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Simulate from the hierarchical meta-d' model across within-participant conditions

Source: R/simulate.R
sim_metad_participant_condition.Rd

Generate a simulated dataset across participants and conditions from the meta-d' model with sensitivity dprime, response bias c, metacognitive efficiency log_M, and distances between confidence thresholds c2_0_diff and c2_1_diff (for the two responses).

Usage

sim_metad_participant_condition(
  N_participants = 100,
  N_trials = 100,
  mu_dprime = rep(1, 2),
  sd_dprime = rep(0.5, 2),
  r_dprime = diag(2),
  mu_c = rep(0, 2),
  sd_c = rep(0.5, 2),
  r_c = diag(2),
  mu_log_M = rep(0, 2),
  sd_log_M = rep(0.5, 2),
  r_log_M = diag(2),
  mu_z_c2_0 = matrix(rep(-1, 6), nrow = 3, ncol = 2),
  sd_z_c2_0_condition = rep(0.1, 2),
  r_z_c2_0_condition = diag(2),
  sd_z_c2_0_confidence = rep(0.1, 3),
  r_z_c2_0_confidence = diag(3),
  mu_z_c2_1 = matrix(rep(-1, 6), nrow = 3, ncol = 2),
  sd_z_c2_1_condition = rep(0.1, 2),
  r_z_c2_1_condition = diag(2),
  sd_z_c2_1_confidence = rep(0.1, 3),
  r_z_c2_1_confidence = diag(3),
  metac_absolute = TRUE,
  summarize = FALSE,
  lcdf = normal_lcdf,
  lccdf = normal_lccdf
)

Arguments

N_trials, N_participants

Total number of participants and trials to simulate per participant. Half of these trials will have stimulus=0 and half will have stimulus=1.

mu_dprime, sd_dprime, r_dprime

The mean, standard deviation, and within-participant correlations of sensitivities of the signal detection agents to simulate

mu_c, sd_c, r_c

The mean, standard deviation, and within-participant correlations of response bias of the signal detection agents to simulate

mu_log_M, sd_log_M, r_log_M

The mean, standard deviation, and within-participant correlations of metacognitive efficiency of the agents on the logarithmic scale, where 0 indicates optimal metacognitive sensitivity, negative numbers indicate metacognitive inefficiency, and positive numbers indicate metacognitive hyper-efficiency.

mu_z_c2_0, mu_z_c2_1

Mean distance between confidence thresholds for "0" and "1" responses on the log_scale, such that meta_c2_0 = meta_c - cumulative_sum(exp(z_c2_0)) and meta_c2_1 = meta_c + cumulative_sum(exp(z_c2_1)).

sd_z_c2_0_condition, sd_z_c2_1_condition

SD of log distances across conditions between confidence thresholds for "0" and "1" responses on the log_scale.

r_z_c2_0_condition, r_z_c2_1_condition

Correlation across conditions of log distances between confidence thresholds for "0" and "1" responses on the log_scale.

sd_z_c2_0_confidence, sd_z_c2_1_confidence

SD of log distances across confidence levels between confidence thresholds for "0" and "1" responses on the log_scale.

r_z_c2_0_confidence, r_z_c2_1_confidence

Correlation across confidence levels of log distances between confidence thresholds for "0" and "1" responses on the log_scale.

metac_absolute

Determines how to fix the type 1 threshold for modeling confidence ratings. If metac_absolute=TRUE, meta_c = c. Otherwise, meta_c = M * c.

summarize

Aggregate the data? If summarize=FALSE, returns a dataset with one row per observation. If summarize=TRUE, returns an aggregated dataset where n is the number of observations per response, accuracy, and confidence level.

lcdf

The log cumulative distribution function of the underlying signal distribution. By default, uses a normal(+/- dprime/2, 1) distribution.

lccdf

The log complement cumulative distribution function of the underlying signal distribution. By default, uses a normal(+/- dprime/2, 1) distribution.

Value

A simulated dataset of type 1 responses and confidence ratings, with columns:

  • trial: the simulated trial number

  • stimulus: the value of the stimulus on each trial (either 0 or 1)

  • response: the simulated type 1 response (either 0 or 1)

  • correct: whether stimulus==response (either 0 or 1)

  • confidence: the simulated type 2 response (from 1 to length(c2_0_diff)+1)

  • dprime:theta_2: the simulated agent's parameter values If summarize=TRUE, the trial column is replaced with an n column indicating the number of simulated type 1/type 2 responses for each possible value.

Examples

sim_metad_participant_condition(10, 10)
#> # A tibble: 200 × 16
#>    participant condition trial stimulus response correct confidence dprime
#>          <int>     <int> <int>    <int>    <int>   <int>      <int>  <dbl>
#>  1           1         1     1        0        0       1          1  0.675
#>  2           1         1     2        0        0       1          1  0.675
#>  3           1         1     3        0        1       0          3  0.675
#>  4           1         1     4        0        1       0          3  0.675
#>  5           1         1     5        0        1       0          4  0.675
#>  6           1         1     1        1        0       0          1  0.675
#>  7           1         1     2        1        0       0          4  0.675
#>  8           1         1     3        1        1       1          1  0.675
#>  9           1         1     4        1        1       1          3  0.675
#> 10           1         1     5        1        1       1          4  0.675
#> # ℹ 190 more rows
#> # ℹ 8 more variables: c <dbl>, meta_dprime <dbl>, M <dbl>, meta_c2_0 <list>,
#> #   meta_c2_1 <list>, theta <dbl>, theta_1 <dbl>, theta_2 <dbl>