HDDM is a hierarchical Bayesian model that fits drift-diffusion models to behavioral data from multiple subjects. It estimates both group-level and subject-specific parameters, leveraging information across subjects to obtain more reliable estimates. This allows modeling experimental effects like difficulty while accounting for individual differences. HDDM implements efficient Markov chain Monte Carlo sampling in Python to estimate the full posterior distribution. It provides tools to assess model fit and visualize parameter estimates.

1. HDDM: Hierarchical Bayesian Drift-Diffusion Modeling Thomas V. Wiecki & Imri Sofer, Michael J. Frank

2. Drift-Diffusion Model

5. Traditional model fitting Fitting separate models to each subject Fitting one model to all subjects e.g. DMAT, fast-dm, EZ Ignores similarities Ignores differences Subject 1 ... Subject n P( data 1 | θ 1 ) ... P( data n | θ n ) P( data| θ ) Subject 1 ... Subject n Subject 1 ... Subject n Subject 1 ... Subject n

6. Hierarchical model estimation Subject 1 ... Subject n Group P( θ group |θ 1 , θ. , , θ n ) P(θ 1 |data, θ group ) ... P(θ n |data, θ group )

8. Needs less data for individual subject estimation

9. Constraining of subject parameters (helps with extreme fits)

10. Estimation of full posterior, not just maximum

12. Correct model behavior can be hard to assess (e.g. chain convergence)

13. Methods still in development

16. Several convergence and goodness-of-fit diagnostics

17. Validated : integrated tests check if parameters from simulated data can be recovered HDDM

18. ...it works!

19. How to get your data into HDDM response, rt, subj_idx, difficulty 1, 1.06, 1, hard 1, 1.052, 1, hard 1, 1.398, 1, hard 0, 0.48, 1, easy 1, 1.798, 1, easy 1, 0.94, 1, easy 1, 2.093, 2, hard 1, 0.91, 2, hard 0, 1.019, 2, hard ...

20. Model specification via configuration file [depends] v = difficulty [mcmc] samples=5000 burn=1000

21. Model fitting $> hddmfit simple_difficulty.conf simple_difficulty.csv Creating model... Sampling: 100% [0000000000000000000000000000000000] Iterations: 5000 name mean std 2.5q 25q 50q 75q 97.5 mc_err a : 2.029 0.034 1.953 2.009 2.028 2.049 2.090 0.002 t : 0.297 0.007 0.282 0.292 0.297 0.302 0.311 0.001 v('easy',): 0.992 0.051 0.902 0.953 0.987 1.028 1.102 0.003 v('hard',): 0.522 0.049 0.429 0.485 0.514 0.561 0.612 0.002 logp: -1171.276303 DIC: 2329.069932 DIC without separate drift rates: 2373.395603

22. Output statistics hard condition easy condition Error responses mirrored along y-axis.

23. Output statistics II

24. Python model creation import hddm # Load data from csv file into a NumPy structured array data = hddm.load_csv('simple_subj_data.csv') # Create a HDDM model multi object model = hddm.HDDM(data, depends_on={'v':'difficulty'}) # Create model and start MCMC sampling model.sample(5000, burn=2000) # Print fitted parameters and other model statistics model.print_stats() # Plot posterior distributions and theoretical RT distributions hddm.plot_posteriors(model) hddm.plot_post_pred(model)

25. Trial-by-trial random effects Cavanagh, Wiecki et al (submitted)

27. Contaminant model

28. Linear Ballistic Accumulator Model

29. Switch-task model Note to developers: it is very easy to add your own models to this framework!

30. http://github.com/hddm-devs/hddm