`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), *t _{0} ϵ [0, ∞)* (non-decision time/response time constant),

You can install the released version of fddm from CRAN with:

`install.packages("fddm")`

And the development version from GitHub with:

As a preliminary example, we will fit the DDM to the data from one participant in the `med_dec`

data that comes with `fddm`

. This dataset contains the accuracy condition reported in Trueblood et al. (2018), which investigates 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 dataset contains 200 decisions 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 of 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 log of sum of densities of the study responses and associated response times. This log-likelihood function will fit the standard parameters in the DDM, but it will fit two versions of the drift rate *v*: one for when the correct response is `"blast"`

(*v _{u}*), and another for when the correct response is

`"non-blast"`

(`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) {
v <- numeric(length(rt))
# the truth is "upper" so use vu
v[truth == "upper"] <- pars[[1]]
# the truth is "lower" so use vl
v[truth == "lower"] <- pars[[2]]
dens <- dfddm(rt = rt, response = resp, a = pars[[3]], v = v,
t0 = pars[[4]], w = pars[[5]], sv = pars[[6]], log = TRUE)
return( ifelse(any(!is.finite(dens)), 1e6, -sum(dens)) )
}
```

We then pass the data and log-likelihood function to an optimization function with the necessary additional arguments. As we are using the optimization function `nlminb`

for this example, the first argument must be the initial values of our DDM parameters that we want optimized. These are input in the order: *v _{u}*,

```
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, .01, 0, 0, 0),
upper = c( Inf, Inf, Inf, min(onep[["rt"]]), 1, Inf))
fit
#> $par
#> [1] 5.6813040 -2.1886617 2.7909124 0.3764464 0.4010116 2.2812984
#>
#> $objective
#> [1] 42.47181
#>
#> $convergence
#> [1] 0
#>
#> $iterations
#> [1] 46
#>
#> $evaluations
#> function gradient
#> 75 335
#>
#> $message
#> [1] "relative convergence (4)"
```