`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:

```
# install.packages("devtools")
::install_github("rtdists/fddm") devtools
```

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[which(med_dec[["rt"]] >= 0), ]
med_dec <- med_dec[ med_dec[["id"]] == "2" & med_dec[["group"]] == "experienced", ]
onep 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.

```
"resp"]] <- ifelse(onep[["response"]] == "blast", "upper", "lower")
onep[["truth"]] <- ifelse(onep[["classification"]] == "blast", "upper", "lower") onep[[
```

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.```
<- function(pars, rt, resp, truth) {
ll_fun <- numeric(length(rt))
v
# the truth is "upper" so use vu
== "upper"] <- pars[[1]]
v[truth # the truth is "lower" so use vl
== "lower"] <- pars[[2]]
v[truth
<- dfddm(rt = rt, response = resp, a = pars[[3]], v = v,
dens 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}*,

```
<- nlminb(c(0, 0, 1, 0, 0.5, 0), objective = ll_fun,
fit 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)"
```