×

zbMATH — the first resource for mathematics

A comparison of correlation and regression approaches for multinomial processing tree models. (English) Zbl 1455.91203
Summary: Multinomial processing tree (MPT) models are a class of stochastic models for categorical data that have recently been extended to account for heterogeneity in individuals by assuming separate parameters per participant. These extensions enable the estimation of correlations among model parameters and correlations between model parameters and external covariates. The present study compares different approaches regarding their ability to estimate both types of correlations. For parameter-parameter correlations, we considered two Bayesian hierarchical MPT models – the beta-MPT approach and the latent-trait approach – and two frequentist approaches that fit the data of each participant separately, either involving a correction for attenuation or not (corrected and uncorrected individual-model approach). Regarding parameter-covariate correlations, we additionally considered the latent-trait regression. Recovery performance was determined via a Monte Carlo simulation varying sample size, number of items, extent of heterogeneity, and magnitude of the true correlation. The results indicate the smallest bias regarding parameter-parameter correlations for the latent-trait approach and the corrected individual-model approach and the smallest bias regarding parameter-covariate correlations for the latent-trait regression and the corrected individual-model approach. However, adequately recovering correlations of MPT parameters generally requires a sufficiently large number of observations and sufficient heterogeneity.
MSC:
91E45 Measurement and performance in psychology
91E40 Memory and learning in psychology
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Arbuckle, T. Y.; Gold, D. P.; Andres, D.; Schwartzman, A.; Chaikelson, J., The role of psychosocial context, age, and intelligence in memory performance of older men, Psychology and Aging, 7, 1, 25-36 (1992)
[2] Arnold, N. R.; Bayen, U. J.; Böhm, M. F., Is prospective memory related to depression and anxiety? A hierarchical MPT modelling approach, Memory, 23, 8, 1215-1228 (2015)
[3] Barbey, A. K., Network neuroscience theory of human intelligence, Trends in Cognitive Sciences, 22, 1, 8-20 (2018)
[4] Batchelder, W. H., Multinomial processing tree models and psychological assessment, Psychological Assessment, 10, 4, 331-344 (1998)
[5] Batchelder, W. H., Cognitive psychometrics: Using multinomial processing tree models as measurement tools, (Embretson, S. E., Measuring psychological constructs: Advances in model-based approaches (2010), American Psychological Association), 71-93
[6] Batchelder, W. H.; Riefer, D. M., Theoretical and empirical review of multinomial process tree modeling, Psychonomic Bulletin and Review, 6, 1, 57-86 (1999)
[7] Batchelder, W. H.; Riefer, D. M., Using multinomial processing tree models to measure cognitive deficits in clinical populations, (Neufeld, R. W.J., Advances in clinical cognitive science: Formal modeling of processes and symptoms (2007), American Psychological Association), 19-50
[8] Bayen, U. J.; Erdfelder, E.; Murnane, K., Source discrimination, item detection, and multinomial models of source monitoring, Journal of Experimental Psychology. Learning, Memory, and Cognition, 22, 1, 197-215 (1996)
[9] Boehm, U.; Marsman, M.; Matzke, D.; Wagenmakers, E.-J., On the importance of avoiding shortcuts in applying cognitive models to hierarchical data, Behavior Research Methods, 50, 1614-1631 (2018)
[10] Calanchini, J.; Sherman, J. W.; Klauer, K. C.; Lai, C. K., Attitudinal and non-attitudinal components of IAT performance, Personality and Social Psychology Bulletin, 40, 10, 1285-1296 (2014)
[11] Chechile, R. A., Pooling data versus averaging model fits for some prototypical multinomial processing tree models, Journal of Mathematical Psychology, 53, 6, 562-576 (2009) · Zbl 1182.91152
[12] Coolin, A.; Erdfelder, E.; Bernstein, D. M.; Thornton, A. E.; Thornton, W. L., Explaining individual differences in cognitive processes underlying hindsight bias, Psychonomic Bulletin and Review, 22, 2, 328-348 (2015)
[13] Denwood, M. J., Runjags: An R package providing interface utilities, model templates, parallel computing methods and additional distributions for MCMC models in JAGS, Journal of Statistical Software, 71, 9, 1-25 (2016)
[14] Dube, C.; Starns, J. J.; Rotello, C. M.; Ratcliff, R., Beyond ROC curvature: Strength effects and response time data support continuous-evidence models of recognition memory, Journal of Memory and Language, 67, 3, 389-406 (2012)
[15] Erdfelder, E.; Auer, T.-S.; Hilbig, B. E.; Aßfalg, A.; Moshagen, M.; Nadarevic, L., Multinomial processing tree models: A review of the literature, Journal of Psychology, 217, 3, 108-124 (2009)
[16] Erdfelder, E.; Küpper-Tetzel, C. E.; Mattern, S. D., Threshold models of recognition and the recognition heuristic, Judgment and Decision Making, 6, 1, 7-22 (2011)
[17] Gelman, A.; Rubin, D. B., Inference from iterative simulation using multiple sequences, Statistical Science, 7, 4, 457-472 (1992) · Zbl 1386.65060
[18] Heck, D. W.; Arnold, N. R.; Arnold, D., TreeBUGS: An R package for hierarchical multinomial-processing-tree modeling, Behavior Research Methods, 50, 1, 264-284 (2018)
[19] Heck, D. W.; Moshagen, M., RRreg: An R package for correlation and regression analyses of randomized response data, Journal of Statistical Software, 85, 2, 1-29 (2018)
[20] Heck, D. W.; Thielmann, I.; Moshagen, M.; Hilbig, B. E., Who lies? A large-scale reanalysis linking basic personality traits to unethical decision making, Judgment and Decision Making, 13, 4, 356-371 (2018)
[21] Hu, X.; Batchelder, W. H., The statistical analysis of general processing tree models with the EM algorithm, Psychometrika, 59, 1, 21-47 (1994) · Zbl 0826.62099
[22] Klauer, K. C., Hierarchical multinomial processing tree models: A latent-class approach, Psychometrika, 71, 1, 7-31 (2006) · Zbl 1306.62452
[23] Klauer, K. C., Hierarchical multinomial processing tree models: a latent-trait approach, Psychometrika, 75, 1, 70-98 (2010) · Zbl 1272.62126
[24] Klein, S. A.; Hilbig, B. E.; Heck, D. W., Which is the greater good? A social dilemma paradigm disentangling environmentalism and cooperation, Journal of Environmental Psychology, 53, 40-49 (2017)
[25] Ly, A.; Boehm, U.; Heathcote, A.; Turner, B. M.; Forstmann, B.; Marsman, M., A flexible and efficient hierarchical Bayesian approach to the exploration of individual differences in cognitive-model-based neuroscience, (Moustafa, A. A., Computational models of brain and behavior (2017), John Wiley & Sons: John Wiley & Sons Hoboken), 467-480
[26] Ly, A.; Marsman, M.; Wagenmakers, E.-J., Analytic posteriors for Pearson’s correlation coefficient, Statistica Neerlandica, 72, 1, 4-13 (2018)
[27] van der Maas, H. L.J.; Dolan, C. V.; Grasman, R. P.P. P.; Wicherts, J. M.; Huizenga, H. M.; Raijmakers, M. E.J., A dynamical model of general intelligence: The positive manifold of intelligence by mutualism, Psychological Review, 113, 4, 842-861 (2006)
[28] Matzke, D.; Dolan, C. V.; Batchelder, W. H.; Wagenmakers, E.-J., Bayesian estimation of multinomial processing tree models with heterogeneity in participants and items, Psychometrika, 80, 1, 205-235 (2015) · Zbl 1314.62275
[29] Moshagen, M., Multitree: A computer program for the analysis of multinomial processing tree models, Behavior Research Methods, 42, 1, 42-54 (2010)
[30] Müller, S.; Moshagen, M., Overclaiming shares processes with the hindsight bias, Personality and Individual Differences, 134, 298-300 (2018)
[31] Naveh-Benjamin, M., Adult age differences in memory performance: Tests of an associative deficit hypothesis, Journal of Experimental Psychology. Learning, Memory, and Cognition, 26, 5, 1170-1187 (2000)
[32] Plummer, M. (2003). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd international workshop on distributed statistical computing. Vienna, Austria. Retrieved from https://www.r-project.org/conferences/DSC-2003/Proceedings/Plummer.pdf.
[33] R Core Team, M., R: a language and environment for statistical computing (2018), R Foundation for Statistical Computing: R Foundation for Statistical Computing Vienna, Austria
[34] Riefer, D. M.; Batchelder, W. H., Multinomial modeling and the measurement of cognitive processes, Psychological Review, 95, 3, 318-339 (1988)
[35] Riefer, D. M.; Knapp, B. R.; Batchelder, W. H.; Bamber, D.; Manifold, V., Cognitive psychometrics: Assessing storage and retrieval deficits in special populations with multinomial processing tree models, Psychological Assessment, 14, 2, 184-201 (2002)
[36] Rouder, J. N.; Lu, J.; Morey, R.; Sun, D.; Speckman, P., A hierarchical process-dissociation model, Journal of Experimental Psychology: General, 137, 370-389 (2008)
[37] Singmann, H.; Kellen, D., MPTinR: Analysis of multinomial processing tree models in R, Behavior Research Methods, 45, 2, 560-575 (2013)
[38] Singmann, H.; Kellen, D.; Klauer, K. C., Investigating the other-race effect of Germans towards Turks and Arabs using multinomial processing tree models, (Proceedings of the annual meeting of the cognitive science society, vol. 35 (2013)), 1330-1335
[39] Smith, J. B.; Batchelder, W. H., Assessing individual differences in categorical data, Psychonomic Bulletin and Review, 15, 4, 713-731 (2008)
[40] Smith, J. B.; Batchelder, W. H., Beta-MPT: Multinomial processing tree models for addressing individual differences, Journal of Mathematical Psychology, 54, 167-183 (2010) · Zbl 1203.91264
[41] Snodgrass, J. G.; Corwin, J., Pragmatics of measuring recognition memory: Applications to dementia and amnesia, Journal of Experimental Psychology: General, 117, 1, 34-50 (1988)
[42] Venables, W. N.; Ripley, B. D., Modern applied statistics with S (2002), Springer: Springer New York · Zbl 1006.62003
[43] Zimmerman, D. W.; Williams, R. H., The theory of test validity and correlated errors of measurement, Journal of Mathematical Psychology, 16, 2, 135-152 (1977) · Zbl 0403.62082
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.