traitMPT {TreeBUGS}R Documentation

Fit a Hierarchical Latent-Trait MPT Model

Description

Fits a latent-trait MPT model (Klauer, 2010) based on a standard MPT model file (.eqn) and individual data table (.csv).

Usage

traitMPT(
  eqnfile,
  data,
  restrictions,
  covData,
  predStructure,
  predType,
  transformedParameters,
  corProbit = TRUE,
  mu = "dnorm(0,1)",
  xi = "dunif(0,10)",
  V,
  df,
  IVprec = "dgamma(.5,.5)",
  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")

predStructure

Defines which variables in covData are included as predictors for which MPT parameters. Either the path to the file that specifies the assignment of MPT parameters to covariates (that is, each row assigns one or more MPT parameters to one or more covariates, separated by a semicolon, e.g., Do g; age extraversion). Can also be provided as a list, e.g., list("Do Dn ; age", "g ; extraversion"). Note that no correlations of MPT parameters and predictors are computed. However, for continuous covariates, the standardized slope parameters slope_std_parameter_predictor can be interpreted as a correlation if a single predictor is included for the corresponding MPT parameter (see Jobst et al., 2020).

predType

a character vector specifying the type of continuous or discrete predictors in each column of covData: "c" = continuous covariate (which are centered to have a mean of zero); "f" = discrete predictor, fixed effect (default for character/factor variables); "r" = discrete predictor, random effect.

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].

mu

hyperprior for group means of probit-transformed parameters in JAGS syntax. Default is a standard normal distribution, which implies a uniform distribution on the MPT probability parameters. A named vector can be used to specify separate hyperpriors for each MPT parameter (the order of parameters is determined by the names of the vector or by the default order as shown in readEQN with paramOrder = TRUE).

xi

hyperprior for scaling parameters of the group-level parameter variances. Default is a uniform distribution on the interval [0,10]. Similarly as for mu, a vector of different priors can be used. Less informative priors can be used (e.g., "dunif(0,100)")) but might result in reduced stability.

V

S x S matrix used as a hyperprior for the inverse-Wishart hyperprior parameters with as many rows and columns as there are core MPT parameters. Default is a diagonal matrix.

df

degrees of freedom for the inverse-Wishart hyperprior for the individual parameters. Minimum is S+1, where S gives the number of core MPT parameters.

IVprec

hyperprior on the precision parameter g (= the inverse of the variance) of the standardized slope parameters of continuous covariates. The default IVprec=dgamma(.5,.5) defines a mixture of g-priors (also known as JZS or Cauchy prior) with the scale parameter s=1. Different scale parameters s can be set via: IVprec=dgamma(.5,.5*s^2). A numeric constant IVprec=1 implies a g-prior (a normal distribution). For ease of interpretation, TreeBUGS reports both unstandardized and standardized regression coefficients. See details below.

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) ).

Value

a list of the class traitMPT with the objects:

Regression Extensions

Continuous and discrete predictors are added on the latent-probit scale via:

\theta = \Phi(\mu + X \beta +\delta ),

where X is a design matrix includes centered continuous covariates and recoded factor variables (using the orthogonal contrast coding scheme by Rouder et al., 2012). Note that both centering and recoding is done internally. TreeBUGS reports unstandardized regression coefficients \beta that correspond to the scale/SD of the predictor variables. Hence, slope estimates will be very small if the covariate has a large variance. TreeBUGS also reports standardized slope parameters (labeled with std) which are standardized both with respect to the variance of the predictor variables and the variance in the individual MPT parameters. If a single predictor variable is included, the standardized slope can be interpreted as a correlation coefficient (Jobst et al., 2020).

For continuous predictor variables, the default prior IVprec = "dgamma(.5,.5)" implies a Cauchy prior on the \beta parameters (standardized with respect to the variance of the predictor variables). This prior is similar to the Jeffreys-Zellner-Siow (JZS) prior with scale parameter s=1 (for details, see: Rouder et. al, 2012; Rouder & Morey, 2012). In contrast to the JZS prior for standard linear regression by Rouder & Morey (2012), TreeBUGS implements a latent-probit regression where the prior on the coefficients \beta is only standardized/scaled with respect to the continuous predictor variables but not with respect to the residual variance (since this is not a parameter in probit regression). If small effects are expected, smaller scale values s can be used by changing the default to IVprec = 'dgamma(.5, .5*s^2)' (by plugging in a specific number for s). To use a standard-normal instead of a Cauchy prior distribution, use IVprec = 'dcat(1)'. Bayes factors for slope parameters of continuous predictors can be computed with the function BayesFactorSlope.

Uncorrelated Latent-Trait Values

The standard latent-trait MPT model assumes a multivariate normal distribution of the latent-trait values, where the covariance matrix follows a scaled-inverse Wishart distribution. As an alternative, the parameters can be assumed to be independent (this is equivalent to a diagonal covariance matrix). If the assumption of uncorrelated parameters is justified, such a simplified model has less parameters and is more parsimonious, which in turn might result in more robust estimation and more precise parameter estimates.

This alternative method can be fitted in TreeBUGS (but not all of the features of TreeBUGS might be compatible with this alternative model structure). To fit the model, the scale matrix V is set to NA (V is only relevant for the multivariate Wishart prior) and the prior on xi is changed: traitMPT(..., V=NA, xi="dnorm(0,1)"). The model assumes that the latent-trait values \delta_i (=random-intercepts) are decomposed by the scaling parameter \xi and the raw deviation \epsilon_i (cf. Gelman, 2006):

\delta_i = \xi \cdot \epsilon_i

\epsilon_i \sim Normal(0,\sigma^2)

\sigma^2 \sim Inverse-\chi^2(df)

Note that the default prior for \xi should be changed to xi="dnorm(0,1)", which results in a half-Cauchy prior (Gelman, 2006).

Author(s)

Daniel W. Heck, Denis Arnold, Nina R. 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

Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Analysis, 1, 515-534.

Jobst, L. J., Heck, D. W., & Moshagen, M. (2020). A comparison of correlation and regression approaches for multinomial processing tree models. Journal of Mathematical Psychology, 98, 102400. doi:10.1016/j.jmp.2020.102400

Klauer, K. C. (2010). Hierarchical multinomial processing tree models: A latent-trait approach. Psychometrika, 75, 70-98. doi:10.1007/s11336-009-9141-0

Matzke, D., Dolan, C. V., Batchelder, W. H., & Wagenmakers, E.-J. (2015). Bayesian estimation of multinomial processing tree models with heterogeneity in participants and items. Psychometrika, 80, 205-235. doi:10.1007/s11336-013-9374-9

Rouder, J. N., Morey, R. D., Speckman, P. L., & Province, J. M. (2012). Default Bayes factors for ANOVA designs. Journal of Mathematical Psychology, 56, 356-374. doi:10.1016/j.jmp.2012.08.001

Rouder, J. N., & Morey, R. D. (2012). Default Bayes Factors for Model Selection in Regression. Multivariate Behavioral Research, 47, 877-903. doi:10.1080/00273171.2012.734737

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 <- traitMPT(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)
[Package TreeBUGS version 1.5.0 Index]