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Simulate from the meta-d' model

Source: R/simulate.R
sim_metad.Rd

Generate a simulated dataset 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(
  N_trials = 100,
  dprime = 1,
  c = 0,
  log_M = 0,
  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

log_M

The metacognitive efficiency of the agent on the logarithmic scale, where 0 indicates optimal metacognitive sensitivity, negative numbers indicate metacognitive inefficiency, and positive numbers 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 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          2      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        1       1          1      1     0           1     1
#>  7     2        1        1       1          2      1     0           1     1
#>  8     3        1        1       1          2      1     0           1     1
#>  9     4        1        1       1          3      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   954      1     0           1     1
#>  2        0        0       1          2   983      1     0           1     1
#>  3        0        0       1          3   725      1     0           1     1
#>  4        0        0       1          4   809      1     0           1     1
#>  5        0        1       0          1   757      1     0           1     1
#>  6        0        1       0          2   439      1     0           1     1
#>  7        0        1       0          3   231      1     0           1     1
#>  8        0        1       0          4   102      1     0           1     1
#>  9        1        0       0          1   741      1     0           1     1
#> 10        1        0       0          2   445      1     0           1     1
#> 11        1        0       0          3   211      1     0           1     1
#> 12        1        0       0          4   125      1     0           1     1
#> 13        1        1       1          1   952      1     0           1     1
#> 14        1        1       1          2   948      1     0           1     1
#> 15        1        1       1          3   736      1     0           1     1
#> 16        1        1       1          4   842      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 [6]
#>    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          2      1     0           1     1
#>  3     3        0        0       1          2      1     0           1     1
#>  4     4        0        1       0          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        0       0          1      1     0           1     1
#>  8     3        1        1       1          1      1     0           1     1
#>  9     4        1        1       1          2      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>