Simulate from the meta-d' model across separate conditions

Generate a simulated dataset across separate 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_condition(
  N_trials = 100,
  dprime = rep(1, 2),
  c = rep(0, 2),
  log_M = rep(0, 2),
  c2_0_diff = list(rep(0.5, 3), rep(0.5, 3)),
  c2_1_diff = list(rep(0.5, 3), 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 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
condition: the simulated condition 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_condition(N_trials = 10)
#> # A tibble: 20 × 15
#>    condition trial stimulus response correct confidence dprime     c meta_dprime
#>        <int> <int>    <int>    <int>   <int>      <int>  <dbl> <dbl>       <dbl>
#>  1         1     1        0        0       1          1      1     0           1
#>  2         1     2        0        0       1          2      1     0           1
#>  3         1     3        0        0       1          4      1     0           1
#>  4         1     4        0        1       0          1      1     0           1
#>  5         1     5        0        1       0          1      1     0           1
#>  6         1     1        1        0       0          3      1     0           1
#>  7         1     2        1        1       1          1      1     0           1
#>  8         1     3        1        1       1          2      1     0           1
#>  9         1     4        1        1       1          3      1     0           1
#> 10         1     5        1        1       1          4      1     0           1
#> 11         2     1        0        0       1          2      1     0           1
#> 12         2     2        0        0       1          2      1     0           1
#> 13         2     3        0        0       1          3      1     0           1
#> 14         2     4        0        1       0          1      1     0           1
#> 15         2     5        0        1       0          2      1     0           1
#> 16         2     1        1        1       1          2      1     0           1
#> 17         2     2        1        1       1          2      1     0           1
#> 18         2     3        1        1       1          3      1     0           1
#> 19         2     4        1        1       1          3      1     0           1
#> 20         2     5        1        1       1          4      1     0           1
#> # ℹ 6 more variables: M <dbl>, meta_c2_0 <list>, meta_c2_1 <list>, theta <dbl>,
#> #   theta_1 <dbl>, theta_2 <dbl>
sim_metad_condition(N_trials = 10000, summarize = TRUE)
#> # A tibble: 32 × 15
#>    condition stimulus response correct confidence     n dprime     c meta_dprime
#>        <int>    <int>    <int>   <int>      <int> <int>  <dbl> <dbl>       <dbl>
#>  1         1        0        0       1          1  1008      1     0           1
#>  2         1        0        0       1          2   927      1     0           1
#>  3         1        0        0       1          3   740      1     0           1
#>  4         1        0        0       1          4   826      1     0           1
#>  5         1        0        1       0          1   750      1     0           1
#>  6         1        0        1       0          2   420      1     0           1
#>  7         1        0        1       0          3   215      1     0           1
#>  8         1        0        1       0          4   114      1     0           1
#>  9         1        1        0       0          1   779      1     0           1
#> 10         1        1        0       0          2   468      1     0           1
#> # ℹ 22 more rows
#> # ℹ 6 more variables: M <dbl>, meta_c2_0 <list>, meta_c2_1 <list>, theta <dbl>,
#> #   theta_1 <dbl>, theta_2 <dbl>
sim_metad_condition(N_trials = 10, c2_0_diff = list(1, .5), c2_1_diff = list(1, .5))
#> # A tibble: 20 × 15
#>    condition trial stimulus response correct confidence dprime     c meta_dprime
#>        <int> <int>    <int>    <int>   <int>      <int>  <dbl> <dbl>       <dbl>
#>  1         1     1        0        0       1          1      1     0           1
#>  2         1     2        0        0       1          1      1     0           1
#>  3         1     3        0        0       1          1      1     0           1
#>  4         1     4        0        0       1          2      1     0           1
#>  5         1     5        0        0       1          2      1     0           1
#>  6         1     1        1        0       0          1      1     0           1
#>  7         1     2        1        1       1          1      1     0           1
#>  8         1     3        1        1       1          1      1     0           1
#>  9         1     4        1        1       1          1      1     0           1
#> 10         1     5        1        1       1          2      1     0           1
#> 11         2     1        0        0       1          2      1     0           1
#> 12         2     2        0        0       1          2      1     0           1
#> 13         2     3        0        0       1          2      1     0           1
#> 14         2     4        0        0       1          2      1     0           1
#> 15         2     5        0        1       0          1      1     0           1
#> 16         2     1        1        0       0          1      1     0           1
#> 17         2     2        1        0       0          1      1     0           1
#> 18         2     3        1        0       0          2      1     0           1
#> 19         2     4        1        0       0          2      1     0           1
#> 20         2     5        1        1       1          2      1     0           1
#> # ℹ 6 more variables: M <dbl>, meta_c2_0 <list>, meta_c2_1 <list>, theta <dbl>,
#> #   theta_1 <dbl>, theta_2 <dbl>