Drift specifications for gddm()

The drift is the mean rate of evidence accumulation, a(x, t). A GDDM lets it depend on the current state x, on time, and on a covariate. Terms are summed: pass one, or a list of several.

Usage

gddm_drift_constant()

gddm_drift_coherence(cmax = 1, cov = 1L)

gddm_drift_leak()

Arguments

cmax

Scale the coherence covariate is divided by, so that the nonlinearity is anchored at a coherence a subject sees. The paper uses the largest coherence in the design.

cov

Which vreal() value carries the coherence, counting from 1.

Value

A gddm_component.

Details

gddm_drift_constant()

a = mu. The textbook drift-diffusion drift. Free parameter mu, identity link, so it is signed.

gddm_drift_coherence()

a = sign(C) mu (|C| / cmax)^alpha, the coherence nonlinearity of Shinn et al. (2020). The covariate C is supplied through vreal() and cmax scales it. Free parameters mu (identity link) and alpha (log link).

gddm_drift_leak()

a = -leak x, added to whichever base term is used. Positive leak is leaky integration, which pulls the accumulator back toward zero; negative leak is unstable integration, which pushes it away. Identity link. Note the sign is the paper's l and the negative of PyDDM's leak.

Exactly one base term, gddm_drift_constant() or gddm_drift_coherence(), must be present and must come first, because it supplies mu, the parameter that receives the model formula.

Writing your own

A drift term is the value of gddm_drift_term(). Its fn is called on the tape as fn(x, t, p, cov) where x is the accumulator state at the grid nodes in the original coordinate, t is the time as a plain number, p is a named list holding one value of each free parameter for the condition being solved, and cov is that condition's vreal() values. It returns the drift at each node, and must contain no comparison against a parameter.

See also

gddm(), gddm_bound_constant(), gddm_start_point()