Delay Discounting Task

Description

Hierarchical Bayesian Modeling of the Delay Discounting Task using the following parameters: "k" (discounting rate), "beta" (inverse temperature).

MODEL: Hyperbolic Model (Mazur, 1987)

Usage

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dd_hyperbolic(data = "choose", niter = 3000, nwarmup = 1000, nchain = 1,
  ncore = 1, nthin = 1, inits = "random", indPars = "mean",
  saveDir = NULL, email = NULL, modelRegressor = FALSE,
  adapt_delta = 0.8, stepsize = 1, max_treedepth = 10)

Arguments

data

A .txt file containing the data to be modeled. Data columns should be labelled as follows: "subjID", "delay_later", "amount_later", "delay_sooner", "amount_sooner", and "choice". See Details below for more information.

niter

Number of iterations, including warm-up.

nwarmup

Number of iterations used for warm-up only.

nchain

Number of chains to be run.

ncore

Integer value specifying how many CPUs to run the MCMC sampling on. Defaults to 1.

nthin

Every i == nthin sample will be used to generate the posterior distribution. Defaults to 1. A higher number can be used when auto-correlation within the MCMC sampling is high.

inits

Character value specifying how the initial values should be generated. Options are "fixed" or "random" or your own initial values.

indPars

Character value specifying how to summarize individual parameters. Current options are: "mean", "median", or "mode".

saveDir

Path to directory where .RData file of model output (modelData) can be saved. Leave blank if not interested.

email

Character value containing email address to send notification of completion. Leave blank if not interested.

modelRegressor

Exporting model-based regressors? TRUE or FALSE. Currently not available for this model.

adapt_delta

Floating point number representing the target acceptance probability of a new sample in the MCMC chain. Must be between 0 and 1. See Details below.

stepsize

Integer value specifying the size of each leapfrog step that the MCMC sampler can take on each new iteration. See Details below.

max_treedepth

Integer value specifying how many leapfrog steps that the MCMC sampler can take on each new iteration. See Details below.

Details

This section describes some of the function arguments in greater detail.

data should be assigned a character value specifying the full path and name of the file, including the file extension (e.g. ".txt"), that contains the behavioral data of all subjects of interest for the current analysis. The file should be a text (.txt) file whose rows represent trial-by-trial observations and columns represent variables. For the Delay Discounting Task, there should be six columns of data with the labels "subjID", "delay_later", "amount_later", "delay_sooner", "amount_sooner", and "choice". It is not necessary for the columns to be in this particular order, however it is necessary that they be labelled correctly and contain the information below:

"subjID"

A unique identifier for each subject within data-set to be analyzed.

"delay_later"

An integer representing the delayed days for the later option within the given trial. (e.g., 1 6 15 28 85 170).

"amount_later"

A floating number representing the amount for the later option within the given trial. (e.g., 10.5 38.3 13.4 31.4 30.9, etc.).

"delay_sooner"

An integer representing the delayed days for the sooner option (e.g., 0 0 0 0).

"amount_sooner"

A floating number representing the amount for the sooner option (e.g., 10 10 10 10).

"choice"

An integer value representing the chosen option within the given trial (e.g., 0=instant amount, 1=delayed amount )

*Note: The data.txt file may contain other columns of data (e.g. "Reaction_Time", "trial_number", etc.), but only the data with the column names listed above will be used for analysis/modeling. As long as the columns above are present and labelled correctly, there is no need to remove other miscellaneous data columns.

nwarmup is a numerical value that specifies how many MCMC samples should not be stored upon the beginning of each chain. For those familiar with Bayesian methods, this value is equivalent to a burn-in sample. Due to the nature of MCMC sampling, initial values (where the sampling chain begins) can have a heavy influence on the generated posterior distributions. The nwarmup argument can be set to a high number in order to curb the effects that initial values have on the resulting posteriors.

nchain is a numerical value that specifies how many chains (i.e. independent sampling sequences) should be used to draw samples from the posterior distribution. Since the posteriors are generated from a sampling process, it is good practice to run multiple chains to ensure that a representative posterior is attained. When sampling is completed, the multiple chains may be checked for convergence with the plot(myModel, type = "trace") command. The chains should resemble a "furry caterpillar".

nthin is a numerical value that specifies the "skipping" behavior of the MCMC samples being chosen to generate the posterior distributions. By default, nthin is equal to 1, hence every sample is used to generate the posterior.

Contol Parameters: adapt_delta, stepsize, and max_treedepth are advanced options that give the user more control over Stan's MCMC sampler. The Stan creators recommend that only advanced users change the default values, as alterations can profoundly change the sampler's behavior. Refer to Hoffman & Gelman (2014, Journal of Machine Learning Research) for more information on the functioning of the sampler control parameters. One can also refer to section 58.2 of the Stan User's Manual for a less technical description of these arguments.

Value

modelData A class "hBayesDM" object with the following components:

model

Character string with the name of the model ("dd_hyperbolic").

allIndPars

"data.frame" containing the summarized parameter values (as specified by "indPars") for each subject.

parVals

A "list" where each element contains posterior samples over different model parameters.

fit

A class "stanfit" object containing the fitted model.

rawdata

"data.frame" containing the raw data used to fit the model, as specified by the user.

References

Mazur, J. E. (1987). An adjustment procedure for studying delayed reinforcement.

Hoffman, M. D., & Gelman, A. (2014). The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. The Journal of Machine Learning Research, 15(1), 1593-1623.

See Also

We refer users to our in-depth tutorial for an example of using hBayesDM: https://rpubs.com/CCSL/hBayesDM

Examples

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## Not run: 
# Run the model and store results in "output"
output <- dd_hyperbolic("example", 2000, 1000, 3, 3)

# Plot the posterior distributions of the hyper-parameters
plot(output)

# Show the WAIC and LOOIC model fit estimates 
printFit(output)

## End(Not run)