Distribution functions for the Memory Measurement Model (M3)

Density and random generation functions for the memory measurement model. Please note that these functions are currently not vectorized.

Usage

dm3(x, pars, m3_model, act_funs = NULL, log = TRUE, ...)

rm3(n, size, pars, m3_model, act_funs = NULL, unpack = FALSE, ...)

Arguments

x: Integer vector of length K where K is the number of response categories and each value is the number of observed responses per category
pars: A named vector of parameters of the memory measurement model. Note: The fixed parameter b does not need to be provided - it will be automatically added from the model specification if missing.
m3_model: A bmmodel object specifying the m3 model that densities or random samples should be generated for
act_funs: A bmmformula object specifying the activation functions for the different response categories. This can be either: (1) Just the activation formulas (one for each response category), or (2) A full bmmformula including both activation formulas and other parameters. If a full formula is provided, only the formulas matching response categories will be extracted. The default will attempt to construct the standard activation functions for the "ss" and "cs" model version. For a custom m3 model you need to specify the act_funs argument manually.
log: Logical; if TRUE (default), values are returned on the log scale.
...: can be used to pass additional variables that are used in the activation functions, but not parameters of the model
n: Integer. Number of observations to generate data for
size: The total number of observations in all 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 for backward compatibility.

Value

dm3 gives the density of the memory measurement model, and rm3 gives the random generation function for the memory measurement model.

References

Oberauer, K., & Lewandowsky, S. (2019). Simple measurement models for complex working-memory tasks. Psychological Review, 126(6), 880–932. https://doi.org/10.1037/rev0000159

Examples

# Basic usage - b parameter is added automatically
model <- m3(
  resp_cats = c("corr", "other", "npl"),
  num_options = c(1, 4, 5),
  choice_rule = "simple",
  version = "ss"
)

# No need to provide b parameter
dm3(x = c(20, 10, 10), pars = c(a = 1, c = 2), m3_model = model)
#> [1] -14.88885
rm3(n = 10, size = 100, pars = c(a = 1, c = 2), m3_model = model)
#>       corr other npl
#>  [1,]   43    54   3
#>  [2,]   40    55   5
#>  [3,]   38    59   3
#>  [4,]   40    49  11
#>  [5,]   51    46   3
#>  [6,]   42    50   8
#>  [7,]   34    60   6
#>  [8,]   41    55   4
#>  [9,]   37    59   4
#> [10,]   37    55   8

# Can also use full formula (activation formulas are extracted automatically)
full_formula <- bmf(
  corr ~ b + a + c,
  other ~ b + a, 
  npl ~ b,
  a ~ 1,
  c ~ 1
)
rm3(n = 10, size = 100, pars = c(a = 1, c = 2), 
    m3_model = model, act_funs = full_formula)
#>       corr other npl
#>  [1,]   39    56   5
#>  [2,]   38    56   6
#>  [3,]   47    48   5
#>  [4,]   39    55   6
#>  [5,]   31    56  13
#>  [6,]   44    51   5
#>  [7,]   40    54   6
#>  [8,]   43    55   2
#>  [9,]   44    48   8
#> [10,]   41    52   7
    
if (FALSE) { # \dontrun{
# Use with dplyr::reframe() for automatic unpacking into columns
library(dplyr)
library(tibble)
param_grid <- expand.grid(a = c(0.5, 1, 1.5), c = c(1, 2, 3))

simulated_data <- param_grid %>%
  rowwise() %>%
  reframe(
    a = a,
    c = c,
    # unpack=TRUE returns named vector; wrap in as_tibble_row for auto-unpacking
    as_tibble_row(rm3(n = 1, size = 100, pars = c(a = a, c = c), 
                      m3_model = model, unpack = TRUE))
  )
# Result has columns: a, c, corr, other, npl
} # }