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multiTree: A computer program for the analysis of multinomial processing tree models

Behavior Research Methods volume 42, pages42–54(2010)Cite this article

Abstract

Multinomial processing tree (MPT) models are a family of stochastic models for psychology and related sciences that can be used to model observed categorical frequencies as a function of a sequence of latent states. For the analysis of such models, the present article presents a platform-independent computer program called multiTree, which simplifies the creation and the analysis of MPT models. This makes them more convenient to implement and analyze. Also, multiTree offers advanced modeling features. It provides estimates of the parameters and their variability, goodness-of-fit statistics, hypothesis testing, checks for identifiability, parametric and nonparametric bootstrapping, and power analyses. In this article, the algorithms underlying multiTree are given, and a user guide is provided. The multiTree program can be downloaded from http://psycho3.uni-mannheim.de/multitree.

References

  1. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723.

    Article  Google Scholar 

  2. 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 

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

    PubMed  Article  Google Scholar 

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

    Article  Google Scholar 

  5. Batchelder, W. H., & Riefer, D. M. (1999). Theoretical and empirical review of multinomial process tree modeling. Psychonomic Bulletin & Review, 6, 57–86.

    Article  Google Scholar 

  6. Birch, M. W. (1964). A new proof of the Pearson-Fisher theorem. Annals of Mathematical Statistics, 35, 817–824.

    Article  Google Scholar 

  7. Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Erlbaum.

    Google Scholar 

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

    Google Scholar 

  9. Dodson, C. S., Prinzmetal, W., & Shimamura, A. P. (1998). Using Excel to estimate parameters from observed data: An example from source memory data. Behavior Research Methods, Instruments, & Computers, 30, 517–526.

    Article  Google Scholar 

  10. Efron, B., & Tibshirani, R. J. (1997). An introduction to the bootstrap. New York: Chapman & Hall.

    Google Scholar 

  11. Erdfelder, E. (2000). Multinomiale Modele in der kognitiven Psychologie [Multinomial models in cognitive psychology]. Unpublished habilitation thesis, Friedrich-Wilhelms University, Bonn.

    Google Scholar 

  12. Erdfelder, E., Auer, T.-S., Hilbig, B. E., Aßfalg, A., Moshagen, M., & Nadarevic, L. (2009). Multinomial processing tree models: A review of the literature. Zeitschrift für Psychologie/Journal of Psychology, 217, 108–124.

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. Erdfelder, E., Faul, F., & Buchner, A. (2005). Power analysis for categorical methods. In B. Everitt & D. Howell (Eds.), Encyclopedia of statistics in behavioral science (pp. 1565–1570). Chichester, U.K.: Wiley.

    Google Scholar 

  15. Faul, F., Erdfelder, E., Lang, A., & Buchner, A. (2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39, 175–191.

    PubMed  Article  Google Scholar 

  16. García-Pérez, M. A. (1994). Parameter estimation and goodness-of-fit testing in multinomial models. British Journal of Mathematical & Statistical Psychology, 47, 247–282.

    Google Scholar 

  17. Hu, X. (1999). Multinomial processing tree models: An implementation. Behavior Research Methods, Instruments, & Computers, 31, 689–695.

    Article  Google Scholar 

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

    Article  Google Scholar 

  19. Hu, X., & Phillips, G. A. (1999). GPT.EXE: A powerful tool for the visualization and analysis of general processing tree models. Behavior Research Methods, Instruments, & Computers, 31, 220–234.

    Article  Google Scholar 

  20. Johnson, M. K., Foley, M. A., & Leach, K. (1988). The consequences for memory of imagining in another person’s voice. Memory & Cognition, 16, 337–342.

    Article  Google Scholar 

  21. Kenny, D. A. (1979). Correlation and causality. New York: Wiley.

    Google Scholar 

  22. Klauer, K. C. (2006). Hierarchical multinomial processing tree models: A latent-class approach. Psychometrika, 71, 7–31.

    Article  Google Scholar 

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

    Google Scholar 

  24. Knapp, B. R., & Batchelder, W. H. (2004). Representing parametric order constraints in multi-trial applications of multinomial processing tree models. Journal of Mathematical Psychology, 48, 215–229.

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  27. Riefer, D. M., & Batchelder, W. H. (1991). Statistical inference for multinomial processing tree models. In J.-P. Doignon & J.-C. Falmagne (Eds.), Mathematical psychology: Current developments (pp. 313–335). Berlin: Springer.

    Google Scholar 

  28. Rose, R. G., Rose, P. R., King, N., & Perez, A. (1975). Bilingual memory for related and unrelated sentences. Journal of Experimental Psychology: Human Learning & Memory, 1, 599–606.

    Article  Google Scholar 

  29. Rothkegel, R. (1999). AppleTree: A multinomial processing tree mod-eling program for Macintosh computers. Behavior Research Methods, Instruments, & Computers, 31, 696–700.

    Article  Google Scholar 

  30. Rouder, J. N., & Batchelder, W. H. (1998). Multinomial models for measuring storage and retrieval processes in paired associate learning. In C. E. Dowling, F. S. Roberts, & P. Theuns (Eds.), Recent progress in mathematical psychology (pp. 195–225). Mahwah, NJ: Erlbaum.

    Google Scholar 

  31. Saegert, J., Hamayan, E., & Ahmar, H. (1975). Memory for language of input in polyglots. Journal of Experimental Psychology: Human Learning & Memory, 1, 607–613.

    Article  Google Scholar 

  32. Schwartz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461–464.

    Article  Google Scholar 

  33. Smith, J. B., & Batchelder, W. H. (2008). Assessing individual differences in categorical data. Psychonomic Bulletin & Review, 15, 713–731.

    Article  Google Scholar 

  34. Smith, P. L. (1998). Attention and luminance detection: A quantitative analysis. Journal of Experimental Psychology: Human Perception & Performance, 24, 105–133.

    Article  Google Scholar 

  35. Stahl, C., & Klauer, K. C. (2007). HMMTree: A computer program for latent-class hierarchical multinomial processing tree models. Behavior Research Methods, 39, 267–273.

    PubMed  Article  Google Scholar 

  36. Wagenmakers, E.-J., & Farrell, S. (2004). AIC model selection using Akaike weights. Psychonomic Bulletin & Review, 11, 192–196.

    Article  Google Scholar 

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Affiliations

  1. University of Düsseldorf, Düsseldorf, Germany

    Morten Moshagen

  2. Lehrstuhl Psychologie III, University of Mannheim, Schloss EO 254, 68131, Mannheim, Germany

    Morten Moshagen

Authors
  1. Morten Moshagen
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Correspondence to Morten Moshagen.

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Moshagen, M. multiTree: A computer program for the analysis of multinomial processing tree models. Behavior Research Methods 42, 42–54 (2010). https://doi.org/10.3758/BRM.42.1.42

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Keywords

  • Parametric Bootstrap
  • Source Monitoring
  • Category Probability
  • Text Field
  • Order Constraint