Distribution functions for Multinomial Processing Tree (MPT) models

Density and random generation functions for multinomial processing tree models specified with mpt(). Please note that these functions are currently not vectorized.

Usage

dmpt(x, pars, mpt_model, tree = NULL, log = TRUE, covariates = NULL, ...)

rmpt(
  n,
  size,
  pars,
  mpt_model,
  tree = NULL,
  unpack = FALSE,
  covariates = NULL,
  ...
)

Arguments

x

Integer vector of length K, where K is the number of response categories, giving the number of observed responses per category. If x is a named vector, its names are matched to the response categories and the vector is reordered accordingly; an unnamed vector is read in the order of the model's response categories, mpt_model$resp_vars$resp_cats, which is the order of the first tree given to mpt() (mpt() stores the branches of every tree in that order, whatever order they were written in). rmpt() returns its columns in the same order.

pars

A named vector or list with the values of at least the latent parameters appearing in the branch expressions of the selected tree, on the probability scale and strictly between 0 and 1, as for fixed parameters in bmm(). Values for parameters the tree does not use are ignored, so one vector can serve every tree of the model. Parameters of a simplex group must sum to 1.

mpt_model

A bmmodel object created with mpt() specifying the model that densities or random samples should be generated for.

tree

Character. For models with multiple trees, the name of the tree to compute probabilities for. Can be omitted for single-tree models.

log

Logical; if TRUE (default), densities are returned on the log scale.

covariates

A named vector or list with the values of all covariates declared in the model that appear in the branch expressions of the selected tree.

...

can be used to pass additional values used in the branch expressions, as an alternative to the covariates argument.

n

Integer. Number of observations to generate data for.

size

The total number of observations across all response categories.

unpack

Logical; if TRUE and n = 1, returns a named vector instead of a matrix. This allows automatic unpacking of response categories into separate columns when used with dplyr::reframe(). Default is FALSE.

Value

dmpt gives the multinomial density of a vector of response counts, and rmpt generates random response counts for the response categories.

Note

Unlike the densities of the circular models in this package (dsdm(), dmixture2p(), dmixture3p(), dimm()) and unlike stats::dmultinom(), dmpt() returns the log density by default, matching dm3().

References

Batchelder, W. H., & Riefer, D. M. (1999). Theoretical and empirical review of multinomial process tree modeling. Psychonomic Bulletin & Review, 6(1), 57-86. https://doi.org/10.3758/BF03210812

Examples

tree_target <- mpt_tree("target", list(
  old = "D + (1 - D) * g",
  new = "(1 - D) * (1 - g)"
))
tree_lure <- mpt_tree("lure", list(
  old = "(1 - D) * g",
  new = "D + (1 - D) * (1 - g)"
))
model <- mpt(list(tree_target, tree_lure), tree_id = "item_type")

dmpt(
  x = c(35, 15), pars = c(D = 0.7, g = 0.5),
  mpt_model = model, tree = "target"
)
#> [1] -5.702642
rmpt(
  n = 10, size = 50, pars = c(D = 0.7, g = 0.5),
  mpt_model = model, tree = "lure"
)
#>       old new
#>  [1,]   6  44
#>  [2,]  13  37
#>  [3,]   3  47
#>  [4,]  10  40
#>  [5,]   6  44
#>  [6,]   9  41
#>  [7,]   6  44
#>  [8,]   4  46
#>  [9,]   9  41
#> [10,]   4  46