Simulate from the hierarchical meta-d' model — sim_metad

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

Usage

sim_metad_participant(
  N_participants = 100,
  N_trials = 100,
  mean_dprime = 1,
  sd_dprime = 0.5,
  mean_c = 0,
  sd_c = 0.5,
  mean_M = 0,
  sd_M = 0.5,
  mean_z_c2_0 = rep(-1, 3),
  sd_z_c2_0 = rep(0.1, 3),
  r_z_c2_0 = diag(3),
  mean_z_c2_1 = rep(-1, 3),
  sd_z_c2_1 = rep(0.1, 3),
  r_z_c2_1 = diag(3),
  metac_absolute = TRUE,
  allow_negative_values = FALSE,
  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.
mean_dprime, sd_dprime: The mean and standard deviation of sensitivities of the signal detection agents to simulate
mean_c, sd_c: The mean and standard deviation of response bias of the signal detection agents to simulate
mean_M, sd_M: The mean and standard deviation of metacognitive efficiency of the agents. If allow_negative_values==TRUE (default), M-ratio is simulated on the logarithmic scale, where 0 indicates optimal metacognitive sensitivity, negative numbers indicate metacognitive inefficiency, and positive numbers indicate metacognitive hyper-efficiency. Otherwise, M-ratio is modeled on its natural scale to allow negative values.
mean_z_c2_0, mean_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, sd_z_c2_1: SD of log distances between confidence thresholds for "0" and "1" responses on the log_scale.
r_z_c2_0, r_z_c2_1: Correlation 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.
allow_negative_values: If allow_negative_values=FALSE (default), M-ratio is simulated using a normal distribution on the logarithmic scale to prohibit negative values. If allow_negative_values=TRUE, then M-ratio is simulated on its natural scale, allowing negative values.
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
participant: the simulated participant 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(N_participants = 10, N_trials = 10)
#> # A tibble: 100 × 15
#>    participant trial stimulus response correct confidence dprime     c
#>          <int> <int>    <int>    <int>   <int>      <int>  <dbl> <dbl>
#>  1           1     1        0        0       1          1  0.498 0.304
#>  2           1     2        0        0       1          2  0.498 0.304
#>  3           1     3        0        0       1          2  0.498 0.304
#>  4           1     4        0        0       1          2  0.498 0.304
#>  5           1     5        0        0       1          3  0.498 0.304
#>  6           1     1        1        0       0          1  0.498 0.304
#>  7           1     2        1        0       0          4  0.498 0.304
#>  8           1     3        1        1       1          1  0.498 0.304
#>  9           1     4        1        1       1          2  0.498 0.304
#> 10           1     5        1        1       1          4  0.498 0.304
#> # ℹ 90 more rows
#> # ℹ 7 more variables: meta_dprime <dbl>, M <dbl>, meta_c2_0 <list>,
#> #   meta_c2_1 <list>, theta <dbl>, theta_1 <dbl>, theta_2 <dbl>
sim_metad_participant(N_participants = 25, mean_dprime = 2, mean_M = -1)
#> # A tibble: 2,500 × 15
#>    participant trial stimulus response correct confidence dprime      c
#>          <int> <int>    <int>    <int>   <int>      <int>  <dbl>  <dbl>
#>  1           1     1        0        0       1          1   2.16 -0.556
#>  2           1     2        0        0       1          1   2.16 -0.556
#>  3           1     3        0        0       1          1   2.16 -0.556
#>  4           1     4        0        0       1          1   2.16 -0.556
#>  5           1     5        0        0       1          1   2.16 -0.556
#>  6           1     6        0        0       1          1   2.16 -0.556
#>  7           1     7        0        0       1          2   2.16 -0.556
#>  8           1     8        0        0       1          2   2.16 -0.556
#>  9           1     9        0        0       1          2   2.16 -0.556
#> 10           1    10        0        0       1          2   2.16 -0.556
#> # ℹ 2,490 more rows
#> # ℹ 7 more variables: meta_dprime <dbl>, M <dbl>, meta_c2_0 <list>,
#> #   meta_c2_1 <list>, theta <dbl>, theta_1 <dbl>, theta_2 <dbl>