Bayesian latent variable models for the analysis of experimental psychology data

Psychonomic Bulletin and Review

Volumn 25, Issue 1, 2018, Pages 256-270

  Merkle, Edgar C ^a   Wang, Ting ^a  

^a UNIVERSITY OF MISSOURI   (United States)

Author keywords

Bayesian statistics; Decision making

Indexed keywords

BAYES THEOREM; DECISION MAKING; FACTOR ANALYSIS; HUMAN; PSYCHOLOGY; RISK; STATISTICAL MODEL; THEORETICAL MODEL;

BAYES THEOREM; CHOICE BEHAVIOR; FACTOR ANALYSIS, STATISTICAL; HUMANS; MODELS, STATISTICAL; MODELS, THEORETICAL; PSYCHOLOGY; PSYCHOLOGY, EXPERIMENTAL; RISK;

EID: 84961207292     PISSN: 10699384     EISSN: 15315320     Source Type: Journal    
DOI: 10.3758/s13423-016-1016-7     Document Type: Article

References (79)

1. Bagozzi, R. P., & Yi, Y. (1989). On the use of structural equation models in experimental designs. Journal of Marketing Research, 26, 271–284.
2. Barnard, J., McCulloch, R., & Meng, X. L. (2000). Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage. Statistica Sinica, 10, 1281–1311.
3. Bartholomew, D.J. (1981). Posterior analysis of the factor model. British Journal of Mathematical and Statistical Psychology, 34, 93–99.
4. Bartholomew, D. J., Knott, M., & Moustaki, I. (2011). Latent variable models and factor analysis: A unified approach, 3rd. Wiley.
5. Bollen, K. A., & Davis, W. R. (2009). Two rules of identification for structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 16(3), 523–536.
6. Browne, M. W. (2001). An overview of analytic rotation in exploratory factor analysis. Multivariate Behavioral Research, 36, 111–150.
7. Chib, S., & Greenberg, E. (1998). Analysis of multivariate probit models. Biometrika, 85, 347–361.
8. Conti, G., Frühwirth-Schnatter, S., Heckman, J. J., & Piatek, R. (2014). Bayesian exploratory factor analysis. Journal of Econometrics, 183, 31–57.
9. Cudeck, R., Harring, J. R., & du Toit, S. H. C. (2009). Marginal maximum likelihood estimation of a latent variable model with interaction. Journal of Educational and Behavioral Statistics, 34, 131–144.
10. Curtis, S. M. (2010). BUGS code for item response theory. Journal of Statistical Software, 36, 1–34.
11. Dickey, J. M., & Lientz, B. P. (1970). The weighted likelihood ratio, sharp hypotheses about chances, the order of a Markov chain. The Annals of Mathematical Statistics, 41, 214–226.
12. Donaldson, G. W. (2003). General linear contrasts on latent variable means: Structural equation hypothesis tests for multivariate clinical trials. Statistics in Medicine, 22, 2893–2917.
13. Dutta, R., & Ghosh, J. K. (2013). Bayes model selection with path sampling: Factor models and other examples. Statistical Science, 28, 95–115.
14. Gelman, A. (2004). Parameterization and Bayesian modeling. Journal of the American Statistical Association, 99, 537–545.
15. Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models. Bayesian Analysis, 3, 515–534.
16. Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2004). Bayesian data analysis 2nd edn. London: Chapman Hall.
17. Meng, X. L. (1998). Simulating normalizing constants: From importance sampling to bridge sampling to path sampling. Statistical Science, 13, 163–185.
18. Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences (with discussion). Statistical Science, 7, 457–511.
19. Ghosh, J., & Dunson, D. B. (2009). Default prior distributions and efficient posterior computation in Bayesian factor analysis. Journal of Computational and Graphical Statistics, 18, 306–320.
20. Hoyle, R. H., & Duvall, J. L. (2004). Determining the number of factors in exploratory and confirmatory factor analysis. In Kaplan, D. (Ed.), The Sage handbook of quantitative methodology for the social sciences (pp. 301–316). Thousand Oaks, CA: Sage.
21. Jefferys, W., & Berger, J. O. (1992). Ockham’s razor and Bayesian analysis. American Scientist, 80, 64–72.
22. Jöreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34, 183–202.
23. Jöreskog, K. G. (1979). Author’s addendum. In Magidson, J. (Ed.), Advances in factor analysis and structural equation models (pp. 40–43). Cambridge: Abt Books.
24. Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90, 773–795.
25. Klein, A., & Moosbrugger, H. (2000). Maximum likelihood estimation of latent interaction effects with the LMS method. Psychometrika, 65, 457–474.
26. Klein, A., & Muthén, B. O. (2007). Quasi-maximum likelihood estimation of structural equation models with multiple interaction and quadratic effects. Multivariate Behavioral Research, 42, 647–673.
27. Lawley, D. N., & Maxwell, A. E. (1971). Factor analysis as a statistical method. New York: American Elsevier Publishing Co.
28. Lee, S. Y. (1981). A Bayesian approach to confirmatory factor analysis. Psychometrika, 46, 153–160.
29. Lee, S. Y. (2007). Structural equation modeling: A Bayesian approach. Chichester: Wiley.
30. Lee, S. Y., & Song, X. Y. (2002). Bayesian selection on the number of factors in a factor analysis model. Behaviormetrika, 29, 23–39.
31. Lee, S. Y., Song, X. Y., & Tang, N. S. (2007). Bayesian methods for analyzing structural equation models with covariates, interaction, and quadratic latent variables. Structural Equation Modeling, 14, 404–434.
32. Lewis, S. M., & Raftery, A. E. (1997). Estimating Bayes factors via posterior simulation with the Laplace-Metropolis estimator. Journal of the American Statistical Association, 92, 648–655.
33. Liu, C. C., & Aitkin, M. (2008). Bayes factors: Prior sensitivity and model generalizability. Journal of Mathematical Psychology, 52, 362–375.
34. Lopes, H. F., & West, M. (2004). Bayesian model assessment in factor analysis. Statistica Sinica, 14, 41–67.
35. Lunn, D., Jackson, C., Best, N., Thomas, A., & Spiegelhalter, D. (2012). The BUGS book: A practical introduction to Bayesian analysis. Chapman & Hall/CRC.
36. MacCallum, R. C., Edwards, M. C., & Cai, L. (2012). Hopes and cautions in implementing Bayesian structural equation modeling. Psychological Methods, 17, 340–345.
37. Marsh, H. W., Wen, Z., Hau, K. T., & Nagengast, B. (2013). Structural equation models of latent interaction and quadratic effects. In Hancock, G R, & Mueller, R O (Eds.), Structural equation modeling: A second course, 2nd edn. (pp. 267–308). Information Age Publishing.
38. Martin, J. K., & McDonald, R. P. (1975). Bayesian estimation in unrestricted factor analysis: A treatment for Heywood cases. Psychometrika, 40, 505–517.
39. Merkle, E. C. (2011). A comparison of imputation methods for Bayesian factor analysis models. Journal of Educational and Behavioral Statistics, 36, 257–276.
40. Merkle, E. C., & Rosseel, Y. (2016). blavaan: Bayesian structural equation models via parameter expansion. Manuscript under review.
41. Millsap, R. E. (2011). Statistical approaches to measurement invariance. New York: Routledge.
42. Miyake, A., Friedman, N. P., Emerson, M. J., Witzki, A. H., & Howerter, A. (2000). The unity and diversity of executive functions and their contributions to complex “frontal lobe” tasks: A latent variable analysis. Cognitive Psychology, 41, 49–100.
43. Muthén, B., & Asparouhov, T. (2012). Bayesian structural equation modeling: A more flexible representation of substantive theory. Psychological Methods, 17, 313–335.
44. Muthén, L. K., & Muthén, B. (1998). Mplus user’s guide, 7th edn. Los Angeles, CA: Muthén & Muthén.
45. Nunez, M. D., Srinivasan, R., & Vandekerckhove, J. (2015). Individual differencesin attention influence perceptual decision making. Frontiers in Psychology, 8(18), 1–13.
46. Palomo, J., Dunson, D. B., & Bollen, K. (2007). Bayesian structural equation modeling. In Lee, S Y. (Ed.), Handbook of latentvariable and related models (pp. 163–188). Elsevier.
47. Peeters, C. F. W. (2012a). Bayesian exploratory and confirmatory factor analysis: Perspectives on constrained-model selection, Utrecht University.
48. Peeters, C. F. W. (2012b). Rotational uniquenessconditions under oblique factor correlation metric. Psychometrika, 77, 288–292.
49. Peeters, C. F. W., Dziura, J., & van Wesel, F. (2014). Pathophysiological domains underlying the metabolic syndrome: An alternative factor analyticstrategy. Annals of Epidemiology, 24, 762–770.
50. Peters, E., & Levin, I. P. (2008). Dissecting the risky-choice framing effect: Numeracy as an individual-difference factor inweighting risky and riskless options. Judgment and Decision Making, 3, 435–448.
51. Plummer, M. (2003). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Hornik, K., Leisch, F., & Zeileis, A. (Eds.), Proceedings of the 3rd international workshop on distributedstatistical computing.
52. Plummer, M. (2014). rjags:Bayesian graphical models using MCMC. http://CRAN.R-project.org/package=rjags. R package version 3-13.
53. Preacher, K. J., & MacCallum, R. C. (2003). Tom Swift’s electric factoranalysis machine. Understanding Statistics, 2, 13–43.
54. Press, S. J. (1972). Applied multivariate analysis: Using Bayesian and frequentist methods of inference. New York: Holt, Rinehart, and Winston.
55. R Development Core Team (2014). R: A language and environment forstatistical computing.Vienna, Austria: http://www.R-project.org. ISBN 3-900051-07-0.
56. Raftery, A. E. (1993). Bayesian model selection in structuralequation models. In Bollen, K. A., & Long, J. S. (Eds.), Testing structural equation models (pp. 163–180). Beverly Hills, CA: Sage.
57. Rigdon, E. E. (1995). A necessary and sufficient identification rule for structural models estimated in practice. Multivariate Behavioral Research, 30(3), 359–383.
58. Roc̆ková, V., & George, E. I. (2014). Fast Bayesian factor analysis via automatic rotations to sparsity. Obtained Jan 8, 2015 from http://www.ssc.upenn.edu/~fdiebold/papers/misc/RockovaAndGeorge2014FactorAnalysis.pdf.
59. Rouder, J. N., & Morey, R. D. (2012). Default Bayes factors for model selection in regression. Multivariate Behavioral Research, 47, 877–903.
60. Rouder, J. N., Morey, R. D., Speckman, P. L., & Province, J. M. (2012). Default Bayes factors for ANOVA designs. Journal of Mathematical Psychology, 56, 356–374.
61. Russell, D. W., Kahn, J. H., Spoth, R., & Altmaier, E. M. (1998). Analyzing data from experimental studies: A latent variable structural equation modelingapproach. Journal of Counseling Psychology, 45, 18–29.
62. Scheines, R., Hoijtink, H., & Boomsma, A. (1999). Bayesian estimation and testing ofstructural equation models. Psychometrika, 64, 37–52.
63. Song, X. Y., & Lee, S. Y. (2012a). Basic and advanced Bayesian structural equation modeling: With applications in the medical and behavioral sciences. Chichester, England: Wiley.
64. Song, X. Y., & Lee, S. Y. (2012b). A tutorial on the Bayesian approach for analyzing structural equation models. Journal of Mathematical Psychology, 56, 135–148.
65. Spiegelhalter, D. J., & Smith, A. F. M. (1982). Bayes factors for linear and log-linear models with vague prior information. Journal of the Royal Statistical Society B, 44, 377–387. Journal of the Royal Statistical Society B, 44, 377–387.
66. Stan Development Team (2014). Stan Modeling Language Users Guide and Reference Manual, Version 2.5.0. http://mc-stan.org/.
67. Steiger, J.H. (2001). Driving fast in reverse. Journal of the American Statistical Association, 96, 331–338.
68. Stromeyer, W. R., Miller, J. W., Sriramachandramurthy, R., & DeMartino, R. (2014). The prowess and pitfalls of Bayesian structural equation modeling: Important considerations for management research. Journal of Management.
69. Tierney, L., & Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association, 81, 82–86.
70. Tuerlinckx, F., & De Boeck, P. (2005). Two interpretations of the discrimination parameter. Psychometrika, 70, 629–650.
71. Turner, B. M., Forstmann, B. U., Wagenmakers, E. J., Brown, S. D., Sederberg, P. B., & Steyvers, M. (2013). A Bayesian framework for simultaneously modeling neural and behavioral data. NeuroImage, 72, 193–206.
72. Turner, B. M., van Maanen, L., & Forstmann, B. U. (2015). Informing cognitive abstractions through neuroimaging: The neural drift diffusionmodel. Psychological Review, 122, 312–336.
73. Tversky, A., & Kahneman, D. (1981). The framing of decisions and the psychology of choice. Science, 211, 453–458.
74. van der Maas, H. L. J., Molenaar, D., Maris, G., Kievit, R. A., & Borsboom, D. (2011). Cognitive psychology meets psychometric theory: On the relation between process models for decision making and latent variable models for individual differences. Psychological Review, 118, 339–356.
75. Vandekerckhove, J. (2014). A cognitive latent variable model for the simultaneous analysis of behavioral and personality data. Journal of Mathematical Psychology, 60, 58–71.
76. Vanpaemel, W. (2010). Prior sensitivity intheory testing: An apologia for the Bayes factor. Journal of Mathematical Psychology, 54, 491–498.
77. Verhagen, A. J., & Fox, J. P. (2013). Bayesian tests of measurement invariance. British Journal of Mathematical and Statistical Psychology, 66, 383–401.
78. Wagenmakers, E. J., Lodewyckx, T., Kuriyal, H., & Grasman, R. (2010). Bayesian hypothesis testing for psychologists: A tutorial on the Savage-Dickeymethod. Cognitive Psychology, 60, 158–189.
79. Wicherts, J. M., Dolan, C. V., & Hessen, D. J. (2005). Stereotype threat and group differences in test performance: A question of measurement invariance. Journal of Personality and Social Psychology, 89(5), 696–716.