# Prediction of Confidence Rating and Reaction Time Distribution in the multiple-threshold log-normal noise race model `predictMTLNR_Conf` predicts the categorical response distribution of decision and confidence ratings, `predictMTLNR_RT` computes the RT distribution (density) in the multiple-threshold log-normal noise race model (Reynolds et al., 2020), given specific parameter constellations. See `dMTLNR` for more information about the models and parameters. ```r predictMTLNR_Conf(paramDf, maxrt = Inf, subdivisions = 100L, stop.on.error = FALSE, .progress = TRUE) predictMTLNR_RT(paramDf, maxrt = 9, subdivisions = 100L, minrt = NULL, scaled = FALSE, DistConf = NULL, .progress = TRUE) ``` ## Arguments - `paramDf`: a list or data frame with one row. Column names should match the names of dMTLNR parameter names (only `mu_v1` and `mu_v2` are not used in this context but replaced by the parameter `v`). 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`,.... (see Details for the correspondence to the data) - `maxrt`: numeric. The maximum RT for the integration/density computation. Default: 15 (for `predictMTLNR_Conf` (integration)), 9 (for `predictMTLNR_RT`). - `subdivisions`: `integer` (default: 100). For `predictMTLNR_Conf` it is used as argument for the inner integral routine. For `predictMTLNR_RT` it is the number of points for which the density is computed. - `stop.on.error`: logical. Argument directly passed on to integrate. Default is FALSE, since the densities invoked may lead to slow convergence of the integrals (which are still quite accurate) which causes R to throw an error. - `.progress`: logical. If TRUE (default) a progress bar is drawn to the console. - `minrt`: numeric or NULL(default). The minimum rt for the density computation. - `scaled`: logical. For `predictMTLNR_RT`. Whether the computed density should be scaled to integrate to one (additional column `densscaled`). Otherwise the output contains only the defective density (i.e. its integral is equal to the probability of a response and not 1). If `TRUE`, the argument `DistConf` should be given, if available. Default: `FALSE`. - `DistConf`: `NULL` or `data.frame`. A `data.frame` or `matrix` with column names, giving the distribution of response and rating choices for different conditions and stimulus categories in the form of the output of `predictMTLNR_Conf`. It is only necessary, if `scaled=TRUE`, because these probabilities are used for scaling. If `scaled=TRUE` and `DistConf=NULL`, it will be computed with the function `predictMTLNR_Conf`, which takes some time and the function will throw a message. Default: `NULL` ## Returns `predictMTLNR_Conf` returns a `data.frame`/`tibble` with columns: `condition`, `stimulus`, `response`, `rating`, `correct`, `p`, `info`, `err`. `p` is the predicted probability of a response and `rating`, given the stimulus category and condition. `info` and `err` refer to the respective outputs of the integration routine used for the computation. `predictMTLNR_RT` returns a `data.frame`/`tibble` with columns: `condition`, `stimulus`, `response`, `rating`, `correct`, `rt` and `dens` (and `densscaled`, if `scaled=TRUE`). ## Details The function `predictMTLNR_Conf` consists merely of an integration of the response time density, `dMTLNR`, over the response time in a reasonable interval (0 to `maxrt`). The function `predictMTLNR_RT` wraps these density functions to a parameter set input and a data.frame output. For the argument `paramDf`, the output of the fitting function `fitRTConf` with the respective model may be used. The names of the accumulation rate parameters differ from those used in `dMTLNR` because the accumulation rates for the two options depend on stimulus and condition. Here, the mean parameter for the accumulation rate of the correct accumulator is `v` (`v1`, `v2`,... respectively) in `paramDf` and the other one has a mean parameter of 0. ## 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. Predict discrete Choice x Confidence distribution: preds_Conf <- predictMTLNR_Conf(paramDf, maxrt=7, subdivisions=50) head(preds_Conf) # 3. Compute RT density preds_RT <- predictMTLNR_RT(paramDf, maxrt=7, subdivisions=50) # same output with scaled density column: preds_RT <- predictMTLNR_RT(paramDf, maxrt=7, subdivisions=50, scaled=TRUE, DistConf = preds_Conf) head(preds_RT) # produces a warning, if scaled=TRUE and DistConf missing preds_RT <- predictMTLNR_RT(paramDf, maxrt=7, subdivisions=50, scaled=TRUE) # Example of visualization library(ggplot2) preds_Conf$rating <- factor(preds_Conf$rating, labels=c("unsure", "medium", "sure")) preds_RT$rating <- factor(preds_RT$rating, labels=c("unsure", "medium", "sure")) ggplot(preds_Conf, aes(x=interaction(rating, response), y=p))+ geom_bar(stat="identity")+ facet_grid(cols=vars(stimulus), rows=vars(condition), labeller = "label_both") ggplot(preds_RT, aes(x=rt, color=interaction(rating, response), y=dens))+ geom_line(stat="identity")+ facet_grid(cols=vars(stimulus), rows=vars(condition), labeller = "label_both")+ theme(legend.position = "bottom") ggplot(aggregate(densscaled~rt+correct+rating+condition, preds_RT, mean), aes(x=rt, color=rating, y=densscaled))+ geom_line(stat="identity")+ facet_grid(cols=vars(condition), rows=vars(correct), labeller = "label_both")+ theme(legend.position = "bottom") # Use PDFtoQuantiles to get predicted RT quantiles # (produces warning because of few rt steps (--> inaccurate calculations)) PDFtoQuantiles(preds_RT, scaled = FALSE) # 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) preds_Conf_asym <- predictMTLNR_Conf(paramDf_asym, maxrt=7, subdivisions=50) head(preds_Conf_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) preds_Conf_multi <- predictMTLNR_Conf(paramDf_multi, maxrt=7, subdivisions=50) head(preds_Conf_multi) ``` ## 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.

predictMTLNR function