# Simulation of confidence ratings and RTs in the Multiple-threshold Log-normal Race Model 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. ```r simulateMTLNR(paramDf, n = 10000, gamma = FALSE, agg_simus = FALSE, stimulus = c(1, 2), seed = NULL) ``` ## Arguments - `paramDf`: a list or dataframe with one row. Column names should match the names of MTLNR model specific parameter names. For different stimulus quality/mean drift rates, names should be `v1`, `v2`, `v3`,.... Additionally, the confidence thresholds should be given by names with `thetaUpper1`, `thetaUpper2`,..., `thetaLower1`,... or, for symmetric thresholds only by `theta1`, `theta2`,.... - `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. ## Returns 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). ## 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. ## Note Different parameters for different conditions are only allowed for drift rate, `v`. All other parameters are used for all conditions. ## Examples ```r # 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, s_v1=0.5, s_v2=0.5, s_d1=0.3, s_d2=0.3, rho_v=0.2, rho_d=0.1, theta1=0.8, theta2=1.5) # 2. Simulate trials for both stimulus categories and all conditions (2) simus <- simulateMTLNR(paramDf) head(simus) library(ggplot2) simus <- simus[simus$response != 0, ] simus$rating <- factor(simus$rating, labels = c("unsure", "medium", "sure")) ggplot(simus, aes(x = rt, group = interaction(correct, rating), color = as.factor(correct), linetype = rating)) + geom_density(linewidth = 1.2) + xlim(c(0, 5)) + facet_grid(rows = vars(condition), labeller = "label_both") # automatically aggregate simulation distribution # to get only accuracy x confidence rating distribution for # all conditions agg_simus <- simulateMTLNR(paramDf, agg_simus = TRUE) head(agg_simus) agg_simus$rating <- factor(agg_simus$rating, labels = c("unsure", "medium", "sure")) library(ggplot2) ggplot(agg_simus, aes(x = rating, group = correct, fill = as.factor(correct), y = p)) + geom_bar(stat = "identity", position = "dodge") + facet_grid(cols = vars(condition), labeller = "label_both") # Compute Gamma correlation coefficients between # confidence and other behavioral measures # output will be a list simu_list <- simulateMTLNR(paramDf, n = 400, gamma = TRUE) simu_list # Example with asymmetric confidence thresholds paramDf_asym <- data.frame(v1=0.5, v2=1.0, t0=0.1, st0=0, mu_d1=1, mu_d2=1, s_v1=0.5, s_v2=0.5, s_d1=0.3, s_d2=0.3, rho_v=0.2, rho_d=0.1, thetaLower1=0.5, thetaLower2=1.2, thetaUpper1=0.7, thetaUpper2=1.8) simus_asym <- simulateMTLNR(paramDf_asym, n = 1000) head(simus_asym) # Example with multiple conditions paramDf_multi <- data.frame(v1=0.3, v2=0.6, v3=1.2, t0=0.1, st0=0, mu_d1=1, mu_d2=1, s_v1=0.5, s_v2=0.5, s_d1=0.3, s_d2=0.3, rho_v=0.2, rho_d=0.1, theta1=0.8, theta2=1.5) simus_multi <- simulateMTLNR(paramDf_multi, n = 1000) table(simus_multi$condition, simus_multi$correct) ``` ## 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 ## Author(s) Sebastian Hellmann.

simulateMTLNR function