betaMPT {TreeBUGS}

Fit a Hierarchical Beta-MPT Model

Description

Fits a Beta-MPT model (Smith & Batchelder, 2010) based on a standard MPT model file (.eqn) and individual data table (.csv).

Usage

betaMPT(
  eqnfile,
  data,
  restrictions,
  covData,
  transformedParameters,
  corProbit = FALSE,
  alpha = "dgamma(1, 0.1)T(1,)",
  beta = "dgamma(1, 0.1)T(1,)",
  n.iter = 20000,
  n.adapt = 2000,
  n.burnin = 2000,
  n.thin = 5,
  n.chains = 3,
  dic = FALSE,
  ppp = 0,
  monitorIndividual = TRUE,
  modelfilename,
  parEstFile,
  posteriorFile,
  autojags = NULL,
  ...
)

Arguments

eqnfile

The (relative or full) path to the file that specifies the MPT model (standard .eqn syntax). Note that category labels must start with a letter (different to multiTree) and match the column names of data. Alternatively, the EQN-equations can be provided within R as a character value (cf. readEQN). Note that the first line of an .eqn-file is reserved for comments and always ignored.

data

The (relative or full) path to the .csv file with the data (comma separated; category labels in first row). Alternatively: a data frame or matrix (rows=individuals, columns = individual category frequencies, category labels as column names)

restrictions

Specifies which parameters should be (a) constant (e.g., "a=b=.5") or (b) constrained to be identical (e.g., "Do=Dn") or (c) treated as fixed effects (i.e., identical for all participants; "a=b=FE"). Either given as the path to a text file with restrictions per row or as a list of restrictions, e.g., list("D1=D2","g=0.5"). Note that numbers in .eqn-equations (e.g., d*(1-g)*.50) are directly interpreted as equality constraints.

covData

Data that contains covariates, for which correlations with individual MPT parameters will be sampled. Either the path to a .csv file (comma-separated: rows=individuals in the same order as data; first row must contain covariate labels). Alternatively: a data frame or matrix (rows=individuals, columns = variables; covariate labels as column names). Note that in betaMPT, correlations are computed for discrete variables that are coded numerically (in traitMPT, this can be suppressed by using predType="f")

transformedParameters

list with parameter transformations that should be computed based on the posterior samples of the group-level means (e.g., for testing parameter differences: list("diffD=Do-Dn")), or path to a text file containing one transformation per line. Transformations of individual-level parameters can also be performed after fitting a model using transformedParameters.

corProbit

whether to use probit-transformed MPT parameters to compute correlations (probit-values of +Inf are truncated to max(5,max(probit)); similarly for -Inf). Default for beta-MPT: MPT parameters are used on the probability scale [0,1].

alpha

Hyperprior for the shape parameters \alpha of the group-level beta distributions (in JAGS syntax). Default: Truncated gamma distributions for \alpha and \beta with shape 1 and rate 0.1 and truncated to be larger than 1 (see plotPrior). A named vector can be used to specify separate hyperpriors for each MPT parameter (if unnamed, the order of parameters is determined by the default order as shown by readEQN with paramOrder = TRUE). Originally, Smith and Batchelder (2008) used the "WinBUGS-zeros-trick" (available in TreeBUGS if alpha="zero" or beta="zero"), which approximates uniform priors on the group-level mean and SD (but often results convergence issues).

beta

Hyperprior for \beta of group-level distributions, see alpha.

n.iter

Number of iterations per chain (including burnin samples). See run.jags for details.

n.adapt

number of adaption samples to adjust MCMC sampler in JAGS. The sampler will be more efficient if it is tuned well. However, MCMC sampling will still give correct results even if the warning appears: "Adaptation incomplete." (this just means that sampling efficiency could be better).

n.burnin

Number of samples for burnin (samples will not be stored and removed from n.iter)

n.thin

Thinning rate.

n.chains

number of MCMC chains (sampled in parallel).

dic

whether to compute DIC using extract.runjags, which requires additional sampling. Can also be computed and added after fitting the model by fittedModel$summary$dic <- runjags::extract(fittedModel$runjags, "dic"). As an alternative information criterion, WAIC can be computed for fitted models.

ppp

number of samples to compute posterior predictive p-value (see posteriorPredictive)

monitorIndividual

whether to store MCMC samples of the MPT parameters theta at the individual level (i.e., the random effects). If FALSE, it is not possible to perform posterior-predictive checks.

modelfilename

name of the generated JAGS model file. Default is to write this information to the tempdir as required by CRAN standards.

parEstFile

Name of the file to with the estimates should be stored (e.g., "parEstFile.txt")

posteriorFile

path to RData-file where to save the model including MCMC posterior samples (an object named fittedModel; e.g., posteriorFile="mcmc.RData")

autojags

JAGS first fits the MPT model as usual and then draws MCMC samples repeatedly until convergence. For this, the function autoextend.jags is used with the arguments provided in autojags (this can be an empty list, in which case the defaults are used). Possible arguments for autoextend.jags are: list(startburnin = 1000, startsample = 5000, adapt = 2000, max.time="30m") (the last of these arguments restricts sampling to 30 minutes, see autoextend.jags).

...

further arguments to be passed to the JAGS sampling function (i.e., to run.jags. Note that reproducible results are obtained by setting a random seed before fitting a model (i.e., set.seed(12345) ).

Details

Note that, in the Beta-MPT model, correlations of individual MPT parameters with covariates are sampled. Hence, the covariates do not affect the estimation of the actual Beta-MPT parameters. Therefore, the correlation of covariates with the individual MPT parameters can equivalently be performed after fitting the model using the sampled posterior parameter values stored in betaMPT$mcmc

Value

a list of the class betaMPT with the objects:

• summary: MPT tailored summary. Use summary(fittedModel)

• mptInfo: info about MPT model (eqn and data file etc.)

• runjags: the object returned from the MCMC sampler. Note that the object fittedModel$runjags is an runjags object, whereas fittedModel$runjags$mcmc is a mcmc.list as used by the coda package (mcmc)

Author(s)

Daniel W. Heck, Nina R. Arnold, Denis Arnold

References

Heck, D. W., Arnold, N. R., & Arnold, D. (2018). TreeBUGS: An R package for hierarchical multinomial-processing-tree modeling. Behavior Research Methods, 50, 264–284. doi:10.3758/s13428-017-0869-7

Smith, J. B., & Batchelder, W. H. (2010). Beta-MPT: Multinomial processing tree models for addressing individual differences. Journal of Mathematical Psychology, 54, 167-183. doi:10.1016/j.jmp.2009.06.007

Examples

## Not run: 
# fit beta-MPT model for encoding condition (see ?arnold2013):
EQNfile <- system.file("MPTmodels/2htsm.eqn", package = "TreeBUGS")
d.encoding <- subset(arnold2013, group == "encoding", select = -(1:4))
fit <- betaMPT(EQNfile, d.encoding,
  n.thin = 5,
  restrictions = list("D1=D2=D3", "d1=d2", "a=g")
)
# convergence
plot(fit, parameter = "mean", type = "default")
summary(fit)

## End(Not run)