Fitting the diffusion model to experimental data: methods and tools

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Fitting the diffusion model to experimental
datamethods and tools

• Joachim Vandekerckhove Francis Tuerlinckx
• Research Group Quantitative Psychology
• University of Leuven, Belgium

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Overview

• The Ratcliff diffusion model
• An example application
• Substantive restrictions in the diffusion model
• The DMA Toolbox for MATLAB

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The Ratcliff diffusion model

• Simultaneous analysis of reaction time and
  accuracy (or binary) data
• Wide applicability good fit to real data
• Basic idea sequential sampling
• Interesting parameters
• a Speed-accuracy trade-off
• z Participant bias
• v Quality of the stimulus
• Ter Nondecision time
• 3 trial-to-trial variability parameters

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The Ratcliff diffusion model
Ter
v
v
Evidence
a
z
0.0
0.125
0.250
0.375
0.500
0.625
0.750
Time (sec)
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Goal of our research

• Develop flexible methods for diffusion model
  analysis
• Handle outliers and guesses
• Implement substantive restrictions on parameters
  across conditions
• Make diffusion modeling easier by publishing
  software

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Example application

• Simple change detection experiment
• One participant
• 3 variables with 2 values each
• Not fully crossed 5 conditions

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Example trial
Change or no change?
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Example application

• Simple change detection experiment
• One participant
• 3 variables with 2 values each
• Not fully crossed 5 conditions

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Data analysis

• Research questions
• Effect of TYPE on drift rate?
• Effect above and beyond effect of QUALITY?
• Interaction TYPE ? QUALITY?
• Any other effects?
• The data

Reaction time
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Substantive restrictions

• Why impose restrictions?
• Parsimonious model
• Test substantive hypotheses
• Formulate competing models
• ? Real interest is in drift rate
• Test significance of difference in badness-of-fit

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Matrix notation

• To formalize constraints, assume the below
  equality

All the drift rates (for all conditions) in one
vector
Parameters to estimate
Restrictions you impose
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Nested model construction
All drift rates equal
Grand mean
13
Nested model construction
Effect of CHANGE
Effect of QUALITY
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Nested model construction
Effect of TYPE
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Change detection

• Summary of models
• Model 1 All parameters constant across
  conditions
• Model 2 Added effect of CHANGE and QUALITY
• Model 3 Added effect of TYPE
• Model 4 Added QUALITY ? TYPE interaction
• Model 5 Added effect on other parameters
• Result of model fitting

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Recapitulation

• Data RT and accuracy
• Fit Ratcliff diffusion model
• Compare models of increasing complexity that
  capture across-condition changes
• ANOVA, but with RT and accuracy data

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The DMA Toolbox

• Diffusion Model Analysis Toolbox
• MATLAB
• Aimed at wide range of practitioners
• No programming knowledge required
• Freely downloadable
• Under review
• Efficient
• Fast (1 minute)
• Accurate (Monte Carlo simulations)

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The DMA Toolbox

• Many features
• Outlier treatment
• Design matrices
• Fix parameters
• Compare model families (queue)
• Custom settings
• Extra tools
• Manual demos

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The DMA Toolbox

• Visualizations