genBetaMPT: Generate Data for Beta MPT Models

Description

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

Usage

genBetaMPT(
  N,
  numItems,
  eqnfile,
  restrictions,
  mean = NULL,
  sd = NULL,
  alpha = NULL,
  beta = NULL,
  warning = TRUE
)

Value

a list including the generated frequencies (data) and the true, underlying parameters (parameters) on the group and individual level.

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 true group means of individual MPT parameters. If the vector is not named, the internal order of parameters is used (can be obtained using readEQN).
sd: named vector of group standard deviations of individual MPT parameters.
alpha: Alternative specification of the group-level distribution using the shape parameters of the beta distribution (see dbeta).
beta: see alpha
warning: whether to show warning in case the naming of data-generating parameters are unnamed or do not match

Details

Data are generated in a two-step procedure. First, person parameters are sampled from the specified beta distributions for each paramter (either based on mean/sd or based on alpha/beta). In a second step, response frequencies are sampled for each person using genMPT.

References

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

Examples

Run this code

# Example: Standard Two-High-Threshold Model (2HTM)
EQNfile <- system.file("MPTmodels/2htm.eqn", package = "TreeBUGS")
genDat <- genBetaMPT(
  N = 100,
  numItems = c(Target = 250, Lure = 250),
  eqnfile = EQNfile,
  mean = c(Do = .7, Dn = .5, g = .5),
  sd = c(Do = .1, Dn = .1, g = .05)
)
head(genDat$data, 3)
plotFreq(genDat$data, eqn = EQNfile)

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