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Applying the Wiener diffusion process as a psychometric measurement model

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## Applying the Wiener diffusion process as a psychometric measurement model

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**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 • Explanatory diffusion models • Conclusions**An example problem**• Speeded category verification task • Participants evaluate item category memberships**An example problem**• Speeded category verification task • Participants evaluate item category memberships**An example problem**• Speeded category verification task • Participants evaluate item category memberships**An example problem**• Speeded category verification task • Participants evaluate item category memberships**An example problem**• Speeded category verification task • Participants evaluate item category memberships**An example problem**• Speeded category verification task • Participants evaluate item category memberships • Measure both RT and response**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**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)**An example problem**• The problem • Standard assumptions violated • Typical problem in mathematical psychology • Approach: use process models**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)**Wiener diffusion model**Process model for choice RT Predicts RT and binary choice simultaneously Principle: Accumulation of information Diffusion model**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**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**Cognitive psychometrics**• Use cognitive models as measurement model • Try to explain differences • between trials, manipulations and persons • by regressing the parameters on covariates**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**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):**Adding random effects**• Not all data points come from the same distribution • Differences between participants/items/… exist, but causes unknown**Adding random effects**• Case of the diffusion model’s drift rate**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**Adding random effects**• Crossed random effects diffusion model**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**Applying to data**• Crossed random effects diffusion model Pop. distr. of Mean Stdev item easiness (distractors) item easiness (targets) person aptitude**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)**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 • …**Explanatory modeling**• Use basic “building blocks” for modeling • Random/Fixed effects • Person/Item side • Hierarchical/Crossed • Use covariates (continuous/categorical/binary)**explaining variability in drift rate**Explanatory modeling**Conclusions**• Category verification data • Variance in person aptitude small (0.04) relative to variance in item easiness (≈ 0.11) • Item easiness correlates with typicality**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)**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**Future work**• Efficient software for fitting hierarchical diffusion models • Model selection and evaluation methods**Thank you**• Questions, comments, suggestions welcome