simulateMTLNR: Simulation of confidence ratings and RTs in the Multiple-threshold Log-normal Race Model

Description

Simulates the decision responses and reaction times together with a discrete confidence judgment in the MTLNR (Reynolds et al., 2020), given specific parameter constellations. See dMTLNR for more information about parameters. Also computes the Gamma rank correlation between the confidence ratings and condition (task difficulty), reaction times and accuracy in the simulated output. Basically, this function is a wrapper for rMTLNR for application in confidence experiments with manipulation of specific parameters.

Usage

simulateMTLNR(paramDf, n = 10000, gamma = FALSE, agg_simus = FALSE,
  stimulus = c(1, 2), seed = NULL)

Value

Depending on gamma and agg_simus.

If gamma is FALSE, returns a data.frame with columns: condition, stimulus, response, correct, rt, conf (the continuous confidence measure) and rating (the discrete confidence rating), and dec and vis

(only if process_results=TRUE) for the final states of accumulators in the simulation or (if agg_simus=TRUE): condition, stimulus,response, correct, rating and p (for the probability of a response and rating, given the condition and stimulus).

If gamma is TRUE, returns a list with elements: simus (the simulated data frame) and gamma, which is again a list with elements condition, rt and correct, each a tibble with two columns (see details for more information).

Arguments

paramDf: a list or data frame with one row. Column names should match the following names (see dMTLNR): For different stimulus quality/mean drift rates, names should be v1, v2, v3,.... (corresponding to the mean parameter for the accumulation rate for the stimulus-corresponding accumulator, therefore mu_v1 and mu_v2 are not used in this context but replaced by the parameter v); mu_d1 and mu_d2 correspond to the mean parameters for boundary distance of the two accumulators; s1 and s2 correspond to the variance parameters of the first and second boundary hitting time; rho corresponds to the correlation of boundary hitting times. Note that s_v1,s_v2,rho_v,s_d1,s_d2, and rho_d are not used in this context, although the accumulation rate-related parameters can be used to replace the above-mentioned variance parameters. Additionally, the confidence thresholds should be given by names with thetaUpper1, thetaUpper2,..., thetaLower1,... or, for symmetric thresholds only by theta1, theta2,.... (see Details for the correspondence to the data)
n: integer. The number of samples (per condition and stimulus direction) generated. Total number of samples is n*nConditions*length(stimulus).
gamma: logical. If TRUE, the gamma correlation between confidence ratings, rt and accuracy is computed.
agg_simus: logical. Simulation is done on a trial basis with RTs outcome. If TRUE, the simulations will be aggregated over RTs to return only the distribution of response and confidence ratings. Default: FALSE.
stimulus: numeric vector. Either 1, 2 or c(1,2) (default). Together with condition represents the experimental situation. In a binary decision task the presented stimulus belongs to one of two categories. In the default setting trials with both categories presented are simulated but one can choose to simulate only trials with the stimulus coming from one category (1 for the category that is associated with positive drift in the decision process where 1 responses are considered correct and 2 correspondingly for negative drifts and 2 correct decisions).
seed: numerical. Seeding for non-random data generation.

Author

Sebastian Hellmann.

Details

Simulation is done by simulating normally distributed logarithms of boundary crossing times for both accumulators based on the MTLNR model. The smaller time determines decision time and response (i.e. the winning accumulator). The confidence variable is computed based on the log-ratio of the loosing boundary crossing time over the winning boundary crossing time.

The confidence values are then binned according to the given thresholds. The output of the fitting function fitRTConf with the respective model fits the argument paramDf for simulation. The Gamma coefficients are computed separately for correct/incorrect responses for the correlation of confidence ratings with condition and rt and separately for conditions for the correlation of accuracy and confidence. The resulting data frames in the output thus have two columns. One for the grouping variable and one for the Gamma coefficient.

References

Reynolds, A., Kvam, P. D., Osth, A. F., & Heathcote, A. (2020). Correlated racing evidence accumulator models. Journal of Mathematical Psychology, 96, 102331. doi: doi: 10.1016/j.jmp.2020.102331

Examples

Run this code

# 1. Define some parameter set in a data.frame
paramDf <- data.frame(v1=0.5, v2=1.0, t0=0.1, st0=0,
                      mu_d1=1, mu_d2=1,
                      s1=0.5, s2=0.5, rho=0.2,
                      theta1=0.8, theta2=1.5)

# 2. Simulate trials for both stimulus categories and all conditions (2)
simus <- simulateMTLNR(paramDf)
head(simus)
# \donttest{
  library(ggplot2)
  simus <- simus[simus$response != 0, ]
  simus$rating <- factor(simus$rating, labels = c("unsure", "medium", "sure"))
  ggplot(simus, aes(x = rt, group = interaction(correct, rating),
                    color = as.factor(correct), linetype = rating)) +
    geom_density(linewidth = 1.2, na.rm=TRUE) + xlim(c(0, 5)) +
    facet_grid(rows = vars(condition), labeller = "label_both")
# }

# automatically aggregate simulation distribution
# to get only accuracy x confidence rating distribution for
# all conditions
agg_simus <- simulateMTLNR(paramDf, agg_simus = TRUE)
head(agg_simus)
# \donttest{
  agg_simus$rating <- factor(agg_simus$rating, labels = c("unsure", "medium", "sure"))
  library(ggplot2)
  ggplot(agg_simus, aes(x = rating, group = correct, fill = as.factor(correct), y = p)) +
    geom_bar(stat = "identity", position = "dodge") +
    facet_grid(cols = vars(condition), labeller = "label_both")
# }
# \donttest{
  # Compute Gamma correlation coefficients between
  # confidence and other behavioral measures
  # output will be a list
  simu_list <- simulateMTLNR(paramDf, n = 400, gamma = TRUE)
  simu_list
# }

# Example with asymmetric confidence thresholds
paramDf_asym <- data.frame(v1=0.5, v2=1.0, t0=0.1, st0=0,
                          mu_d1=1, mu_d2=1,
                          s1=0.5, s2=0.5, rho=0.2,
                          thetaLower1=0.5, thetaLower2=1.2,
                          thetaUpper1=0.7, thetaUpper2=1.8)

simus_asym <- simulateMTLNR(paramDf_asym, n = 1000)
head(simus_asym)

# Example with multiple conditions
paramDf_multi <- data.frame(v1=0.3, v2=0.6, v3=1.2, t0=0.1, st0=0,
                           mu_d1=1, mu_d2=1,
                           s1=0.5, s2=0.5, rho=0.2,
                           theta1=0.8, theta2=1.5)

simus_multi <- simulateMTLNR(paramDf_multi, n = 1000)
table(simus_multi$condition, simus_multi$correct)

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