Published

2014-07-01

Hierarchical Graphical Bayesian Models in Psychology

Modelos Bayesianos gráficos jerárquicos en psicología

DOI:

https://doi.org/10.15446/rce.v37n2spe.47940

Keywords:

Visual Statistics, Graphical Models, Bayesian Statistics, Hierarchical Models, Psychology, Statistical Cognition (en)
Cognición estadística, Estadística Bayesiana, Estadística visual, Modelos gráficos, Modelos jerárquicos, Psicología (es)

Downloads

Authors

  • Guillermo Campitelli Edith Cowan University, Mount Lawley, Australia
  • Guillermo Macbeth Universidad Nacional de Entre Ríos, Argentina

The improvement of graphical methods in psychological research can promote their use and a better comprehension of their expressive power. The application of hierarchical Bayesian graphical models has recently become more frequent in psychological research. The aim of this contribution is to introduce suggestions for the improvement of hierarchical Bayesian graphical models in psychology. This novel set of suggestions stems from the description and comparison between two main approaches concerned with the use of plate notation and distribution pictograms. It is concluded that the combination of relevant aspects of both models might improve the use of powerful hierarchical Bayesian graphical models in psychology.

El mejoramiento de los métodos gráficos en la investigación en psicología puede promover su uso y una mejor compresión de su poder de expresión. La aplicación de modelos Bayesianos gráficos jerárquicos se ha vuelto más frecuente en la investigación en psicología. El objetivo de este trabajo es introducir sugerencias para el mejoramiento de los modelos Bayesianos gráficos jerárquicos en psicología. Este conjunto de sugerencias se apoya en la descripción y comparación entre los dos enfoques principales con el uso de notación y pictogramas de distribución. Se concluye que la combinación de los aspectos relevantes de ambos puede mejorar el uso de los modelos Bayesianos gráficos jerárquicos en psicología

https://doi.org/10.15446/rce.v37n2spe.47940

Hierarchical Graphical Bayesian Models in Psychology

Modelos Bayesianos gráficos jerárquicos en psicología

GUILLERMO CAMPITELLI1, GUILLERMO MACBETH2

1Edith Cowan University, School of Psychology and Social Science, Mount Lawley, Australia. Lecturer. Email: gjcampitelli@gmail.com
2Universidad Nacional de Entre Ríos, Facultad de Ciencias de la Educación, Argentina. Professor. Email: g.macbeth@conicet.gov.ar

Abstract

The improvement of graphical methods in psychological research can promote their use and a better comprehension of their expressive power. The application of hierarchical Bayesian graphical models has recently become more frequent in psychological research. The aim of this contribution is to introduce suggestions for the improvement of hierarchical Bayesian graphical models in psychology. This novel set of suggestions stems from the description and comparison between two main approaches concerned with the use of plate notation and distribution pictograms. It is concluded that the combination of relevant aspects of both models might improve the use of powerful hierarchical Bayesian graphical models in psychology.

Key words: Visual Statistics, GraphicalModels, Bayesian Statistics, Hierarchical Models, Psychology, StatisticalCognition.

Resumen

El mejoramiento de los métodos gráficos en la investigación en psicología puede promover su uso y una mejor compresión de su poder de expresión. La aplicación de modelos Bayesianos gráficos jerárquicos se ha vuelto más frecuente en la investigación en psicología. El objetivo de este trabajo es introducir sugerencias para el mejoramiento de los modelos Bayesianos gráficos jerárquicos en psicología. Este conjunto de sugerencias se apoya en la descripción y comparación entre los dos enfoques principales con el uso de notación y pictogramas de distribución. Se concluye que la combinación de los aspectos relevantes de ambos puede mejorar el uso de los modelos Bayesianos gráficos jerárquicos en psicología

Palabras clave: cognición estadística, estadística Bayesiana, estadística visual, modelos gráficos, modelos jerárquicos, psicología.

Texto completo disponible en PDF

References

1. Ahn, W.-Y., Krawitz, A., Kim, W., Busemeyer, J. R. & Brown, J. W. (2011), 'A model-based FMRI analysis with hierarchical Bayesian parameter estimation', Journal of Neuroscience, Psychology, and Economics 4(2), 95-110.

2. Bauer, M. I. & Johnson-Laird, P. N. (1993), 'How diagrams can improve reasoning', Psychological Science 4(6), 372-378.

3. Beyth Marom, R., Fidler, F. & Cumming, G. (2008), 'Statistical cognition: towards evidence-based practice in statistics and statistics education', Statistics Education Research Journal 7(2), 20-39.

4. Bolstad, W. M. (2007), Introduction to Bayesian Statistics, 2 edn, Wiley Jobs in Hoboken, New York.

5. Bridwell, D. A., Hecker, E. A., Serences, J. T. & Srinivasan, R. (2013), 'Individual differences in attention strategies during detection, fine discrimination, and coarse discrimination', Journal of Neurophysiology 110, 784-794.

6. Buntine, W. L. (1994), 'Operations for learning with graphical models', Journal of Artificial Intelligence Research 2, 159-225.

7. Bååth, R. (2013), Distribution diagram R scripts. *https://github.com/rasmusab/distribution_diagrams

8. Dienes, Z. (2011), 'Bayesian versus orthodox statistics: which side are you on?', Perspectives on Psychological Science 6, 274-290.

9. Dyjas, O., Grasman, R. P., Wetzels, R., van der Maas, H. L. & Wagenmakers, E. (2012), 'A Bayesian hierarchical analysis of the name-letter effect', Frontiers in Psychology 3(334), 1-14. doi: 10.3389/fpsyg.2012.00334.

10. Edwards, W., Lindman, H. & Savage, L. J. (1963), 'Bayesian statistical inference for psychological research', Psychological Review 70, 193-242.

11. Gilks, W. R., Thomas, A. & Spiegelhalter, D. J. (1994), 'A language and program for complex Bayesian modelling', The Statistician 43, 169-177.

12. Good, I. J. (1980), 'Some history of the hierarchical Bayesian methodology', Trabajos de Estadística y de Investigación Operativa 31(1), 489-519.

13. Gray, K. & Wegner, D. M. (2013), 'Six guidelines for interesting research', Perspectives on Psychological Science 8(5), 549-553.

14. Griffiths, T. L., Kemp, C. & Tenenbaum, J. B. (2008), Bayesian models of cognition, 'The Cambridge Handbook of Computational Psychology', Cambridge University Press, Cambridge, New York, p. 59-100.

15. Heit, E. & Rotello, C. (2005), Are there two kinds of reasoning?, 'Proceedings of the 27th Annual Conference of the Cognitive Science Society', Lawrence, Erlbaum, Mahwah, New Jersey.

16. Jordan, M. I. (2004), 'Graphical models', Statistical Science 19, 140-155.

17. Koller, D. & Friedman, N. (2009), Probabilistic Graphical Models: Principles and Techniques, MIT press, Cambridge, MA.

18. Koller, D., Friedman, N., Getoor, L. & Taskar, B. (2007), Graphical models in a nutshell, 'Introduction to statistical relational learning', MIT Press, Cambridge, Massachusetts.

19. Kruschke, J. K. (2010a), Doing Bayesian Data Analysis: A Tutorial with R and BUGS, Academic Press, Burlington, MA.

20. Kruschke, J. K. (2010b), 'What to believe: bayesian methods for data analysis', Trends in Cognitive Science 14, 293-300.

21. Kruschke, J. K. (2013), 'Bayesian estimation supersedes the t test', Journal of Experimental Psychology: General 142, 573-603.

22. Kruschke, J. K., Aguinis, H. & Joo, H. (2012), 'The time has come: Bayesian methods for data analysis in the organizational sciences', Organizational Research Methods 15, 722-752.

23. Lee, M. D. (2008), 'Three case studies in the Bayesian analysis of cognitive models', Psychonomic Bulletin and Review 15, 1-15.

24. Lee, M. D. (2011), 'How cognitive modeling can benefit from hierarchical Bayesian models', Journal of Mathematical Psychology 55, 1-7.

25. 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.

26. Lee, M. D. & Wagenmakers, E.-J. (2005), 'Postscript: Bayesian statistical inference in psychology: Comment on Trafimow (2003)', Psychological Review 112(3), 662-668.

27. Lee, M. D. & Wagenmakers, E.-J. (2014), 'Bayesian cognitive modeling: A practical course', New York: Cambridge University Press.

28. Lodewyckx, T., Kim, W., Lee, M. D., Tuerlinckx, F., Kuppens, P. & Wagenmakers, E. J. (2011), 'A tutorial on Bayes factor estimation with the product space method', Journal of Mathematical Psychology 55, 331-347.

29. Lunn, D. J., Thomas, A., Best, N. & Spiegelhalter, D. (2000), 'A Bayesian modelling framework: Concepts, structure, and extensibility', Statistics and Computing 10, 325-337.

30. Nosofsky, R. M. (1984), 'Choice, similarity, and the context theory of classification', Journal of Experimental Psychology: Learning, Memory and Cognition 10, 104-114.

31. Nosofsky, R. M. (1986), 'Attention, similarity, and the identification\textendashcategorization relationship', Journal of Experimental Psychology: General 115, 39-57.

32. Orhan, A. E. & Jacobs, R. A. (2013), 'A probabilistic clustering theory of the organization of visual short-term memory', Psychological Review 120, 297-328.

33. Pearl, J. (2009), 'Causal inference in statistics: an overview', Statistics Surveys 3, 96-146.

34. R Development Core Team, (2013), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. *http://www.R-project.org

35. Scheibehenne, B., Rieskamp, J. & Wagenmakers, E.-J. (2013), 'Testing adaptive toolbox models: A Bayesian hierarchical approach', Psychological Review 120, 39-64.

36. Schneider, T. (2013), Diagram for Hierarchical Models. *https://github.com/tinu-schneider/DBDA_hierach_diagram

37. Shepard, R. N. (1962), 'The analysis of proximities: multidimensional scaling with an unknown distance function. I', Psychometrika 27(2), 125-140.

38. Shepard, R. N. (1980), 'Multidimensional scaling, tree-fitting, and clustering', Science 210, 390-398.

39. Spiegelhalter, D., Thomas, A., Best, N. & Gilks, W. (1996), BUGS 0.5* Examples Volume 2 (version ii), 2 edn, MRC Biostatistics Unit.

40. Stenning, K. & Oberlander, J. (1995), 'A cognitive theory of graphical and linguistic reasoning: logic and implementation', Cognitive Science 19(1), 97-140.

41. Steyvers, M., Lee, M. D. & Wagenmakers, E.-J. (2009), 'Bayesian analysis of human decision-making on bandit problems', Journal of Mathematical Psychology 53(3), 168-179.

42. Wagenmakers, E. (2007), 'A practical solution to the pervasive problems of p values', Psychonomic Bulletin and Review 14, 779-804.

43. Wickens, C. D., Merwin, D. H. & Lin, E. L. (1994), 'Implications of graphics enhancements for the visualization of scientific data: dimensional integrality, stereopsis, motion, and mesh', Human Factors 36(1), 44-61.

44. van Ravenzwaaij, D., Moore, C. P., Lee, M. D. & Newell, B. R. (2014), 'A hierarchical Bayesian modeling approach to searching and stopping in multi-attribute judgment', Cognitive Science 38, 1384-1405.

[Recibido en mayo de 2014. Aceptado en septiembre de 2014]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv37n2a05,
    AUTHOR  = {Campitelli, Guillermo and Macbeth, Guillermo},
    TITLE   = {{Hierarchical Graphical Bayesian Models in Psychology}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2014},
    volume  = {37},
    number  = {2},
    pages   = {319-339}
}

References

Ahn, W.-Y., Krawitz, A., Kim, W., Busemeyer, J. R. & Brown, J. W. (2011), ‘A model-based FMRI analysis with hierarchical Bayesian parameter estimation’, Journal of Neuroscience, Psychology, and Economics 4(2), 95–110.

Bauer, M. I. & Johnson-Laird, P. N. (1993), ‘How diagrams can improve reasoning’, Psychological Science 4(6), 372–378.

Beyth Marom, R., Fidler, F. & Cumming, G. (2008), ‘Statistical cognition: Towards evidence-based practice in statistics and statistics education’, Statistics Education Research Journal 7(2), 20–39.

Bolstad, W. M. (2007), Introduction to Bayesian Statistics, 2 edn, Wiley Jobs in Hoboken, New York.

Bridwell, D. A., Hecker, E. A., Serences, J. T. & Srinivasan, R. (2013), ‘Individual differences in attention strategies during detection, fine discrimination, and coarse discrimination’, Journal of Neurophysiology 110, 784–794.

Bååth, R. (2013), Distribution diagram R scripts. *https://github.com/rasmusab/distribution_diagrams

Buntine, W. L. (1994), ‘Operations for learning with graphical models’, Journal of Artificial Intelligence Research 2, 159–225.

Dienes, Z. (2011), ‘Bayesian versus orthodox statistics: Which side are you on?’, Perspectives on Psychological Science 6, 274–290.

Dyjas, O., Grasman, R. P., Wetzels, R., van der Maas, H. L. & Wagenmakers, E. (2012), ‘A Bayesian hierarchical analysis of the name-letter effect’, Frontiers in Psychology 3(334), 1–14. doi: 10.3389/fpsyg.2012.00334.

Edwards, W., Lindman, H. & Savage, L. J. (1963), ‘Bayesian statistical inference for psychological research’, Psychological Review 70, 193–242.

Gilks, W. R., Thomas, A. & Spiegelhalter, D. J. (1994), ‘A language and program for complex Bayesian modelling’, The Statistician 43, 169–177.

Good, I. J. (1980), ‘Some history of the hierarchical Bayesian methodology’, Trabajos de Estadística y de Investigación Operativa 31(1), 489–519.

Gray, K. & Wegner, D. M. (2013), ‘Six guidelines for interesting research’, Perspectives on Psychological Science 8(5), 549–553.

Griffiths, T. L., Kemp, C. & Tenenbaum, J. B. (2008), Bayesian models of cognition, in R. Sun, ed., ‘The Cambridge Handbook of Computational Psychology’, Cambridge University Press, Cambridge, New York, pp. 59–100.

Heit, E. & Rotello, C. (2005), Are there two kinds of reasoning?, in B. G. Bara, L. W. Barsalou & M. Bucciarelli, eds, ‘Proceedings of the 27th Annual Conference of the Cognitive Science Society’, Lawrence, Erlbaum, Mahwah, New Jersey.

Jordan, M. I. (2004), ‘Graphical models’, Statistical Science 19, 140–155.

Koller, D. & Friedman, N. (2009), Probabilistic Graphical Models: Principles and Techniques, MIT press, Cambridge, MA.

Koller, D., Friedman, N., Getoor, L. & Taskar, B. (2007), Graphical models in a nutshell, in L. Getoor & B. Taskar, eds, ‘Introduction to statistical relational learning’, MIT Press, Cambridge, Massachusetts.

Kruschke, J. K. (2010a), Doing Bayesian Data Analysis: A Tutorial with R and BUGS, Academic Press, Burlington, MA.

Kruschke, J. K. (2010b), ‘What to believe: Bayesian methods for data analysis’, Trends in Cognitive Science 14, 293–300.

Kruschke, J. K. (2013), ‘Bayesian estimation supersedes the t test’, Journal of Experimental Psychology: General 142, 573–603.

Kruschke, J. K., Aguinis, H. & Joo, H. (2012), ‘The time has come: Bayesian methods for data analysis in the organizational sciences’, Organizational Research Methods 15, 722–752.

Lee, M. D. (2008), ‘Three case studies in the Bayesian analysis of cognitive models’, Psychonomic Bulletin and Review 15, 1–15.

Lee, M. D. (2011), ‘How cognitive modeling can benefit from hierarchical Bayesian models’, Journal of Mathematical Psychology 55, 1–7.

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.

Lee, M. D. & Wagenmakers, E.-J. (2005), ‘Postscript: Bayesian statistical inference in psychology: Comment on Trafimow (2003)’, Psychological Review 112(3), 662–668.

Lee, M. D. & Wagenmakers, E.-J. (2014), ‘Bayesian cognitive modeling: A practical course’, New York: Cambridge University Press .

Lodewyckx, T., Kim, W., Lee, M. D., Tuerlinckx, F., Kuppens, P. &Wagenmakers, E. J. (2011), ‘A tutorial on Bayes factor estimation with the product space method’, Journal of Mathematical Psychology 55, 331–347.

Lunn, D. J., Thomas, A., Best, N. & Spiegelhalter, D. (2000), ‘A Bayesian modelling framework: Concepts, structure, and extensibility’, Statistics and Computing 10, 325–337.

Nosofsky, R. M. (1984), ‘Choice, similarity, and the context theory of classification’, Journal of Experimental Psychology: Learning, Memory and Cognition 10, 104–114.

Nosofsky, R. M. (1986), ‘Attention, similarity, and the identification– categorization relationship’, Journal of Experimental Psychology: General 115, 39–57.

Orhan, A. E. & Jacobs, R. A. (2013), ‘A probabilistic clustering theory of the organization of visual short-term memory’, Psychological Review 120, 297– 328.

Pearl, J. (2009), ‘Causal inference in statistics: An overview’, Statistics Surveys 3, 96–146.

R Development Core Team (2013), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.

*http://www.R-project.org

Scheibehenne, B., Rieskamp, J. & Wagenmakers, E.-J. (2013), ‘Testing adaptive toolbox models: A Bayesian hierarchical approach’, Psychological Review 120, 39–64.

Schneider, T. (2013), Diagram for Hierarchical Models.

*https://github.com/tinu-schneider/DBDA_hierach_diagram

Shepard, R. N. (1962), ‘The analysis of proximities: Multidimensional scaling with an unknown distance function. I’, Psychometrika 27(2), 125–140.

Shepard, R. N. (1980), ‘Multidimensional scaling, tree-fitting, and clustering’, Science 210, 390–398.

Spiegelhalter, D., Thomas, A., Best, N. & Gilks, W. (1996), BUGS 0.5* Examples Volume 2 (version ii), 2 edn, MRC Biostatistics Unit.

Stenning, K. & Oberlander, J. (1995), ‘A cognitive theory of graphical and linguistic reasoning: Logic and implementation’, Cognitive Science 19(1), 97–140.

Steyvers, M., Lee, M. D. & Wagenmakers, E.-J. (2009), ‘Bayesian analysis of human decision-making on bandit problems’, Journal of Mathematical Psychology 53(3), 168–179.

van Ravenzwaaij, D., Moore, C. P., Lee, M. D. & Newell, B. R. (2014), ‘A hierarchical Bayesian modeling approach to searching and stopping in multi-attribute judgment’, Cognitive Science 38, 1384–1405.

Wagenmakers, E. (2007), ‘A practical solution to the pervasive problems of p values’, Psychonomic Bulletin and Review 14, 779–804.

Wickens, C. D., Merwin, D. H. & Lin, E. L. (1994), ‘Implications of graphics enhancements for the visualization of scientific data: Dimensional integrality, stereopsis, motion, and mesh’, Human Factors 36(1), 44–61.

How to Cite

APA

Campitelli, G. and Macbeth, G. (2014). Hierarchical Graphical Bayesian Models in Psychology. Revista Colombiana de Estadística, 37(2Spe), 319–339. https://doi.org/10.15446/rce.v37n2spe.47940

ACM

[1]
Campitelli, G. and Macbeth, G. 2014. Hierarchical Graphical Bayesian Models in Psychology. Revista Colombiana de Estadística. 37, 2Spe (Jul. 2014), 319–339. DOI:https://doi.org/10.15446/rce.v37n2spe.47940.

ACS

(1)
Campitelli, G.; Macbeth, G. Hierarchical Graphical Bayesian Models in Psychology. Rev. colomb. estad. 2014, 37, 319-339.

ABNT

CAMPITELLI, G.; MACBETH, G. Hierarchical Graphical Bayesian Models in Psychology. Revista Colombiana de Estadística, [S. l.], v. 37, n. 2Spe, p. 319–339, 2014. DOI: 10.15446/rce.v37n2spe.47940. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/47940. Acesso em: 18 mar. 2025.

Chicago

Campitelli, Guillermo, and Guillermo Macbeth. 2014. “Hierarchical Graphical Bayesian Models in Psychology”. Revista Colombiana De Estadística 37 (2Spe):319-39. https://doi.org/10.15446/rce.v37n2spe.47940.

Harvard

Campitelli, G. and Macbeth, G. (2014) “Hierarchical Graphical Bayesian Models in Psychology”, Revista Colombiana de Estadística, 37(2Spe), pp. 319–339. doi: 10.15446/rce.v37n2spe.47940.

IEEE

[1]
G. Campitelli and G. Macbeth, “Hierarchical Graphical Bayesian Models in Psychology”, Rev. colomb. estad., vol. 37, no. 2Spe, pp. 319–339, Jul. 2014.

MLA

Campitelli, G., and G. Macbeth. “Hierarchical Graphical Bayesian Models in Psychology”. Revista Colombiana de Estadística, vol. 37, no. 2Spe, July 2014, pp. 319-3, doi:10.15446/rce.v37n2spe.47940.

Turabian

Campitelli, Guillermo, and Guillermo Macbeth. “Hierarchical Graphical Bayesian Models in Psychology”. Revista Colombiana de Estadística 37, no. 2Spe (July 1, 2014): 319–339. Accessed March 18, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/47940.

Vancouver

1.
Campitelli G, Macbeth G. Hierarchical Graphical Bayesian Models in Psychology. Rev. colomb. estad. [Internet]. 2014 Jul. 1 [cited 2025 Mar. 18];37(2Spe):319-3. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/47940

Download Citation

CrossRef Cited-by

CrossRef citations3

1. Guillermo Campitelli, Guillermo Macbeth, Raydonal Ospina, Fernando Marmolejo-Ramos. (2017). Three Strategies for the Critical Use of Statistical Methods in Psychological Research. Educational and Psychological Measurement, 77(5), p.881. https://doi.org/10.1177/0013164416668234.

2. Samantha Low-Choy, Tasha Riley, Clair Alston-Knox. (2017). Using Bayesian statistical modelling as a bridge between quantitative and qualitative analyses: illustrated via analysis of an online teaching tool. Educational Media International, 54(4), p.317. https://doi.org/10.1080/09523987.2017.1397404.

3. David A. Ellis, Hannah L. Merdian. (2015). Thinking Outside the Box: Developing Dynamic Data Visualizations for Psychology with Shiny. Frontiers in Psychology, 6 https://doi.org/10.3389/fpsyg.2015.01782.

Dimensions

PlumX

Plum Print visual indicator of research metrics
  • Citations
  • CrossRef - Citation Indexes: 3
  • Scopus - Citation Indexes: 4
  • Usage
  • Digital Commons - Downloads: 264
  • Digital Commons - Abstract Views: 7
  • SciELO - Full Text Views: 4416
  • SciELO - Abstract Views: 1753
  • Captures
  • Mendeley - Readers: 22
  • Social Media
  • Facebook - Shares, Likes & Comments: 308
-
see details

Article abstract page views

510

Downloads

License

Copyright (c) 2014 Revista Colombiana de Estadística

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).