The Component Functions of A Model

Functions to get or set the "component functions" of an object. The component functions are a list of functions providing the drift rate, boundary, starting point distribution, and non-decision time distribution They are at the heart of the package and shape the model's behavior.

Usage

comp_funs(object, ...) <- value

# S3 method for class 'drift_dm'
comp_funs(object, ..., eval_model = FALSE) <- value

comp_funs(object, ...)

# S3 method for class 'drift_dm'
comp_funs(object, ...)

# S3 method for class 'fits_ids_dm'
comp_funs(object, ...)

Arguments

object: an object of type drift_dm or fits_ids_dm (see load_fits_ids).
...: additional arguments passed down to the specific method.
value: a named list which provides the component functions to set (see Details)
eval_model: logical, indicating if the model should be re-evaluated or not when updating the component funtions (see re_evaluate_model). Default is False.

Value

For comp_funs() the list of component functions.

For comp_funs<-() the updated drift_dm object.

Details

comp_funs() is a generic accessor function, and comp_funs<-() is a generic replacement function. The default methods get and set the "component functions". The component functions are a list of functions, with the following names (see also vignette("use_ddm_models", "dRiftDM") for examples):

mu_fun and mu_int_fun, provide the drift rate and its integral, respectively, across the time space.
x_fun provides a distribution of the starting point across the evidence space.
b_fun and dt_b_fun provide the values of the upper decision boundary and its derivative, respectively, across the time space. It is assumed that boundaries are symmetric.
nt_fun provides a distribution of the non-decision component across the time space.

All of the listed functions are stored in the list comp_funs of the respective model (see also drift_dm()).

Each component function must take the model's parameters (i.e., one row of prms_matrix), the parameters for deriving the PDFs, the time or evidence space, a condition, and a list of optional values as arguments. These arguments are provided with values when dRiftDM internally calls them.

In order to work with dRiftDM, mu_fun, mu_int_fun, b_fun, dt_b_fun, and nt_fun must have the following declaration: my_fun = function(prms_model, prms_solve, t_vec, one_cond, ddm_opts). Here, prms_model is one row of prms_matrix, prms_solve the parameters relevant for deriving the PDFs, t_vec the time space, going from 0 to t_max with length nt + 1 (see drift_dm), and one_cond a single character string, indicating the current condition. Finally dmm_opts may contain additional values. Each function must return a numeric vector of the same length as t_vec. For mu_fun, mu_int_fun, b_fun, dt_b_fun the returned values provide the respective boundary/drift rate (and their derivative/integral) at every time step $t$. For nt_fun the returned values provide the density of the non-decision time across the time space (which get convoluted with the pdfs when solving the model)

In order to work with dRiftDM, x_fun must have the following declaration: my_fun = function(prms_model, prms_solve, x_vec, one_cond, ddm_opts). Here, x_vec is the evidence space, going from -1 to 1 with length nx + 1 (see drift_dm). Each function must return a numeric vector of the same length as x_vec, providing the density values of the starting points across the evidence space.

Drift rate and its integral:

The drift rate is the first derivative of the expected time-course of the diffusion process. For instance, if we assume that the diffusion process $X$ is linear with a slope of $v$... $$E(X) = v \cdot t$$ ...then the drift rate at every time step $t$ is the constant $v$, obtained by taking the derivative of the expected time-course with respect to $t$: $$\mu(t) = v$$ Conversely, the integral of the drift rate is identical to the expected time-course: $$\mu_{int}(t) = v \cdot t$$

For the drift rate mu_fun, the default function when calling drift_dm() is a numeric vector containing the number $3$. Its integral counterpart mu_int_fun will return a numeric vector containing the values t_vec*3.

Starting Point Distribution:

The starting point of a diffusion model refers to the initial value taken by the evidence accumulation process at time $t=0$. This is a PDF over the evidence space.

The default function when calling drift_dm() will be a function returning a dirac delta on zero, meaning that every potential diffusion process starts at 0.

Boundary:

The Boundary refers to the values of the absorbing boundaries at every time step $t$ in a diffusion model. In most cases, this will be a constant. For instance: $$b(t) = b$$ In this case, its derivative with respect to $t$ is 0.

The default function when calling drift_dm() will be function for b_fun returning a numeric vector of length length(t_vec) containing the number $0.5$. Its counterpart dt_b will return a numeric vector of the same length containing its derivative, namely, 0.

Non-Decision Time:

The non-decision time refers to an additional time-requirement. Its distribution across the time space will be convoluted with the PDFs derived from the diffusion process.

In psychology, the non-decision time captures time-requirements outside the central decision process, such as stimulus perception and motor execution.

The default function when calling drift_dm() returns a dirac delta on $t = 0.3$.

Note

There is only a replacement function for drift_dm objects. This is because replacing the component functions after the model has been fitted (i.e., for a fits_ids_dm object) doesn't make sense.

Examples

# get a pre-built model for demonstration
my_model <- ratcliff_dm()
names(comp_funs(my_model))
#> [1] "mu_fun"     "mu_int_fun" "x_fun"      "b_fun"      "dt_b_fun"  
#> [6] "nt_fun"    

# direct replacement (see the pre-print/vignette for a more information on
# how to write custom component functions)
# 1. Choose a uniform non-decision time from the pre-built component_shelf()
nt_uniform <- component_shelf()$nt_uniform
# swap it in
comp_funs(my_model)[["nt_fun"]] <- nt_uniform

# now update the flex_prms object to ensure that this model has the required
# parameters
prms <- c(muc = 3, b = 0.6, non_dec = 0.3, range_non_dec = 0.05)
conds <- "null"
new_flex_prms <- flex_prms(prms, conds = conds)
flex_prms(my_model) <- new_flex_prms

# accessor method also available for fits_ids_dm objects
# (see estimate_model_ids)
# get an exemplary fits_ids_dm object
fits <- get_example_fits_ids()
names(comp_funs(fits))
#> [1] "mu_fun"     "mu_int_fun" "x_fun"      "b_fun"      "dt_b_fun"  
#> [6] "nt_fun"