Bayesian Estimation of Multinomial Processing Tree Models with Heterogeneity in Participants and Items
- 851 Downloads
Multinomial processing tree (MPT) models are theoretically motivated stochastic models for the analysis of categorical data. Here we focus on a crossed-random effects extension of the Bayesian latent-trait pair-clustering MPT model. Our approach assumes that participant and item effects combine additively on the probit scale and postulates (multivariate) normal distributions for the random effects. We provide a WinBUGS implementation of the crossed-random effects pair-clustering model and an application to novel experimental data. The present approach may be adapted to handle other MPT models.
Key wordsmultinomial processing tree model parameter heterogeneity crossed-random effects model hierarchical Bayesian modeling
We thank Helen Steingroever for her help with the data collection and Ute Bayen for her considerable effort in providing us with data, which we were unfortunately unable to analyze.
- 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, 144–151. Google Scholar
- Batchelder, W.H. (2009). Cognitive psychometrics: using multinomial processing tree models as measurement tools. In S.E. Embretson (Ed.), Measuring psychological constructs: Advances in model based measurement (pp. 71–93). Washington: American Psychological Association. Google Scholar
- Batchelder, W.H., & Riefer, D.M. (2007). Using multinomial processing tree models to measure cognitive deficits in clinical populations. In R. Neufeld (Ed.), Advances in clinical cognitive science: formal modeling of processes and symptoms (pp. 19–50). Washington: American Psychological Association. CrossRefGoogle Scholar
- Brooks, S.B., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics, 7, 434–455. Google Scholar
- De Boeck, P., & Partchev, I. (2012). IRTTrees: tree-based item response models of the GLMM family. Journal of Statistical Software, 48, 1–28. Google Scholar
- Deese, J. (1960). Frequency of usage and number of words in free recall: the role of association. Psychological Reports, 337–344. Google Scholar
- Gamerman, D., & Lopes, H.F. (2006). Markov chain Monte Carlo: stochastic simulation for Bayesian inference. Boca Raton: Chapman & Hal/CRC. Google Scholar
- Gelman, A., Carlin, J.B., Stern, H.S., & Rubin, D.B. (2003). Bayesian data analysis. Boca Raton: Chapman & Hall. Google Scholar
- Gelman, A., & Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge: Cambridge University Press. Google Scholar
- Gelman, A., Meng, X., & Stern, H. (1996). Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica, 6, 733–807. Google Scholar
- Gilks, W.R., Richardson, S., & Spiegelhalter, D.J. (1996). Markov chain Monte Carlo in practice. Boca Raton: Chapman & Hall/CRC. Google Scholar
- Gill, J. (2002). Bayesian methods: a social and behavioral sciences approach. New York: Chapman & Hall. Google Scholar
- Gregg, V.H. (1976). Word frequency, recognition and recall. In J. Brown (Ed.), Recall and recognition (pp. 183–216). London: Wiley. Google Scholar
- Hall, J.F. (1954). Learning as a function of word-frequency. The American Journal of Psychology, 138–140. Google Scholar
- Hintze, J.L., & Nelson, R.D. (1998). Violin plots: a box plot-density trace synergism. American Statistician, 52, 181–184. Google Scholar
- Kruschke, J.K. (2010). Doing Bayesian data analysis: a tutorial introduction with R and BUGS. Burlington: Academic Press. Google Scholar
- Lee, M.D., & Newell, B.R. (2011). Using hierarchical Bayesian methods to examine the tools of decision-making. Judgment and Decision Making, 6, 832–842. Google Scholar
- Lee, M. D., & Wagenmakers, E.J. (in press). Bayesian modeling for cognitive science: a practical course. Cambridge: Cambridge University Press. Google Scholar
- Lord, F.M., & Novick, M.R. (1986). Statistical theories of mental test scores. Reading: Addison-Wesley. Google Scholar
- Lunn, D., Jackson, C., Best, N., Thomas, A., & Spiegelhalter, D. (2012). The BUGS book: a practical introduction to Bayesian analysis. Boca Raton: CRC Press/Chapman and Hall. Google Scholar
- Plummer, M. (2003). JAGS: a program for analysis of Bayesian graphical models using Gibbs sampling [Computer software manual]. Retrieved from http://citeseer.ist.psu.edu/plummer03jags.html.
- Spiegelhalter, D.J., Thomas, A., Best, N.G., Gilks, W.R., & Lunn, D. (2003). BUGS: Bayesian inference using Gibbs sampling [Computer software manual]. Retrieved from http://www.mrc-bsu.cam.ac.uk/bugs/.
- Stan Development Team (2012). Stan modeling language [Computer software manual]. Retrieved from http://mc-stan.org/.
- Wickelmaier, F. (2011). Mpt: multinomial processing tree (MPT) models [Computer software manual]. Retrieved from http://cran.r-project.org/web/packages/mpt/index.html.