1 / 34

Applying the Wiener diffusion process as a psychometric measurement model

Applying the Wiener diffusion process as a psychometric measurement model. Joachim Vandekerckhove and Francis Tuerlinckx Research Group Quantitative Psychology, K.U.Leuven. Overview. An example problem The diffusion model Cognitive psychometrics Random effects diffusion models

moya
Download Presentation

Applying the Wiener diffusion process as a psychometric measurement model

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Applying the Wiener diffusion process as a psychometric measurement model Joachim Vandekerckhove and Francis Tuerlinckx Research Group Quantitative Psychology, K.U.Leuven

  2. Overview • An example problem • The diffusion model • Cognitive psychometrics • Random effects diffusion models • Explanatory diffusion models • Conclusions

  3. An example problem • Speeded category verification task • Participants evaluate item category memberships

  4. An example problem • Speeded category verification task • Participants evaluate item category memberships

  5. An example problem • Speeded category verification task • Participants evaluate item category memberships

  6. An example problem • Speeded category verification task • Participants evaluate item category memberships

  7. An example problem • Speeded category verification task • Participants evaluate item category memberships

  8. An example problem • Speeded category verification task • Participants evaluate item category memberships • Measure both RT and response

  9. An example problem • Speeded category verification task • Participants evaluate item category memberships • Measure both RT and response • Each participant evaluates each item exactly once • Expectation: “Typical” members (e.g., Dog, Cat) are easier

  10. An example problem • The problem • Standard assumptions violated • Bivariate data (RT and binary response) do not conform to the assumptions made by standard models (e.g., normality) • Different sources of variability • RT and response are partly determined by both participants (ability) and items (difficulty)

  11. An example problem • The problem • Standard assumptions violated • Typical problem in mathematical psychology • Approach: use process models

  12. An example problem • The problem • Standard assumptions violated • Typical problem in mathematical psychology • Approach: use process models • Different sources of variability • Typical problem in psychometrics • Approach: hierarchical models (multilevel models; mixed models; e.g., crossed random effects of persons and items)

  13. Wiener diffusion model Process model for choice RT Predicts RT and binary choice simultaneously Principle: Accumulation of information Diffusion model

  14. τ d Evidence a z = ba 0.0 0.125 0.250 0.375 0.500 0.625 0.750 (For persons p, conditions i, and trials j.) time

  15. Diffusion model • Many associated problems • Technical issues • Parameter estimation / Model comparison • Substantive issues • Difficult to combine information across participants • Problem if many participants with few data each • Problem if items are presented only once (e.g., words) • Unlikely that parameters are constant in time (i.e., unexplained variability) • Almost completely descriptive – differences over persons/trials/conditions cannot be explained

  16. Cognitive psychometrics • Use cognitive models as measurement model • Try to explain differences • between trials, manipulations and persons • by regressing the parameters on covariates

  17. Indexes p for persons, i for conditions Cognitive psychometrics • Most common measurement model: Gaussian • Normal linear model (linear regression, ANOVA): • But often not a realistic model • Unsuited for choice RT

  18. Measurement level describes the data Regression component explains differences Transform the parameter(s) to a linear scale Cognitive psychometrics • Common measurement model in psychometrics: Logistic • Two-parameter logistic model (item response theory):

  19. Adding random effects • Not all data points come from the same distribution • Differences between participants/items/… exist, but causes unknown

  20. Adding random effects • Case of the diffusion model’s drift rate

  21. Ratcliff diffusion model Measurement level (Wiener process) Trial-to-trial variability in bias Trial-to-trial variability in information uptake rate Trial-to-trial variability in nondecision time Adding random effects

  22. Adding random effects • Crossed random effects diffusion model

  23. Adding random effects • Addition of random effects • Allows for excess variability • Due to item differences • Due to person differences • Allows to build “levels of randomness” • Importantly, can be accomplished with the diffusion model • Only feasible in a Bayesian statistical framework

  24. Applying to data • Crossed random effects diffusion model Pop. distr. of Mean Stdev item easiness (distractors) item easiness (targets) person aptitude

  25. Explanatory modeling • Previous models were descriptive • Didn’t use covariates • Mixed models merely quantify variability • Use external factors as predictors to • analyze the data • explain the differences in parameter values (i.e., reduce unexplained variance)

  26. Explanatory modeling • Variability in choice RT due to • Inherent (stochastic) variability in sampling • Trial-to-trial differences • Participant effects • Participant’s group membership • Item effects • Item type • Combination of the above • …

  27. Explanatory modeling • Use basic “building blocks” for modeling • Random/Fixed effects • Person/Item side • Hierarchical/Crossed • Use covariates (continuous/categorical/binary)

  28. explaining variability in drift rate Explanatory modeling

  29. Applying to data

  30. Conclusions • Category verification data • Variance in person aptitude small (0.04) relative to variance in item easiness (≈ 0.11) • Item easiness correlates with typicality

  31. Conclusions • More results (not discussed) • Other parameters besides drift rate may be analyzed • e.g., encoding time is negatively correlated with word length (at ±7ms/letter) • Results hold across semantic categories (not just for mammals)

  32. General conclusion • Hierarchical diffusion models • combine a realistic process model for choice and reaction time with random effects and explanatory covariates • allow to analyze complex data sets in a statistically (and substantively) principled fashion with relative ease

  33. Future work • Efficient software for fitting hierarchical diffusion models • Model selection and evaluation methods

  34. Thank you • Questions, comments, suggestions welcome

More Related