fddm provides function dfddm() which evaluates the density function (or probability density function, PDF) for the Ratcliff diffusion decision model (DDM) using different methods for approximating the full PDF, which contains an infinite sum. Our implementation of the DDM has the following parameters: a ϵ (0, ∞) (threshold separation), v ϵ (-∞, ∞) (drift rate), t0 ϵ [0, ∞) (non-decision time/response time constant), w ϵ (0, 1) (relative starting point), and sv ϵ (0, ∞) (inter-trial-variability of drift).
You can install the released version of fddm from CRAN with:
install.packages("fddm")And the development version from GitHub with:
As an example data set, we use the med_dec data that comes with fddm. This data contains the accuracy condition reported in @trueblood_impact_2018 investigating medical decision making among medical professionals (pathologists) and novices (i.e., undergraduate students). The task of participants was to judge whether pictures of blood cells show cancerous cells (i.e., blast cells) or non-cancerous cells (i.e., non-blast cells). The data set contains 200 decision per participant, based on pictures of 100 true cancerous cells and pictures of 100 true non-cancerous cells.
As a preliminary example, we will fit data from one participant from the med_dec data that comes with fddm. This data contains the accuracy condition reported in Trueblood et al. (2018) investigating medical decision making among medical professionals (pathologists) and novices (i.e., undergraduate students). The task of participants was to judge whether pictures of blood cells show cancerous cells (i.e., blast cells) or non-cancerous cells (i.e., non-blast cells). The data set contains 200 decision per participant, based on pictures of 100 true cancerous cells and pictures of 100 true non-cancerous cells. Here we use the data collected from the trials one experienced medical professional (pathologist). First, we load the fddm package, remove any invalid responses from the data, and select the individual whose data we will use for fitting.
library("fddm")
data(med_dec, package = "fddm")
med_dec <- med_dec[which(med_dec$rt >= 0), ]
onep <- med_dec[ med_dec$id == "2" & med_dec$group == "experienced", ]
str(onep)
#> 'data.frame': 200 obs. of 9 variables:
#> $ id : int 2 2 2 2 2 2 2 2 2 2 ...
#> $ group : chr "experienced" "experienced" "experienced" "experienced" ...
#> $ block : int 3 3 3 3 3 3 3 3 3 3 ...
#> $ trial : int 1 2 3 4 5 6 7 8 9 10 ...
#> $ classification: chr "blast" "non-blast" "non-blast" "non-blast" ...
#> $ difficulty : chr "easy" "easy" "hard" "hard" ...
#> $ response : chr "blast" "non-blast" "blast" "non-blast" ...
#> $ rt : num 0.853 0.575 1.136 0.875 0.748 ...
#> $ stimulus : chr "blastEasy/BL_10166384.jpg" "nonBlastEasy/16258001115A_069.jpg" "nonBlastHard/BL_11504083.jpg" "nonBlastHard/MY_9455143.jpg" ...We further prepare the data by defining upper and lower responses and the correct response bounds.
onep$resp <- ifelse(onep$response == "blast", "upper", "lower")
onep$truth <- ifelse(onep$classification == "blast", "upper", "lower")For fitting, we need a simple likelihood function; here we will use a straightforward sum of densities of the study responses and associated response times. A detailed explanation of the log-likelihood function is provided in the Example Vignette (vignette("example", package = "fddm")). Note that this likelihood function returns the negative log-likelihood as we can simply minimize this function to get the maximum likelihood estimate.
ll_fun <- function(pars, rt, resp, truth) {
rtu <- rt[truth == "upper"]
rtl <- rt[truth == "lower"]
respu <- resp[truth == "upper"]
respl <- resp[truth == "lower"]
# the truth is "upper" so use vu
densu <- dfddm(rt = rtu, response = respu, a = pars[[3]], v = pars[[1]],
t0 = pars[[4]], w = pars[[5]], sv = pars[[6]], log = TRUE)
# the truth is "lower" so use vl
densl <- dfddm(rt = rtl, response = respl, a = pars[[3]], v = pars[[2]],
t0 = pars[[4]], w = pars[[5]], sv = pars[[6]], log = TRUE)
densities <- c(densu, densl)
if (any(!is.finite(densities))) return(1e6)
return(-sum(densities))
}We then pass the data and log-likelihood function with the necessary additional arguments to an optimization function. As we are using the optimization function nlminb for this example, we must input as the first argument the initial values of our DDM parameters that we want optimized. These are input in the order: vu, vl, a, t0, w, and sv; we also need to define upper and lower bounds for each parameters. Fitting the DDM to this data is basically instantaneous using this setup.
fit <- nlminb(c(0, 0, 1, 0, 0.5, 0), objective = ll_fun,
rt = onep$rt, resp = onep$resp, truth = onep$truth,
# limits: vu, vl, a, t0, w, sv
lower = c(-Inf, -Inf, 0, 0, 0, 0),
upper = c( Inf, Inf, Inf, Inf, 1, Inf))
fit
#> $par
#> [1] 5.6813024 -2.1886620 2.7909111 0.3764465 0.4010116 2.2812989
#>
#> $objective
#> [1] 42.47181
#>
#> $convergence
#> [1] 0
#>
#> $iterations
#> [1] 41
#>
#> $evaluations
#> function gradient
#> 60 301
#>
#> $message
#> [1] "relative convergence (4)"