Simulate from the meta-d' model — sim

Generate a simulated dataset 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(
  N_trials = 100,
  dprime = 1,
  c = 0,
  M = 1,
  c2_0_diff = rep(0.5, 3),
  c2_1_diff = rep(0.5, 3),
  metac_absolute = TRUE,
  summarize = FALSE,
  lcdf = normal_lcdf,
  lccdf = normal_lccdf
)

Arguments

N_trials

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

dprime

The sensitivity of the signal detection agent to simulate

c

The response bias of the signal detection agent to simulate

M

The metacognitive efficiency of the agent, where negative values indicate below chance metacognitive sensitivity, 0 indicates an absence of metacognitive sensitivity, values between 0 and 1 indicate metacognitive inefficiency, 1indicates optimal metacognitive sensitivity, and values greater than1` indicate metacognitive hyper-efficiency.

c2_0_diff, c2_1_diff

Distances between confidence thresholds for "0" and "1" responses, such that meta_c2_0 = meta_c - cumsum(c2_0_diff) and meta_c2_1 = meta_c + cumsum(c2_1_diff).

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, 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(N_trials = 10)
#> # A tibble: 10 × 14
#> # Groups:   stimulus, response, confidence [8]
#>    trial stimulus response correct confidence dprime     c meta_dprime     M
#>    <int>    <int>    <int>   <int>      <int>  <dbl> <dbl>       <dbl> <dbl>
#>  1     1        0        0       1          1      1     0           1     1
#>  2     2        0        0       1          1      1     0           1     1
#>  3     3        0        0       1          2      1     0           1     1
#>  4     4        0        0       1          4      1     0           1     1
#>  5     5        0        1       0          1      1     0           1     1
#>  6     1        1        0       0          2      1     0           1     1
#>  7     2        1        0       0          4      1     0           1     1
#>  8     3        1        1       1          1      1     0           1     1
#>  9     4        1        1       1          1      1     0           1     1
#> 10     5        1        1       1          4      1     0           1     1
#> # ℹ 5 more variables: meta_c2_0 <list>, meta_c2_1 <list>, theta <dbl>,
#> #   theta_1 <dbl>, theta_2 <dbl>
sim_metad(N_trials = 10000, summarize = TRUE)
#> # A tibble: 16 × 14
#> # Groups:   stimulus [2]
#>    stimulus response correct confidence     n dprime     c meta_dprime     M
#>       <int>    <int>   <int>      <int> <int>  <dbl> <dbl>       <dbl> <dbl>
#>  1        0        0       1          1   967      1     0           1     1
#>  2        0        0       1          2   951      1     0           1     1
#>  3        0        0       1          3   727      1     0           1     1
#>  4        0        0       1          4   828      1     0           1     1
#>  5        0        1       0          1   706      1     0           1     1
#>  6        0        1       0          2   487      1     0           1     1
#>  7        0        1       0          3   213      1     0           1     1
#>  8        0        1       0          4   121      1     0           1     1
#>  9        1        0       0          1   754      1     0           1     1
#> 10        1        0       0          2   455      1     0           1     1
#> 11        1        0       0          3   241      1     0           1     1
#> 12        1        0       0          4   110      1     0           1     1
#> 13        1        1       1          1   981      1     0           1     1
#> 14        1        1       1          2   937      1     0           1     1
#> 15        1        1       1          3   766      1     0           1     1
#> 16        1        1       1          4   756      1     0           1     1
#> # ℹ 5 more variables: meta_c2_0 <list>, meta_c2_1 <list>, theta <dbl>,
#> #   theta_1 <dbl>, theta_2 <dbl>
sim_metad(N_trials = 10, c2_0_diff = 1, c2_1_diff = 1)
#> # A tibble: 10 × 14
#> # Groups:   stimulus, response, confidence [5]
#>    trial stimulus response correct confidence dprime     c meta_dprime     M
#>    <int>    <int>    <int>   <int>      <int>  <dbl> <dbl>       <dbl> <dbl>
#>  1     1        0        0       1          1      1     0           1     1
#>  2     2        0        0       1          1      1     0           1     1
#>  3     3        0        0       1          1      1     0           1     1
#>  4     4        0        0       1          1      1     0           1     1
#>  5     5        0        1       0          1      1     0           1     1
#>  6     1        1        0       0          1      1     0           1     1
#>  7     2        1        1       1          1      1     0           1     1
#>  8     3        1        1       1          1      1     0           1     1
#>  9     4        1        1       1          1      1     0           1     1
#> 10     5        1        1       1          2      1     0           1     1
#> # ℹ 5 more variables: meta_c2_0 <list>, meta_c2_1 <list>, theta <dbl>,
#> #   theta_1 <dbl>, theta_2 <dbl>