First_Passage_Time: First_Passage_Time

In lbaModel: The Linear Ballistic Accumulation Model

First_Passage_Time

Description

The functions, fptpdf, fptcdf, and n1PDF, calculate first passage time distributions for the Linear Ballistic Accumulation model. This includes the probability density function fptpdf, the cumulative distribution function fptcdf, and the node 1 density function, n1PDF.

Usage

fptpdf(rt_r, parameter_r, is_positive_drift_r, verbose = FALSE)

fptcdf(rt_r, parameter_r, is_positive_drift_r, verbose = FALSE)

n1PDF(rt_r, parameter_r, is_positive_drift_r, verbose = FALSE)

Arguments

rt_r	A numeric vector of response times (RTs).
parameter_r	A numeric matrix of model parameters, with each row representing a core model parameter and each column representing an accumulator. Expected row (in fixed order): A, b, mean_v, sd_v, st0, and t0.
is_positive_drift_r	A logical vector indicating whether the drift rate must be positive for each trial.
verbose	A logical value indicating whether to print debug information.

Details

The three functions, respectively, are designed to:

• fptpdf: Calculates the probability density function for (PDF; 1 accumulator).

• fptcdf: Calculates the cumulative distribution function (CDF; 1 accumulator).

• n1PDF: Calculates the node 1 PDF for the multi-accumulator LBA model freeing the non-decision time. node 1 refers to the accumulator passing the threshold first.

Value

A numeric vector of probabilities corresponding to input response times.

Examples

#-------------------#
# n1PDF example
#-------------------#
if (requireNamespace("ggdmcModel", quietly = TRUE)) {
  BuildModel <- getFromNamespace("BuildModel", "ggdmcModel")

  model <- BuildModel(
    p_map = list(
      A = "1", B = "1", t0 = "1", mean_v = "M", sd_v = "1",
      st0 = "1"
    ),
    match_map = list(M = list("s1" = "r1", "s2" = "r2")),
    factors = list(S = c("s1", "s2")),
    constants = c(sd_v = 1, st0 = 0),
    accumulators = c("r1", "r2"),
    type = "lba"
  )
}


#---------------------------------------#
pop_mean <- c(
  A = .4, B = 1.6, mean_v.true = 3.5, mean_v.false = 2.38,
  t0 = 0.05
)
pop_scale <- c(
  A = 2, B = .2, mean_v.true = .25, mean_v.false = .1,
  t0 = 0.01
)

if (requireNamespace("ggdmcPrior", quietly = TRUE)) {
  BuildPrior <- getFromNamespace("BuildPrior", "ggdmcPrior")

  pop_dist <- BuildPrior(
    p0 = pop_mean,
    p1 = pop_scale,
    lower = rep(NA, model@npar),
    upper = rep(NA, model@npar),
    dists = rep("tnorm", model@npar),
    log_p = rep(FALSE, model@npar)
  )
}

#---------------------------------------#
rt_model <- setLBA(model, population_distribution = pop_dist)
res_process_model <- simulate(rt_model)

param_list2mat <- function(param_list) {
  n_row <- length(param_list[[1]])
  n_col <- length(param_list)

  tmp <- matrix(NA, nrow = n_row, ncol = n_col)

  for (i in seq_len(n_col)) {
    tmp[, i] <- param_list[[i]]
  }
  t(tmp)
}

params_tmp <- list(
  A = c(0.74, 0.74),
  b = c(1.25 + 0.74, 1.25 + 0.74),
  mean_v = c(2.52, 1.50),
  sd_v = c(1.0, 1.0),
  st0 = c(0.0, 0.0),
  t0 = c(0.04, 0.04)
)

# Store the LBA parameter as a list of vectors
print(params_tmp)
# $A: 0.74 0.74
# $b: 1.99 1.99
# $mean_v: 2.52 1.50
# $sd_v: 1 1
# $st0: 0 0
# $t0: 0.04 0.04

# Convert it to a matrix, each row represents a parameter,
# and each column corresponds to an accumulator.
params <- param_list2mat(params_tmp)

print(params)
#      [,1] [,2]
# [1,] 0.74 0.74
# [2,] 1.99 1.99
# [3,] 2.52 1.50
# [4,] 1.00 1.00
# [5,] 0.00 0.00
# [6,] 0.04 0.04

n_acc <- 2
is_positive_drift <- rep(TRUE, n_acc)
res <- n1PDF(res_process_model$RT, params, is_positive_drift, TRUE)
cat("Print first 30 density values from the LBA node 1 function: \n")
print(head(round(res, 2), 30))

#----------------------------#
# fptpdf computes only 1 RT
#----------------------------#
mean_v <- 2.4
A <- 1.2
b <- 2.7
t0 <- .2
sd_v <- 1
st0 <- 0
positive_drift_r <- TRUE

params <- list(
  A = rep(A, 2),
  b = rep(b, 2),
  mean_v = rep(mean_v, 2),
  sd_v = rep(sd_v, 2),
  st0 = rep(st0, 2),
  t0 = rep(t0, 2)
)

n_accumulator <- length(params$A)
is_positive_drift <- rep(TRUE, n_accumulator)
params_mat <- param_list2mat(params)

RT <- 0.3
result <- fptpdf(RT, params_mat, is_positive_drift, TRUE)

#---------------------------------------#
# fptpdf and fptcdf computes a range RTs
#---------------------------------------#
RT <- seq(0, 10, .01) + t0
result1 <- fptpdf(RT, params_mat, is_positive_drift)
result2 <- fptcdf(RT, params_mat, is_positive_drift)

lbaModel documentation built on Sept. 15, 2025, 9:08 a.m.