Hierarchical diffusion models for two-choice response times.

Two-choice response times are a common type of data, and much research has been devoted to the development of process models for such data. However, the practical application of these models is notoriously complicated, and flexible methods are largely nonexistent. We combine a popular model for choice response times-the Wiener diffusion process-with techniques from psychometrics in order to construct a hierarchical diffusion model. Chief among these techniques is the application of random effects, with which we allow for unexplained variability among participants, items, or other experimental units. These techniques lead to a modeling framework that is highly flexible and easy to work with. Among the many novel models this statistical framework provides are a multilevel diffusion model, regression diffusion models, and a large family of explanatory diffusion models. We provide examples and the necessary computer code.

[1]  L. Cronbach.  The two disciplines of scientific psychology. , 1957 .

[2]  Donald Laming,et al.  Information theory of choice-reaction times , 1968 .

[3]  Richard C. Atkinson,et al.  Human Memory: A Proposed System and its Control Processes , 1968, Psychology of Learning and Motivation.

[4]  H. H. Clark.  The language-as-fixed-effect fallacy: A critique of language statistics in psychological research. , 1973 .

[5]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[6]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[7]  L. Cronbach.  Beyond the Two Disciplines of Scientific Psychology. , 1975 .

[8]  S. Link,et al.  A sequential theory of psychological discrimination , 1975 .

[9]  Roger Ratcliff,et al.  A Theory of Memory Retrieval. , 1978 .

[10]  J. Fleiss,et al.  Intraclass correlations: uses in assessing rater reliability. , 1979, Psychological bulletin.

[11]  R. Ratcliff.  Theoretical interpretations of the speed and accuracy of positive and negative responses. , 1985, Psychological review.

[12]  R. Ratcliff,et al.  A retrieval theory of priming in memory. , 1988, Psychological review.

[13]  Anthony S. Bryk,et al.  Hierarchical Linear Models: Applications and Data Analysis Methods , 1992 .

[14]  Arthur F. Kramer,et al.  Strategies and automaticity. I: Basic findings and conceptual framework , 1994 .

[15]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[16]  W. Batchelder.  Multinomial processing tree models and psychological assessment. , 1998 .

[17]  Jeffrey N. Rouder,et al.  Modeling Response Times for Two-Choice Decisions , 1998 .

[18]  David M. Riefer,et al.  Theoretical and empirical review of multinomial process tree modeling , 1999, Psychonomic bulletin & review.

[19]  R. Ratcliff,et al.  Connectionist and diffusion models of reaction time. , 1999, Psychological review.

[20]  Hoon Kim,et al.  Monte Carlo Statistical Methods , 2000, Technometrics.

[21]  M Brysbaert,et al.  Age-of-acquisition effects in semantic processing tasks. , 2000, Acta psychologica.

[22]  Francis Tuerlinckx,et al.  A Hierarchical IRT Model for Criterion-Referenced Measurement , 2000 .

[23]  Simon Jackman,et al.  Estimation and Inference via Bayesian Simulation: An Introduction to Markov Chain Monte Carlo , 2000 .

[24]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[25]  Francis Tuerlinckx,et al.  Diagnostic checks for discrete data regression models using posterior predictive simulations , 2000 .

[26]  Jeffrey N. Rouder,et al.  A diffusion model account of masking in two-choice letter identification. , 2000, Journal of experimental psychology. Human perception and performance.

[27]  M. J. Bayarri,et al.  P Values for Composite Null Models , 2000 .

[28]  R Ratcliff,et al.  The effects of aging on reaction time in a signal detection task. , 2001, Psychology and aging.

[29]  Ana Ivelisse Avilés,et al.  Linear Mixed Models for Longitudinal Data , 2001, Technometrics.

[30]  David M. Riefer,et al.  Multinomial Modeling and the Measurement of Cognitive Processes , 2001 .

[31]  R. Ratcliff,et al.  The effects of aging on reaction time in a signal detection task. , 2001, Psychology and aging.

[32]  F A Wichmann,et al.  Ning for Helpful Comments and Suggestions. This Paper Benefited Con- Siderably from Conscientious Peer Review, and We Thank Our Reviewers the Psychometric Function: I. Fitting, Sampling, and Goodness of Fit , 2001 .

[33]  R. Ratcliff.  A diffusion model account of response time and accuracy in a brightness discrimination task: Fitting real data and failing to fit fake but plausible data , 2002, Psychonomic bulletin & review.

[34]  Jeff Gill,et al.  Bayesian Methods : A Social and Behavioral Sciences Approach , 2002 .

[35]  R. Ratcliff,et al.  Estimating parameters of the diffusion model: Approaches to dealing with contaminant reaction times and parameter variability , 2002, Psychonomic bulletin & review.

[36]  David M. Riefer,et al.  Cognitive psychometrics: assessing storage and retrieval deficits in special populations with multinomial processing tree models. , 2002, Psychological assessment.

[37]  J. Singer,et al.  Applied Longitudinal Data Analysis , 2003 .

[38]  Francis Tuerlinckx,et al.  A nonlinear mixed model framework for item response theory. , 2003, Psychological methods.

[39]  R. Ratcliff,et al.  A diffusion model analysis of the effects of aging on letter discrimination. , 2003, Psychology and aging.

[40]  F. Tuerlinckx.  The efficient computation of the cumulative distribution and probability density functions in the diffusion model , 2004, Behavior research methods, instruments, & computers : a journal of the Psychonomic Society, Inc.

[41]  A. Voss,et al.  Interpreting the parameters of the diffusion model: An empirical validation , 2004, Memory & cognition.

[42]  Philip L. Smith,et al.  A comparison of sequential sampling models for two-choice reaction time. , 2004, Psychological review.

[43]  Roger Ratcliff,et al.  A diffusion model account of the lexical decision task. , 2004, Psychological review.

[44]  Philip L. Smith,et al.  Attention orienting and the time course of perceptual decisions: response time distributions with masked and unmasked displays , 2004, Vision Research.

[45]  van der Linden,et al.  A hierarchical framework for modeling speed and accuracy on test items , 2007 .

[46]  A. Brix.  Bayesian Data Analysis, 2nd edn , 2005 .

[47]  Jun Lu,et al.  An introduction to Bayesian hierarchical models with an application in the theory of signal detection , 2005, Psychonomic bulletin & review.

[48]  Roger Ratcliff,et al.  A Theory of Order Relations in Perceptual Matching , 2005 .

[49]  G. Molenberghs,et al.  Models for Discrete Longitudinal Data , 2005 .

[50]  M. Shadlen,et al.  The effect of stimulus strength on the speed and accuracy of a perceptual decision. , 2005, Journal of vision.

[51]  Jeffrey N. Rouder,et al.  A hierarchical model for estimating response time distributions , 2005, Psychonomic bulletin & review.

[52]  Stan Lipovetsky,et al.  Generalized Latent Variable Modeling: Multilevel,Longitudinal, and Structural Equation Models , 2005, Technometrics.

[53]  Francis Tuerlinckx,et al.  Two interpretations of the discrimination parameter , 2005 .

[54]  T. Griffiths,et al.  Modeling individual differences using Dirichlet processes , 2006 .

[55]  Gun Ho Jang.  Invariant P-values for Model Checking and Checking for Prior-data Conflict , 2006 .

[56]  J. Tenenbaum,et al.  Special issue on “Probabilistic models of cognition , 2022 .

[57]  Denny Borsboom,et al.  The attack of the psychometricians , 2006, Psychometrika.

[58]  Deniz Senturk-Doganaksoy,et al.  Explanatory Item Response Models: A Generalized Linear and Nonlinear Approach , 2006, Technometrics.

[59]  Alex Huk,et al.  Optimal weighting of speed and accuracy in a sequential decision-making task , 2007 .

[60]  Karl Christoph Klauer,et al.  Process components of the Implicit Association Test: a diffusion-model analysis. , 2007, Journal of personality and social psychology.

[61]  Johan Wagemans,et al.  The concavity effect is a compound of local and global effects , 2007, Perception & psychophysics.

[62]  Andreas Voss,et al.  Fast-dm: A free program for efficient diffusion model analysis , 2007, Behavior research methods.

[63]  J WIM,et al.  A HIERARCHICAL FRAMEWORK FOR MODELING SPEED AND ACCURACY ON TEST ITEMS , 2007 .

[64]  Lesa Hoffman,et al.  Multilevel models for the experimental psychologist: Foundations and illustrative examples , 2007, Behavior research methods.

[65]  Jun Lu,et al.  Signal Detection Models with Random Participant and Item Effects , 2007 .

[66]  Francis Tuerlinckx,et al.  Fitting the ratcliff diffusion model to experimental data , 2007, Psychonomic bulletin & review.

[67]  Richard D. Morey,et al.  Problematic effects of aggregation in zROC analysis and a hierarchical modeling solution , 2008 .

[68]  Michael D. Lee,et al.  A Bayesian approach to diffusion process models of decision-making , 2008 .

[69]  Charles Kemp,et al.  Bayesian models of cognition , 2008 .

[70]  K. McRae,et al.  Proceedings of the 30th Annual Conference of the Cognitive Science Society. , 2008 .

[71]  R. Baayen,et al.  Mixed-effects modeling with crossed random effects for subjects and items , 2008 .

[72]  R. Ratcliff,et al.  A Diffusion Model Account of Criterion Shifts in the Lexical Decision Task. , 2008, Journal of memory and language.

[73]  Richard D. Morey,et al.  A statistical model for discriminating between subliminal and near-liminal performance , 2008 .

[74]  M. Lee.  Three case studies in the Bayesian analysis of cognitive models , 2008, Psychonomic bulletin & review.

[75]  Francis Tuerlinckx,et al.  A double-structure structural equation model for three-mode data. , 2008, Psychological methods.

[76]  Francis Tuerlinckx,et al.  Diffusion model analysis with MATLAB: A DMAT primer , 2008, Behavior research methods.

[77]  D. Navarro,et al.  Fast and accurate calculations for first-passage times in Wiener diffusion models , 2009 .

[78]  Joseph Hilbe,et al.  Data Analysis Using Regression and Multilevel/Hierarchical Models , 2009 .

[79]  Klaus Oberauer,et al.  How to use the diffusion model: Parameter recovery of three methods: EZ, fast-dm, and DMAT , 2009 .

[80]  E. Wagenmakers,et al.  Psychological interpretation of the ex-Gaussian and shifted Wald parameters: A diffusion model analysis , 2009, Psychonomic bulletin & review.

[81]  Jean-Paul Fox,et al.  Evaluating cognitive theory: a joint modeling approach using responses and response times. , 2009, Psychological methods.

[82]  Eric-Jan Wagenmakers,et al.  Methodological and empirical developments for the Ratcliff diffusion model of response times and accuracy , 2009 .

[83]  E. Wagenmakers,et al.  A diffusion model decomposition of the practice effect , 2009, Psychonomic bulletin & review.

[84]  E. Wagenmakers,et al.  Bayesian parameter estimation in the Expectancy Valence model of the Iowa gambling task , 2010 .

[85]  F. Tuerlinckx,et al.  A crossed random effects diffusion model for speeded semantic categorization decisions. , 2010, Acta psychologica.

[86]  E. Wagenmakers,et al.  Diffusion versus linear ballistic accumulation: different models but the same conclusions about psychological processes? , 2010, Psychonomic bulletin & review.

[87]  M. Manosevitz,et al.  High-Speed Scanning in Human Memory , 2022 .