emfit toolbox

A set of Matlab scripts which performs fixed-effects empirical Bayes batch EM inference by first fitting priors for a set of models from each model class, plotting the inferred posterior parameters, performing approximate model comparison, generating surrogate data and performing some visual comparisons of the true and surrogate data.

A general overview over this modelling approach can be found here: Huys (2017): Bayesian approaches to Learning and Decision Making. In: Computational Psychiatry: Mathematical Modelling of Mental Disorders. Editors: Alan Anticevic and John Murray

Currently models for the following tasks are implemented:

• 'mBasicRescorlaWagner' - a basic Rescorla-Wagner example
• 'mAffectiveGoNogo' - Guitart et al. 2012, Neuroimage 62(1):154-66
• 'mProbabilisticReward' - Huys et al., 2013 Biology of Mood & Anxiety Disorders 3:12
• 'mTwostep' - Daw et al., 2011 Neuron 69:1204
• 'mEffortCollins' - Gold et al., 2013 Biological Psychiatry 74:130
• 'mPruning' - Lally et al., 2017 J. Neurosci 37(42):10215
• 'mEffortDDM' - Berwian et al., 2020 JAMA Psychiatry

try it out

You can try these out by simply changing into the emfit directory within matlab and then running

batchRunEMfit('mAffectiveGoNogo')

which will generate an example dataset from the model, and then run a series of models on the data, do model comparison and generate some plots.

fit some data

If your data is already in the correct format (see dataformat.txt files in each of the model folders), then you can fit the data by

Data = load('mydata.mat');
batchRunEMfit('mAffectiveGoNogo',Data);

The results will be saved to a folder named fitResults in a separate .mat file for each model. This contains * individual posterior parameter means 'E' * individual posterior parameter variances 'V' * group mean prior 'alpha' * group prior precision 'nui' Additional aspects such as ML parameter estimates, diagnostics etc. are contained within 'stats'.

add your own

Each set of models includes

• dataformat.txt - this describes the format in which the data needs to be
• modelList.m - a file with brief descriptions of each of the models included
• ll***.m - the actual model likelihood files. In general, this takes the form [l,dl,dsurr] = yourlikelihood(x,D,mu,nui,doprior,options); where
  • l is either the total log likelihood of the data, or the (unnormalized) log posterior if doprior=1.
  • dl is a vector of gradients of the total log likelihood with respect to each of the parameters
  • dsurr is surrogate data drawn from the model (if included)
  • x are the parameters (NB: unconstrained)
  • mu is the mean vector of the Gaussian group prior
  • nui is the inverse covariance of the Gaussian group prior
  • doprior is either 0 or 1. When set to 1, l and dl refer to the log posterior
  • options.generatesurrogatedata sets whether dsurr is generated or not
• generateExampleDataset.m - this generates an example dataset when called by batchGenerateSurrogateData.m (which in turn is called by the above batchRunEMfit.m)
• surrogateDataPlots.m - this file will be run by batchRunEMfit.m and should compare surrogate data drawn from the fitted models to the real data.

To add your own, just add these sets of files. Easiest is probably to copy/adapt some of the existing ones.

Important details

The core functionality is contained within lib/emfit.m, which can be run directly without the various wrapper scripts. It allows GLM-style regressions at the group level, for instance.

Parameters are assumed to be drawn from Gaussian priors, and the means and variances of these are empirically estimated. Parameters are constrained to be positive via exp(.), and within bounds via a sigmoid transform.