues relevant to the creation and evaluation of MPT models, including model development, model validity, discrete-state assumptions, statistical issues, and the relation between MPT models and other mathematical models. In the conclusion, we consider the current role of MPT models in psychological research and possible future directions.

References

  1. Agresti, A. (1990).Categorical data analysis. New York: Wiley.

    Google Scholar 

  2. Anderson, J. A. (1995).An introduction to neural networks. Cambridge, MA: MIT Press.

    Google Scholar 

  3. Anderson, N. H. (1982).Foundations of information integration theory. New York: Academic Press.

    Google Scholar 

  4. Anderson, N. H. (1990). Integration psychophysics. In H.-G. Geissler (Ed.),Psychophysical explorations of mental structures (pp. 71–93). Lewiston, NY: Hogrefe & Huber.

    Google Scholar 

  5. Ashby, F. G. (Ed.) (1992).Multidimensional models of perception and cognition. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  6. Ashby, F. G., Prinzmetal, W., Ivry, R., &Maddox, W. T. (1996). A formal theory of feature binding in object perception.Psychological Review,103, 165–192.

    PubMed  Article  Google Scholar 

  7. Baker, F. B. (1992).Item response theory. New York: Marcel Dekker.

    Google Scholar 

  8. Bamber, D., &van Santen, J. P. H. (1985). How many parameters can a model have and still be testable?Journal of Mathematical Psychology,29, 443–473.

    Article  Google Scholar 

  9. Batchelder, W. H. (1975). Individual differences and the all-or-none vs. incremental learning controversy.Journal of Mathematical Psychology,12, 53–74.

    Article  Google Scholar 

  10. Batchelder, W. H. (1991). Getting wise about minimum distance measures.Journal of Mathematical Psychology,35, 267–273.

    Article  Google Scholar 

  11. Batchelder, W. H. (1998). Multinomial processing, tree models and psychological assessment.Psychological Assessment,10, 331–344.

    Article  Google Scholar 

  12. Batchelder, W. H., Chosak-Reiter, J., Shankle, W. R., &Dick, M. B. (1997). A multinomial modeling analysis of memory deficits in Alzheimer’s and vascular dementia.Journal of Gerontology: Psychological Sciences,52B, 206–215.

    Google Scholar 

  13. Batchelder, W. H., &Crowther, C. S. (1997). Multinomial processing tree models of factorial categorization.Journal of Mathematical Psychology,41, 45–55.

    Article  Google Scholar 

  14. Batchelder, W. H., Hu, X., &Riefer, D. M. (1994). Analysis of a model for source monitoring. In G. Fischer & D. Laming (Eds.),Contributions to mathematical psychology, psychometrics, and methodology (pp. 51–65). New York: Springer-Verlag.

    Google Scholar 

  15. Batchelder, W. H., Kumbasar, E., &Boyd, J. P. (1997). Consensus analysis of three-way social network data.Journal of Mathematical Psychology,22, 29–58.

    Google Scholar 

  16. Batchelder, W. H., &Riefer, D. M. (1980). Separation of storage and retrieval factors in free recall of clusterable pairs.Psychological Review,87, 375–397.

    Article  Google Scholar 

  17. Batchelder, W. H., &Riefer, D. M. (1986). The statistical analysis of a model for storage and retrieval processes in human memory.British Journal of Mathematical & Statistical Psychology,39, 120–149.

    Google Scholar 

  18. Batchelder, W. H., &Riefer, D. M. (1990). Multinomial processing models of source monitoring.Psychological Review,97, 548–564.

    Article  Google Scholar 

  19. Batchelder, W. H., Riefer, D. M., &Hu, X. (1994). Measuring memory factors in source monitoring: Reply to Kinchla.Psychological Review,101, 172–176.

    Article  Google Scholar 

  20. Batchelder, W. H., &Romney, A. K. (1986). The statistical analysis of a general Condorcet model for dichotomous choice situations. In B. Grofman & G. Owen (Eds.),Information pooling and group decision making (pp. 103–112). Greenwich, CT: JAI Press.

    Google Scholar 

  21. Batchelder, W. H., &Romney, A. K. (1988). Test theory without an answer key.Psychometrika,53, 71–92.

    Article  Google Scholar 

  22. Batchelder, W. H., &Romney, A. K. (1989). New results in test theory without an answer key. In E. Roskam (Ed.),Advances in mathematical psychology: Vol. II (pp. 229–248). New York: Springer-Verlag.

    Google Scholar 

  23. Bäuml, K.-H. (1991). Experimental analysis of storage and retrieval processes involved in retroactive inhibition: The effect of presentation mode.Acta Psychologica,77, 103–119.

    Article  Google Scholar 

  24. Bäuml, K.-H. (1996a). A Markov model for measuring storage loss and retrieval failure in retroactive inhibition.Acta Psychologica,92, 231–250.

    Article  Google Scholar 

  25. Bäuml, K.-H. (1996b). Revisiting an old issue: Retroactive interference as a function of the degree of original and interpolated learning.Psychonomic Bulletin & Review,3, 380–384.

    Google Scholar 

  26. Bayen, U. J., &Murnane, K. (1996). Aging and the use of perceptual and temporal information in source memory tasks.Psychology & Aging,11, 293–303.

    Article  Google Scholar 

  27. Bayen, U. J., Murnane, K., &Erdfelder, E. (1996). Source discrimination, item detection, and multinomial models of source monitoring.Journal of Experimental Psychology: Learning, Memory, & Cognition,22, 197–215.

    Article  Google Scholar 

  28. Begg, I. A., Anas, A., &Farinacci, S. (1992). Dissociation of processing in belief: Source recollection, statement familiarity, and the illusion of truth.Journal of Experimental Psychology: General,121, 446–458.

    Article  Google Scholar 

  29. Bender, R. H., Wallsten, T. S., &Ornstein, P. A. (1996). Age differences in encoding and retrieving details of a pediatric examination.Psychonomic Bulletin & Review,3, 188–198.

    Google Scholar 

  30. Bishop, Y. M. M., Fienberg, S. E., &Holland, P. W. (1975).Discrete multivariate analysis: Theory and practice. Cambridge, MA: MIT Press.

    Google Scholar 

  31. Bower, G. H. (1961). Application of a model to paired-associate learning.Psychometrika,26, 255–280.

    Article  Google Scholar 

  32. Brainerd, C. J.,Reyna, V. F.,Howe, M. L., &Kingma, J. (1990). The development of forgetting and reminiscence.Monographs of the Society for Research in Child Development,55 (3–4, Serial No. 222).

    Google Scholar 

  33. Brown, V. R. (1998). Comparing parallel and sequential multinomial models of letter identification. In C. Dowling, F. Roberts, & P. Theuns (Eds.),Recent progress in mathematical psychology (pp. 253–284). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  34. Buchner, A., &Erdfelder, E. (1996). On assumptions of, relations between, and evaluations of some dissociation measurement models.Consciousness & Cognition,5, 581–594.

    Article  Google Scholar 

  35. Buchner, A., Erdfelder, E., Steffens, M. C., &Martensen, H. (1997). The nature of memory processes underlying recognition judgments in the process-dissociation procedure.Memory & Cognition,25, 508–517.

    Google Scholar 

  36. Buchner, A., Erdfelder, E., &Vaterrodt-Plunnecke, B. (1995). Toward unbiased measurement of conscious and unconscious memory processes within the process dissociation framework.Journal of Experimental Psychology: General,124, 137–160.

    Article  Google Scholar 

  37. Buchner, A., Steffens, M. C., Erdfelder, E., &Rothkegel, R. (1997). A multinomial model to assess fluency and recollection in a sequence learning task.Quarterly Journal of Experimental Psychology,50A, 631–663.

    Article  Google Scholar 

  38. Buchner, A., &Wippich, W. (1996). Unconscious gender bias in fame judgments.Consciousness & Cognition,5, 197–220.

    Article  Google Scholar 

  39. Butler, K., &Chechile, R. [A.] (1976). “Acid bath” effects on storage and retrieval PI.Bulletin of the Psychonomic Society,8, 349–352.

    Google Scholar 

  40. Chandler, J. P. (1969). STEPIT—Finds local minima of a smooth function of several parameters.Behavioral Science,14, 81–82.

    Google Scholar 

  41. Chechile, R. [A.] (1977). Storage-retrieval analysis of acoustic similarity.Memory & Cognition,5, 535–540.

    Article  Google Scholar 

  42. Chechile, R. A. (1987). Trace susceptibility theory.Journal of Experimental Psychology: General,116, 203–222.

    Article  Google Scholar 

  43. Chechile, R. A. (1993, August).Two models for measuring fractional storage for list learning tasks. Paper presented at the 26th Annual Meeting of the Society for Mathematical Psychology, Norman, OK.

  44. Chechile, R. A., &Butler, K. (1975). Storage and retrieval changes that occur in the development and release of PI.Journal of Verbal Learning & Verbal Behavior,14, 430–437.

    Article  Google Scholar 

  45. Chechile, R. A., &Ehrensbeck, K. (1983). Long-term storage losses: A dilemma for multistore models.Journal of General Psychology,109, 15–30.

    Article  Google Scholar 

  46. Chechile, R. A., &Meyer, D. L. (1976). A Bayesian procedure for separately estimating storage and retrieval components of forgetting.Journal of Mathematical Psychology,13, 269–295.

    Article  Google Scholar 

  47. Chechile, R. A., &Richman, C. L. (1982). The interaction of semantic memory with storage and retrieval processes.Developmental Review,2, 237–250.

    Article  Google Scholar 

  48. Chechile, R. A., Richman, C. L., Topinka, C., &Ehrensbeck, K. (1981). A developmental study of the storage and retrieval of information.Child Development,52, 251–259.

    Article  Google Scholar 

  49. Chechile, R. A., &Roder, B. (1998). Model-based measurement of group differences: An application directed toward understanding the information-processing mechanisms of developmental dyslexia. In S. A. Soraci & W. J. McIlvane (Eds.),Perspectives on fundamental processes in intellectual functioning: Vol. 1. A survey of research approaches (pp. 91–112). Norwich, CT: JAI Press.

    Google Scholar 

  50. Clark, S. E., &Gronlund, S. D. (1996). Global matching models of recognition memory: How the models match the data.Psychonomic Bulletin & Review,3, 37–60.

    Google Scholar 

  51. Cohen, J. (1988).Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  52. Cohen, J. (1992). A power primer.Psychological Bulletin,112, 155–159.

    PubMed  Article  Google Scholar 

  53. Corbett, A. T., &Wickelgren, W. A. (1978). Semantic memory retrieval: Analysis by speed accuracy tradeoff functions.Quarterly Journal of Experimental Psychology,30, 1–15.

    PubMed  Google Scholar 

  54. Crowther, C. S., Batchelder, W. H., &Hu, X. (1995). A measurementtheoretic analysis of the fuzzy logic model of perception.Psychological Review,102, 134–148.

    Article  Google Scholar 

  55. Curran, T., &Hintzman, D. L. (1995). Violations of the independence assumption in process dissociation.Journal of Experimental Psychology: Learning, Memory, & Cognition,21, 531–547.

    Article  Google Scholar 

  56. DaPolito, F. J. (1967). Proactive effects with independent retrieval of competing responses.Dissertation Abstracts,27, 2522–2523.

    Google Scholar 

  57. David, H. A. (1988).The method of paired comparisons (2nd ed.). London: Griffin.

    Google Scholar 

  58. Dehn, D. M., &Engelkamp, J. (1997). Process dissociation procedure: Double dissociations following divided attention and speeded responding.Quarterly Journal of Experimental Psychology,50A, 318–336.

    Google Scholar 

  59. Dehn, D. M., &Erdfelder, E. (1998). What kind of bias is hindsight bias?.Psychological Research,61, 135–146.

    Article  Google Scholar 

  60. Dempster, A. P., Laird, N. M., &Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm.Journal of the Royal Statistical Society: Series B,39, 1–38.

    Google Scholar 

  61. Erdfelder, E., &Bredenkamp, J. (1998). Recognition of script-typical versus script-atypical information: Effects of cognitive elaboration.Memory & Cognition,26, 922–938.

    Google Scholar 

  62. Erdfelder, E., &Buchner, A. (1998a). Decomposing the hindsight bias: A multinomial processing tree model for separating recollection and reconstruction in hindsight.Journal of Experimental Psychology: Learning, Memory, & Cognition,24, 387–414.

    Article  Google Scholar 

  63. Erdfelder, E., &Buchner, A. (1998b). Process dissociation measurement models: Threshold theory or detection theory?Journal of Experimental Psychology: General,127, 83–96.

    Article  Google Scholar 

  64. Erdfelder, E., Faul, F., &Buchner, A. (1995). GPOWER: A general power analysis program.Behavior Research Methods, Instruments, & Computers,28, 1–11.

    Google Scholar 

  65. Evans, J. St. B. (1977). Toward a statistical theory of reasoning.Quarterly Journal of Experimental Psychology,29, 621–635.

    Article  Google Scholar 

  66. Evans, J. St. B., &Lynch, J. S. (1973). Matching bias in the selection task.British Journal of Psychology,64, 391–397.

    Google Scholar 

  67. Ferguson, S. A., Hashtroudi, S., &Johnson, M. K. (1992). Age differences using source-relevant cues.Psychology & Aging,7, 443–452.

    Article  Google Scholar 

  68. Fischer, G. H., &Molenaar, I. W. (Eds.) (1995).Rasch models: Foundations, recent developments, and applications. New York: Springer-Verlag.

    Google Scholar 

  69. Flexser, A. J., &Tulving, E. (1978). Retrieval independence in recognition and recall.Psychological Review,85, 153–171.

    Article  Google Scholar 

  70. Garcia-Perez, M. A. (1987). A finite theory of performance in multiplechoice tests. In E. E. Roskam & R. Suck (Eds.),Progress in mathematical psychology 1 (pp. 455–464). Amsterdam: Elsevier.

    Google Scholar 

  71. Garcia-Perez, M. A. (1989). Item sampling, guessing, partial information and decision-making in achievement testing. In E. E. Roskam (Ed.),Mathematical psychology in progress (pp. 249–265). Berlin: Springer-Verlag.

    Google Scholar 

  72. Garcia-Perez, M. A. (1990). A comparison of two models of performance in objective tests: Finite state versus continuous distributions.British Journal of Mathematical & Statistical Psychology,43, 73–91.

    Google Scholar 

  73. Garcia-Perez, M. A. (1993). In defence of “none of the above.”British Journal of Mathematical & Statistical Psychology,46, 213–229.

    Google Scholar 

  74. Garcia-Perez, M. A., &Frary, R. B. (1991a). Finite state polynomic item characteristic curves.British Journal of Mathematical & Statistical Psychology,44, 45–73.

    Google Scholar 

  75. Garcia-Perez, M. A., &Frary, R. B. (1991b). Testing finite-state models of performance in objective tests using items with “none of the above” as an option. In J.-P. Doignon & J.-C. G. Falmagne (Eds.),Mathematical psychology: Current developments (pp. 273–291). New York: Springer-Verlag.

    Google Scholar 

  76. Gerrein, J. R., &Chechile, R. A. (1977). Storage and retrieval processes of alcohol-induced amnesia.Journal of Abnormal Psychology,86, 285–294.

    PubMed  Article  Google Scholar 

  77. Golden, R. M. (1995). Making correct statistical inferences using a wrong probability model.Journal of Mathematical Psychology,39, 3–20.

    Article  Google Scholar 

  78. Gondran, M., Minoux, M., &Vajda, S. (1984).Graphs and algorithms. New York: Wiley.

    Google Scholar 

  79. Green, D. M., &Birdsall, T. G. (1978). Detection and recognition.Psychological Review,85, 192–206.

    Article  Google Scholar 

  80. Greeno, J. G., James, C. T., DaPolito, F., &Polson, P. G. (1978).Associate learning: A cognitive analysis. Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  81. Gutowski, W. E., &Chechile, R. A. (1987). Encoding, storage, and retrieval components of associative memory deficits of mildly retarded adults.American Journal of Mental Deficiency,92, 85–93.

    PubMed  Google Scholar 

  82. Hawkins, S. A., &Hastie, R. (1990). Hindsight: Biased judgments of past events after the outcomes are known.Psychological Bulletin,107, 311–327.

    Article  Google Scholar 

  83. Hintzman, D. L. (1980). Simpson’s paradox and the analysis of memory retrieval.Psychological Review,87, 398–410.

    Article  Google Scholar 

  84. Hintzman, D. L. (1992). Mathematical constraints and the “Tulving-Wiseman Law.”Psychological Review,99, 536–542.

    Article  Google Scholar 

  85. Hintzman, D. L. (1993). On variability, Simpson’s paradox, and the relation between recognition and recall: Reply to Tulving and Flexser.Psychological Review,100, 143–148.

    PubMed  Article  Google Scholar 

  86. Howe, M. L. (1990). Development of a mathematical model of memory for clinical research applications in aging. In M. L. Howe, M. J. Stones, & C. J. Brainerd (Eds.),Cognitive and behavioral performance factors in atypical aging (pp. 3–36). New York: Springer-Verlag.

    Google Scholar 

  87. Howe, M. L. (1991). Misleading children’s story recall: Forgetting and reminiscence of the facts.Developmental Psychology,27, 746–762.

    Article  Google Scholar 

  88. Howe, M. L. (1995). Interference effects in young children’s long-term retention.Developmental Psychology,31, 579–596.

    Article  Google Scholar 

  89. Howe, M. L., &Brainerd, C. J. (1989). Development of children’s long-term retention.Developmental Review,9, 301–340.

    Article  Google Scholar 

  90. Howe, M. L., Courage, M. L., &Bryant-Brown, L. (1993). Reinstating preschooler’s memories.Developmental Psychology,29, 854–869.

    Article  Google Scholar 

  91. Howe, M. L., &Hunter, M. A. (1986). Long-term memory in adulthood: An examination of the development of storage and retrieval processes at acquisition and retention.Developmental Review,6, 334–364.

    Article  Google Scholar 

  92. Howe, M. L., Kelland, A., Bryant-Brown, L., &Clark, S. L. (1992). Measuring the development of children’s amnesia and hypermnesia. In M. L. Howe, C. J. Brainerd, & V. F. Reyna (Eds.),Development of long-term retention (pp. 56–102). New York: Springer-Verlag.

    Google Scholar 

  93. Howe, M. L., &O’Sullivan, J. T. (1997). What children’s memories tell us about recalling our childhood: A review of storage and retrieval processes in the development of long-term retention.Developmental Review,17, 148–204.

    Article  Google Scholar 

  94. Howe, M. L., &Rabinowitz, F. M. (1996). Reasoning from memory: A lifespan inquiry into the necessity of remembering when reasoning about class inclusion.Journal of Experimental Child Psychology,61, 1–42.

    PubMed  Article  Google Scholar 

  95. Hu, X., &Batchelder, W. H. (1994a, August).Empirical Bayes approach for GPT models. Paper presented at the 27th Annual Meeting of the Society for Mathematical Psychology, Seattle.

  96. Hu, X., &Batchelder, W. H. (1994b). The statistical analysis of general processing tree models with the EM algorithim.Psychometrika,59, 21–47.

    Article  Google Scholar 

  97. Hulme, C., Roodenrys, S., Schweickert, R., Brown, G. D., Martin, S., &Stuart, G. (1997). Word-frequency effects on short-term memory tasks: Evidence for a redintegration process in immediate serial recall.Journal of Experimental Psychology: Learning, Memory, & Cognition,5, 1217–1232.

    Article  Google Scholar 

  98. Humphreys, M. S., &Bain, J. D. (1983). Recognition memory: A cue and information analysis.Memory & Cognition,11, 583–600.

    Article  Google Scholar 

  99. Humphreys, M. S., &Bowyer, P. A. (1980). Sequential testing effects and the relationship between recognition and recognition failure.Memory & Cognition,8, 271–277.

    Article  Google Scholar 

  100. Hutchinson, T. P. (1982). Some theories of performance in multiple choice tests and their implications for variants of the task.British Journal of Mathematical & Statistical Psychology,35, 71–89.

    Google Scholar 

  101. Jacoby, L. L. (1991). A process dissociation framework: Separating automatic from intentional uses of memory.Journal of Memory & Language,30, 513–541.

    Article  Google Scholar 

  102. Jacoby, L. L. (1998). Invariance in automatic influences of memory: Towards a user’s guide for the process-dissociation procedure.Journal of Experimental Psychology: Learning, Memory, & Cognition,24, 3–26.

    Article  Google Scholar 

  103. Jacoby, L. L., Toth, J. P., &Yonelinas, A. P. (1993). Separating conscious and unconscious influences of memory: Measuring recollection.Journal of Experimental Psychology: General,122, 139–154.

    Article  Google Scholar 

  104. Johnson, M. K., Kounios, J., &Reeder, J. A. (1994). Time-course studies of reality monitoring and recognition.Journal of Experimental Psychology: Learning, Memory, & Cognition,20, 1409–1419.

    Article  Google Scholar 

  105. Johnson-Laird, P. N., Byrne, R. M., &Schaeken, W. (1992). Propositional reasoning by model.Psychological Review,99, 418–439.

    PubMed  Article  Google Scholar 

  106. Jones, G. V. (1976). A fragmentation hypothesis of memory: Cued recall of pictures and of sequential position.Journal of Experimental Psychology: General,105, 277–293.

    Article  Google Scholar 

  107. Kail, R., Hale, C. A., Leonard, L. B., &Nippold, M. (1984). Lexical storage and retrieval in language-impaired children.Applied Psycholinguistics,5, 37–49.

    Article  Google Scholar 

  108. Kinchla, R. A. (1994). Comments on Batchelder and Riefer’s multinomial model for source monitoring.Psychological Review,101, 166–171.

    PubMed  Article  Google Scholar 

  109. Klauer, K. C., &Batchelder, W. H. (1996). Structural analysis of subjective categorical data.Psychometrika,61, 199–240.

    Article  Google Scholar 

  110. Klauer, K. C., &Oberauer, K. (1995). Testing the mental model theory of propositional reasoning.Quarterly Journal of Experimental Psychology,48A, 671–687.

    Google Scholar 

  111. Klauer, K. C., &Wegener, I. (1998). Unraveling social categorization in the “Who said what?” paradigm.Journal of Personality & Social Psychology,75, 1155–1178.

    Article  Google Scholar 

  112. Kraemer, H. C., Peabody, C. A., Tinklenberg, J. R., &Yesavage, J. A. (1983). Mathematical and empirical development of a test of memory for clinical and research use.Psychological Bulletin,94, 367–380.

    Article  Google Scholar 

  113. Krauth, J. (1982). Formulation and experimental verification of models in propositional reasoning.Quarterly Journal of Experimental Psychology,34, 285–298.

    Google Scholar 

  114. LaBerge, D., &Brown, V. (1989). Theory of attentional operations in shape identification.Psychological Review,96, 101–124.

    Article  Google Scholar 

  115. Light, L. L., LaVoie, D., Valencia-Laver, D., Albertson Owens, S. A., &Mead, G. (1992). Direct and indirect measures of memory for modality in young and older adults.Journal of Experimental Psychology: Learning, Memory, & Cognition,18, 1284–1297.

    Article  Google Scholar 

  116. Lindsay, D. S. (1993). Eyewitness suggestibility.Current Directions in Psychological Science,2, 86–89.

    Article  Google Scholar 

  117. Lindsay, D. S., Johnson, M. K., &Kwon, P. (1991). Developmental changes in memory source monitoring.Journal of Experimental Child Psychology,52, 297–318.

    PubMed  Article  Google Scholar 

  118. Loftus, E. F., Donders, K., Hoffman, H. G., &Schooler, J. W. (1989). Creating new memories that are quickly accessed and confidently held.Memory & Cognition,17, 607–616.

    Article  Google Scholar 

  119. Luce, R. D. (1959).Individual choice behavior. New York: Wiley.

    Google Scholar 

  120. Luce, R. D. (1963). A threshold theory for simple detection experiments.Psychological Review,70, 61–79.

    PubMed  Article  Google Scholar 

  121. Macmillan, N. A., &Creelman, C. D. (1991).Detection theory: A user’s guide. New York: Cambridge University Press.

    Google Scholar 

  122. Mandler, G. (1980). Recognizing: The judgment of previous occurrence.Psychological Review,87, 252–271.

    Article  Google Scholar 

  123. Marche, T. A., &Howe, M. L. (1995). Preschoolers report misinformation despite accurate memory.Developmental Psychology,31, 554–567.

    Article  Google Scholar 

  124. Massaro, D. W. (1987).Speech perception by ear and eye: A paradigm for psychological inquiry. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  125. McCloskey, M., &Zaragoza, M. (1985). Postevent information and memory: Reply to Loftus, Schooler, and Wagenaar.Journal of Experimental Psychology: General,114, 381–387.

    Article  Google Scholar 

  126. McLachlan, G. J., &Krishnan, T. (1997).The EM algorithm and extensions. New York: Wiley.

    Google Scholar 

  127. Mulder, G.,Sanders, A. F., &van Galen, G. P. (Eds.) (1995). Discrete and continuous information processing [Special issue].Acta Psychologica,90 (1–3).

    Google Scholar 

  128. Mulligan, N. W. (1996). The effects of perceptual interference at encoding on implicit memory, explicit memory, and memory for source.Journal of Experimental Psychology: Learning, Memory, & Cognition,22, 1067–1087.

    Article  Google Scholar 

  129. Mulligan, N. W., &Hirshman, E. (1997). Measuring the bases or recognition memory: An investigation of the process-dissociation framework.Journal of Experimental Psychology: Learning, Memory, & Cognition,23, 280–304.

    Article  Google Scholar 

  130. Nilsson, L.-G., &Gardiner, J. M. (1993). Identifying exceptions in a database of recognition failure studies from 1973 to 1992.Memory & Cognition,21, 397–410.

    Google Scholar 

  131. Offir, J. (1972). Stochastic learning models with distributions of parameters.Journal of Mathematical Psychology,9, 404–417.

    Article  Google Scholar 

  132. Payne, D. G., &Roediger, H. L., III (1987). Hypermnesia occurs in recall but not recognition.American Journal of Psychology,100, 145–165.

    PubMed  Article  Google Scholar 

  133. Piaget, J. (1952).The origins of intelligence in children. New York: International University Press.

    Google Scholar 

  134. Prinzmetal, W., Henderson, D., &Ivry, R. (1995). Loosening the constraints on illusory conjunctions: Assessing the roles of exposure duration and attention.Journal of Experimental Psychology: Human Perception & Performance,21, 1362–1375.

    Article  Google Scholar 

  135. Rabinowitz, F. M., Howe, M. L., &Lawrence, J. A. (1989). Class inclusion and working memory.Journal of Experimental Child Psychology,48, 379–409.

    Article  Google Scholar 

  136. Rasch, G. (1960).Probabilistic models for some intelligence and attainment tests. Copenhagen: Paedagogiske Institute.

    Google Scholar 

  137. Read, T. R. C., &Cressie, N. A. C. (1988).Goodness-of-fit statistics for discrete multivariate data. New York: Springer-Verlag.

    Google Scholar 

  138. Riefer, D. M. (1982). The advantages of mathematical modeling over traditional methods in the analysis of category clustering.Journal of Mathematical Psychology,26, 97–123.

    Article  Google Scholar 

  139. Riefer, D. M., &Batchelder, W. H. (1987, November).Further tests of a model for measuring storage and retrieval. Paper presented at the annual meeting of the Psychonomic Society, Seattle.

  140. Riefer, D. M., &Batchelder, W. H. (1988). Multinomial modeling and the measurement of cognitive processes.Psychological Review,95, 318–339.

    Article  Google Scholar 

  141. Riefer, D. M., &Batchelder, W. H. (1991a). Age differences in storage and retrieval: A multinomial modeling analysis.Bulletin of the Psychonomic Society,29, 415–418.

    Google Scholar 

  142. Riefer, D. M., &Batchelder, W. H. (1991b). Statistical inference for multinomial processing tree models. In. J.-P. Doignon & J.-C. G. Falmagne (Eds.),Mathematical psychology: Current developments (pp. 313–336). New York: Springer-Verlag.

    Google Scholar 

  143. Riefer, D. M., &Batchelder, W. H. (1995). A multinomial modeling analysis of the recognition-failure paradigm.Memory & Cognition,23, 611–630.

    Article  Google Scholar 

  144. Riefer, D. M., Hu, X., &Batchelder, W. H. (1994). Response strategies in source monitoring.Journal of Experimental Psychology: Learning, Memory, & Cognition,20, 680–693.

    Article  Google Scholar 

  145. Riefer, D. M., &LaMay, M. L. (1998). Memory for common and bizarre stimuli: A storage-retrieval analysis.Psychonomic Bulletin & Review,5, 312–317.

    Google Scholar 

  146. Riefer, D. M., &Rouder, J. N. (1992). A multinomial modeling analysis of the mnemonic benefits of bizarre imagery.Memory & Cognition,20, 601–611.

    Google Scholar 

  147. Rips, L. J. (1983). Cognitive processes in propositional reasoning.Psychological Review,90, 38–71.

    Article  Google Scholar 

  148. Romney, A. K., Batchelder, W. H., &Weller, S. C. (1987). Recent applications of consensus theory.American Behavior Scientist,31, 163–177.

    Article  Google Scholar 

  149. Romney, A. K., Weller, S. C., &Batchelder, W. H. (1986). Culture as consensus: A theory of culture and accuracy.American Anthropologist,88, 313–338.

    Article  Google Scholar 

  150. Ross, B. H., &Bower, G. H. (1981). Comparisons of models of associative recall.Memory & Cognition,9, 1–16.

    Article  Google Scholar 

  151. Ross, S. M. (1983).Stochastic processes. New York: Wiley.

    Google Scholar 

  152. 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.),Progress in mathematical psychology (pp. 195–225). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  153. Rumelhart, D. E., McClelland, J. L., &the PDP Research Group. (1986).Parallel distributed processing: Explorations in the microstructure of cognition. Vol. 1: Foundations. Cambridge, MA: MIT Press.

    Google Scholar 

  154. Schonfield, D., &Robertson, B. A. (1966). Memory storage and aging.Canadian Journal of Psychology,20, 228–236.

    PubMed  Google Scholar 

  155. Schweickert, R. (1993). A multinomial processing tree model for degradation and redintegration in immediate recall.Memory & Cognition,21, 168–175.

    Google Scholar 

  156. Skoff, B., &Chechile, R. A. (1977). Storage and retrieval processes in the serial position effect.Bulletin of the Psychonomic Society,9, 265–268.

    Google Scholar 

  157. Trabasso, T., &Bower, G. H. (1964).Attention in learning: Theory and research. New York: Wiley.

    Google Scholar 

  158. Treisman, A. M., &Schmidt, H. (1982). Illusory conjunctions in the perception of objects.Cognitive Psychology,14, 107–141.

    PubMed  Article  Google Scholar 

  159. Tulving, E., &Psotka, J. (1971). Retroactive inhibition in free recall: Inaccessibility of information available in the memory store.Journal of Experimental Psychology,87, 1–8.

    Article  Google Scholar 

  160. Tulving, E., &Wiseman, S. (1975). Relation between recognition and recognition failure of recallable words.Bulletin of the Psychonomic Society,6, 79–82.

    Google Scholar 

  161. Wagenaar, W. A., &Boer, J. P. A. (1987). Misleading postevent information: Testing parameterized models of integration in memory.Acta Psychologica,66, 291–306.

    Article  Google Scholar 

  162. Wainwright, M. J., &Reingold, E. M. (1996). Response bias correction in the process dissociation procedure: Approaches, assumptions, and evaluation.Consciousness & Cognition,5, 232–254.

    Article  Google Scholar 

  163. Wason, P. C. (1966). Reasoning. In B. M. Foss (Ed.),New horizons in psychology I (pp. 135–151). Harmondsworth, U.K.: Penguin.

    Google Scholar 

  164. Waugh, N. C., &Norman, D. A. (1965). Primary memory.Psychological Review,72, 89–104.

    PubMed  Article  Google Scholar 

  165. White, H. (1982). Maximum likelihood estimation of misspecified models.Econometrika,50, 1–26.

    Article  Google Scholar 

  166. White, H. (1994).Estimation, inference, and specification analysis. New York: Cambridge University Press.

    Google Scholar 

  167. Wickens, T. D. (1982).Models for behavior: Stochastic processes in psychology. San Francisco: Freeman.

    Google Scholar 

  168. Yonelinas, A. P. (1994). Receiver-operating characteristics in recognition memory: Evidence for a dual-process model.Journal of Experimental Psychology: Learning, Memory, & Cognition,20, 1341–1354.

    Article  Google Scholar 

  169. Yonelinas, A. P., &Jacoby, L. L. (1996). Response bias and the process dissociation procedure.Journal of Experimental Psychology: General,125, 422–434.

    Article  Google Scholar 

  170. Yonelinas, A. P., Regehr, G., Jacoby, L. L. (1995). Incorporating response bias in a dual-process theory of memory.Journal of Memory & Language,34, 821–835.

    Article  Google Scholar 

Download references

Author information

Affiliations

  1. Department of Cognitive Sciences, University of California, 92697, Irvine, CA

    William H. Batchelder

  2. California State University, San Bernardino, California

    David M. Riefer

Authors
  1. William H. Batchelder
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David M. Riefer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to William H. Batchelder.

Additional information

This research was supported by NSF Grant SBR-9309667. The authors thank Associate Editor Richard Schweickert and Richard Chechile, Mark Howe, Kevin Murnane, and James Townsend for helpful reviews of an earlier draft of this paper. The authors also thank Ece Batchelder, Edgar Erdfelder, Xiangen Hu, and Christoph Klauer for comments on various aspects of this project.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Batchelder, W.H., Riefer, D.M. Theoretical and empirical review of multinomial process tree modeling. Psychonomic Bulletin & Review 6, 57–86 (1999). https://doi.org/10.3758/BF03210812

Download citation

Keywords

  • Journal ofExperimental Psychology
  • Source Monitoring
  • Hindsight Bias
  • Recognition Failure
  • Illusory Conjunction