Introduction

:Author: Thomas V. Wiecki, Imri Sofer, Mads L. Pedersen, Alexander Fengler, Lakshmi Govindarajan, Krishn Bera, Michael J. Frank :Contact: thomas.wiecki@gmail.com, imri_sofer@brown.edu, madslupe@gmail.com, alexander_fengler@brown.edu, krishn_bera@brown.edu, michael_frank@brown.edu :Web site: https://hddm.readthedocs.io :Github: http://github.com/hddm-devs/hddm :Mailing list: https://groups.google.com/group/hddm-users/ :Copyright: This document has been placed in the public domain. :License: HDDM is released under the BSD 2 license. :Version: 1.0.1

.. image:: https://secure.travis-ci.org/hddm-devs/hddm.png?branch=master

Purpose

HDDM is a python toolbox for hierarchical Bayesian parameter estimation of the Drift Diffusion Model (via PyMC). Drift Diffusion Models are used widely in psychology and cognitive neuroscience to study decision making.

Check out the tutorial_ on how to get started. Further information can be found below as well as in the howto_ section and the documentation_.

Features

• Uses hierarchical Bayesian estimation (via PyMC) of DDM parameters to allow simultaneous estimation of subject and group parameters, where individual subjects are assumed to be drawn from a group distribution. HDDM should thus produce better estimates when less RT values are measured compared to other methods using maximum likelihood for individual subjects (i.e. DMAT_ or fast-dm_).

• Heavily optimized likelihood functions for speed (Navarro & Fuss, 2009).

• Flexible creation of complex models tailored to specific hypotheses (e.g. estimation of separate drift-rates for different task conditions; or predicted changes in model parameters as a function of other indicators like brain activity).

• Estimate trial-by-trial correlations between a brain measure (e.g. fMRI BOLD) and a diffusion model parameter using the HDDMRegression model.

• Built-in Bayesian hypothesis testing and several convergence and goodness-of-fit diagnostics.

• As of version 0.7.1 HDDM includes modules for analyzing reinforcement learning data with the reinforcement learning drift diffusion
  model (RLDDM), including a module for estimating the impact of continuous regressors onto RLDDM parameters, and a reinforcement learning (RL) model. See tutorial for the RLDDM and RL modules here: https://nbviewer.jupyter.org/github/hddm-devs/hddm/blob/master/hddm/examples/demo_RLHDDMtutorial.ipynb and in the paper here: https://rdcu.be/b4q6Z

• HDDM 0.9.0 brings a host of new features. HDDM includes likelihood approximation networks_ via the HDDMnn, HDDMnnRegressor and HDDMnnStimCoding classes. This allows fitting of a number of variants of sequential sampling models. You can now easily use custom likelihoods for model fitting. We included a range of new simulators, which allow data generation for a host of variants of sequential sampling models. There are some new out of the box plots, in the hddm.plotting module. Fast posterior predictives for regression based models. Some sampler settings are now exposed to the user via a customizable model_config dictionary. Lastly you are now able to save and load HDDMRegression models with custom link functions. Please see the documentation (under LAN Extension) for illustrations on how to use the new features.

• HDDM 0.9.1 improved documentation for LAN models. Comprehensive tutorial using LAN included. Bugfixes for simulator_h_c() function.

• HDDM 0.9.2 major overhaul of the plotting functions under hddm.plotting. Old capabilities are preserved under hddm.plotting_old, but will be deprecated. The new plotting functions replicate the existing functionality, but improve on various aspects of the plot and provide a more abstracted and extensible interface. Fixes an error with posterior predictive sampling using hierarchical regression models based on LANs with HDDMnnRegressor(). HDDMnnRegressor() now issues a single warning for boundary condition violations instead of flagging all occurences.

• HDDM 0.9.3 Lot's of minor improvements. Model plots now working for race and lca models with n > 2 choices (use _plot_func_model_n as plot_func argument in hddm.plotting.plot_posterior_predictive). model_config files are simplified and class construction is a bit more robust to lack of specification, improving ease of use with custom models. Various plots received a bit more styling features. Better defaults for simulator_h_c function in hddm.simulators.hddm_dataset_generators. Posterior predictives now properly take into account the p_outlier parameter when generating data from the implicit mixture model. p_outlier percent of the data, now explicitly come from random choices with uniform reaction times. The documentation is updated to reflect / illustrate the improvements.

• HDDM 0.9.4 Bug fixes and one major new functionality. HDDMnnRegressor now allows you to define indirect regressors, latent parameters that are driven by their own regression and link to model parameters. See the documentation for more information on this. Note this functionality is experimental for now. Model fitting will work, but extraenous functionality may not, including posterior predictives for models that include such indirect regressors. Including indirect regressors might demand you to think carefully about the supplied model_config. E.g. in the race_no_bias_3 model, the usual lower bounds on the v0, v1 ,v2, v3 parameters are 0. If we allow these parameters to be driven by an indirect regressor v, which is added to the regressions of v0, v1, v2, v3, then v0, v1, v2, v3

• HDDM 0.9.5 Bug fixes and another new functionality. HDDMnnRegressor now allows you to also define indirect betas, latent parameters that can be used in regression models. E.g. in the race_no_bias_3 model, you can define a v beta, which will be expressed in the regression models for v0, v1, v2 like so:

         **v0 = beta0 * covariate0 + ... + v * covariate_v_0**
  
         **v1 = beta0 * covariate0 + ... + v * covariate_v_1**
  
         **v2 = beta0 * covariate0 + ... + v * covariate_v_2**
  
         The **v0**, **v1**, **v2** parameters might be drifts in a preference based choice task, and dedicated to respective choice 
         options in a stimulus screen. You may be interested in making these slopes dependent on the respective values of these options
         in a given trial, but wish to use a central **beta**, (**v** in this example) that relates option value to drift for all drifts.
  
         Note that first, this is **complementary** to the **indirect regressors** defined above, and second that the usual modelling caveats,
         such as potential convergence problems apply. 
  
         Note also that the usage of **indirect betas** as well as **indirect regressors** may affect the speed of sampling in general.
         Both translate into more computational work at the stage of regression likelihood evaluation.
  

• HDDM 0.9.6 brings a host of new features. HDDM now includes use of likelihood approximation networks_ in conjunction with reinforcement learning models via the HDDMnnRL class. This allows researchers to study not only the across-trial dynamics of learning but the within-trial dynamics of choice processes, using a single model. This module greatly extends the previous functionality for fitting RL+DDM models (via HDDMrl class) by allowing fitting of a number of variants of sequential sampling models in conjuction with a learning process (RL+SSM models). We have included a new simulator, which allows data generation for a host of variants of sequential sampling models in conjunction with the Rescorla-Wagner update rule on a 2-armed bandit task environment. There are some new, out-of-the-box plots and utility function in the hddm.plotting and hddm.utils modules, respectively, to facilitate posterior visualization and posterior predictive checks. Lastly you can also save and load HDDMnnRL models. Please see the documentation (under HDDMnnRL Extension) for illustrations on how to use the new features.

• HDDM 0.9.7 adds the HDDMnnRLRegressor class, the equivalent to the HDDMrlRegressor with support for many more SSMs via LANs. Please check the documentation for usage examples.

• HDDM 0.9.8 adds a breaking change. To accommodate some user requests, all parameters that should be estimated for a given model should be made explicitly in the include argument of the calling class (HDDM, HDDMnn, etc.). The remaining parameters can now be set to arbitrary, user defined, defaults. Check the documentation for a new tutorial on parameter defaults. Moreover, model plot is made much more flexible (new tutorial included to showcase some of the options). Two tutorials are added to showcase the capabilities for simulation based inference via custom likelihoods. The legacy models with "vanilla" in their name are globally renamed to instead include "hddm_base". The simulator backend is now completely outsourced to the ssms_ package (severe code simplifications).

Comparison to other packages

A recent paper by Roger Ratcliff quantitatively compared D