Simulate trial-level SS-vs-LL choice data

Generates binary choices from either the structural or descriptive choice model. When mode = "structural" (default) choices are drawn from the structural model: P(LL) = plogis(beta0 + gamma * ((ll/ss) * D(k, delay) - 1)), k_i = exp(log_k_pop + sigma_u * u_i). When mode = "descriptive" choices follow Young's (2018) correlated random-slope logistic model: each subject receives per-subject slopes drawn from a bivariate normal with mean theta and covariance Sigma, and P(LL) = plogis((theta[1] + b_i[1]) * log(ll/ss) + (theta[2] + b_i[2]) * log(delay + 1)). The descriptive branch is the known-truth generator used by recovery tests.

Usage

simulate_dd_choice(
  n_subjects = 50,
  ss_amount = c(40, 55, 31, 14, 47, 25, 78, 40, 11, 67),
  ll_amount = c(65, 75, 85, 25, 60, 30, 80, 65, 30, 75),
  delay = c(25, 61, 14, 19, 160, 7, 4, 62, 7, 119),
  mode = c("structural", "descriptive"),
  log_k_pop = log(0.02),
  sigma_u = 0.5,
  gamma = 4,
  beta0 = 0,
  equation = c("mazur", "exponential"),
  theta = c(1.5, -0.4),
  re_sd = c(0.5, 0.3),
  re_cor = -0.2,
  return_truth = FALSE,
  seed = NULL
)

Arguments

n_subjects

Integer number of subjects.

ss_amount, ll_amount, delay

Numeric trial-design vectors (same length); each subject is presented all trials. Defaults are a built-in grid.

mode

"structural" (default) or "descriptive". Selects the generative model.

log_k_pop, sigma_u, gamma, beta0

Structural truth (used only when mode = "structural").

equation

"mazur" or "exponential" (structural mode only).

theta

Length-2 numeric vector of population-level slopes for the descriptive model: theta[1] on log(ll/ss), theta[2] on log(delay + 1).

re_sd

Length-2 numeric vector of random-effect standard deviations (descriptive mode only).

re_cor

Correlation between the two random slopes (descriptive mode only).

return_truth

Logical. If TRUE and mode = "descriptive", the returned tibble carries two attributes: subject_slopes (n_subjects x 2 matrix of realized b_i values) and Sigma (the 2x2 covariance matrix).

seed

Optional integer seed for reproducibility.

Value

A tibble with columns id, ss_amount, ll_amount, delay, choice (0/1, 1 = LL chosen). When mode = "descriptive" and return_truth = TRUE, the tibble also carries subject_slopes and Sigma attributes.

Examples

# Structural (default)
sim <- simulate_dd_choice(n_subjects = 20, seed = 1)
head(sim)
#> # A tibble: 6 × 5
#>   id    ss_amount ll_amount delay choice
#>   <chr>     <dbl>     <dbl> <dbl>  <int>
#> 1 1            40        65    25      0
#> 2 1            55        75    61      0
#> 3 1            31        85    14      1
#> 4 1            14        25    19      1
#> 5 1            47        60   160      0
#> 6 1            25        30     7      0

# Descriptive (Young 2018 correlated random-slope model)
sim_desc <- simulate_dd_choice(n_subjects = 20, mode = "descriptive",
                               theta = c(1.5, -0.4), seed = 42)
head(sim_desc)
#> # A tibble: 6 × 5
#>   id    ss_amount ll_amount delay choice
#>   <chr>     <dbl>     <dbl> <dbl>  <int>
#> 1 1            40        65    25      0
#> 2 1            55        75    61      0
#> 3 1            31        85    14      0
#> 4 1            14        25    19      0
#> 5 1            47        60   160      0
#> 6 1            25        30     7      0