Core DDM Parameters: Impact on RTs and Accuracy

In this vignette, we explore how the core parameters of the drift diffusion model influence mean RTs and accuracy.

We can create the classical (Ratcliff) DDM, which is pre-built in dRiftDM, in its simplest version using the function ratcliff_dm():

model <- ratcliff_dm()

coef(model)
#>     muc       b non_dec 
#>     3.0     0.6     0.3

Here, we can see the core parameters of the classical DDM and their current values: the drift rate muc is 3.0, the boundary b is 0.6, and the non-decision time non_dec is 0.3 (seconds). We can alter the parameter settings like this:

coef(model)["muc"] <- 2.5
coef(model)["b"] <- 0.5
coef(model)
#>     muc       b non_dec 
#>     2.5     0.5     0.3

To visualize the model, we can simulate some evidence accumulation trajectories, using the function simulate_traces() and the generic plot() method.

set.seed(1)
traces <- simulate_traces(model, k = 10)
plot(traces, col = "black")

You might wonder why these trajectories appear so “coarse.” This results from the discretization settings of the underlying solver that computes the first-passage times when fitting the model. To obtain a smoother plot, we can temporarily increase the resolution in the time domain:

prms_solve(model)["dt"] = .001 # set to 1 ms step size (for a nice plot)
set.seed(1)
traces <- simulate_traces(model, k = 10)
plot(traces, col = "black")

Sometimes, we might want to visualize the model without noise. In this case, the argument sigma of the simulate_traces() function comes in handy.

traces <- simulate_traces(model, k = 1, sigma = 0)
plot(traces, col = "black")

To derive basic model predictions for mean response times (RTs) and accuracy, we can use the calc_stats() method and the argument type = "basic_stats":

prms_solve(model)["dt"] = .010 # set it back to a 10 ms step size (for speed)
calc_stats(model, type = "basic_stats")
#> Type of Statistic: basic_stats
#> 
#>   Source Cond Mean_corr Mean_err SD_corr SD_err P_corr
#> 1   pred null     0.469    0.469   0.123  0.123  0.924
#> 
#> (access the data.frame's columns/rows as usual)

Note that the mean predicted RTs for correct and incorrect responses are actually identical for the classical Ratcliff DDM! This hold as long as the model doesn’t include trial-by-trial variability in the starting point or drift rate. Once we incorprate the respective variability parameters, we produce fast and slow errors, respectively.

Let’s illustrates the effects of each parameter on predicted mean correct RTs and accuracy by systematically varying each parameter one after the other. For this example demonstration, let’s use the following parameter ranges:

The following code iterates over each parameter, plotting the influence of each parameter on RTs (upper panels) and accuracy (lower panels).

par(mfcol = c(1, 2))

# define the parameter ranges
muc_seq <- seq(1.5, 5.0, by = 0.5)
b_seq <- seq(0.2, 0.9, by = 0.1)
t0_seq <- seq(0.1, 0.45, by = 0.05)

# small helper function
get_stats <- function(prm_val, prm_label) {
  coef(model)[prm_label] <- prm_val
  stats <- calc_stats(model, type = "basic_stats")
  stats <- stats[c("Mean_corr", "P_corr")]
  return(as.numeric(stats))
}

# Drift Rate Plots
par(mfcol = c(1, 2))
stats_mu <- sapply(muc_seq, get_stats, prm_label = "muc")
plot(stats_mu[1, ] ~ muc_seq,
  type = "l",
  ylim = c(0.2, 0.8), xlab = "muc", ylab = "correct RTs", main = "Influence: Drift Rate"
)
plot(stats_mu[2, ] ~ muc_seq,
  type = "l",
  ylim = c(0.5, 1), xlab = "muc", ylab = "Accuarcy", main = "Influence: Drift Rate"
)


# Boundary Plots
par(mfcol = c(1, 2))
stats_b <- sapply(b_seq, get_stats, prm_label = "b")
plot(stats_b[1, ] ~ b_seq,
  type = "l",
  ylim = c(0.2, 0.8), xlab = "b", ylab = "correct RTs", main = "Influence: Boundary"
)
plot(stats_b[2, ] ~ b_seq,
  type = "l",
  ylim = c(0.5, 1), xlab = "b", ylab = "Accuarcy", main = "Influence: Boundary"
)


# Non-Decision Time Plots
par(mfcol = c(1, 2))
stats_non_dec <- sapply(t0_seq, get_stats, prm_label = "non_dec")
plot(stats_non_dec[1, ] ~ t0_seq,
  type = "l",
  ylim = c(0.2, 0.8), xlab = "non_dec", ylab = "correct RTs", main = "Influence: Non-Decision Time"
)
plot(stats_non_dec[2, ] ~ t0_seq,
  type = "l",
  ylim = c(0.5, 1), xlab = "non_dec", ylab = "Accuarcy", main = "Influence: Non-Decision Time"
)