genTraitMPT {TreeBUGS}

Generate Data for Latent-Trait MPT Models

Description

Generating a data set with known parameter structure using the Trait-MPT. Useful for simulations and robustness checks.

Usage

genTraitMPT(
  N,
  numItems,
  eqnfile,
  restrictions,
  mean,
  mu,
  sigma,
  rho,
  warning = TRUE
)

Arguments

N

number of participants

numItems

number of responses per tree (a named vector with tree labels)

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.

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.

mean

named vector of data-generating group means of the individual MPT parameters on the probability scale. If the vector is not named, the internal order of parameters is used (can be obtained using readEQN).

mu

an alternative way to define the group-level means on the latent-probit scale (i.e., mu = qnorm(mean) or equivalently, mean = pnorm(mu)).

sigma

(named) vector of group standard deviations of individual MPT parameters on the latent probit scale. Default is zero (no person heterogeneity).

rho

(named) correlation matrix for individual MPT parameters on the latent probit scale. Must be symmetric and positive definite (e.g., no correlations of 1 or -1 allowed). Default: a diagonal matrix (i.e., zero correlations).

warning

whether to show warning in case the naming of data-generating parameters are unnamed or do not match

Details

This functions implements a two-step sampling procedure. First, the person parameters on the latent probit-scale are sampled from the multivariate normal distribution (based on the mean mu = qnorm(mean), the standard deviations sigma, and the correlation matrix rho). These person parameters are then transformed to the probability scale using the probit-link. In a last step, observed frequencies are sampled for each person using the MPT equations.

Note that the user can generate more complex structures for the latent person parameters, and then supply these person parameters to the function genMPT.

Value

a list including the generated frequencies per person (data) and the sampled individual parameters (parameters) on the probit and probability scale (thetaLatent and theta, respectively).

References

Klauer, K. C. (2010). Hierarchical multinomial processing tree models: A latent-trait approach. Psychometrika, 75, 70-98.

See Also

genMPT

Examples

# Example: Standard Two-High-Threshold Model (2HTM)
EQNfile <- system.file("MPTmodels/2htm.eqn", package = "TreeBUGS")
rho <- matrix(c(
  1, .8, .2,
  .8, 1, .1,
  .2, .1, 1
), nrow = 3)
colnames(rho) <- rownames(rho) <- c("Do", "Dn", "g")
genDat <- genTraitMPT(
  N = 100,
  numItems = c(Target = 250, Lure = 250),
  eqnfile = EQNfile,
  mean = c(Do = .7, Dn = .7, g = .5),
  sigma = c(Do = .3, Dn = .3, g = .15),
  rho = rho
)
head(genDat$data, 3)
plotFreq(genDat$data, eqn = EQNfile)