Michael David Wilson, Timothy Ballard and I have recently released the Fatigue Impairment Prediction Suite, an
open source R package implementing biomathematical models of fatigue. In addition to the front-facing package content, we are actively developing and testing
Bayesian parameter estimation of fatigue models using Stan.
Michael gives a brief speech on FIPS and some potential applications for applied research below.
PM trigger failures
15 Nov 2018
Modelling Prospective Memory Lapses
In previous research, my collaborators and I
have proposed that evidence accumulation models could potentially measure lapses of Prospective Memory (i.e., forgetting).
I have implemented one such measurement framework
in the Dynamic Models of Choice (DMC) suite of functions. Press here to download the model code.
As with all custom DMC models, the user must
add it to the 'models' directory. It is a variant of the Linear Ballistic Accumulator
(LBA) model (Brown & Heathcote, 2008), and so it makes sense to store it in the LBA
subdirectory. As with all DMC model files, the code defines a transform, likelihood, and random function.
The memory lapse model is a modified version of the linear ballistic accumulator. Two things happen in the event of a memory failure: 1) the PM accumulator fails to run
(e.g., in a three-choice task, that only the two ongoing task accumulators run), and 2) PM stimulus
input will fail to inhibit ongoing task accumulation. Incorporating these failures requires modifications
to the PMDC likelihood. The likelihood of PM responses is reduced in proportion to the probability of PM failure:
$$L_P = (1-p_{pmf})f(t|\theta_P) \prod_{i=1}^nS(t|\theta_i)$$
\(L_P (t)\) refers to the probability of observing a PM response with decision time \(t\),
where \(t\) is RT minus non-decision time. \(p_{pmf}\) is the probability of PM failure.
\(f(t│\theta_P )\) is the probability density that PM accumulator would reach threshold at time \(t\).
\(S(t│\theta_i )\) is the probability that an ongoing task accumulator \(i\) would not reach threshold
before time \(t\) (i.e., the survivor function), \(\prod_{i=1}^nS(t|\theta_i)\) and thus is the probability that
none of the ongoing task accumulators \(i = 1 … n\) would pre-empt the PM accumulator before time t.
The likelihood of each ongoing task response i is a mixture of two scenarios,
1) the scenario in which PM fails, and only the ongoing task accumulators race to
threshold with no inhibition from PM inputs, and 2), the scenario in which the
PM accumulator is present and PM inputs can inhibit ongoing task accumulation.
$$L_i = p_{pmf}f(t|\theta_i) \prod_{j \ne i}S(t|\theta_j) +
(1-p_{pmf})f(t|\theta_{i,inh})S(t|\theta_P) \prod_{j \ne i}S(t|\theta_{j,inh})
$$
Note that in the above \(L_i (t)\) refers to the probability of observing the ongoing task response
\(i\) with decision time \(t\). \(S(t|\theta_j)\) refers to the survivor function for any alternative ongoing
task response \(j\) in \(j… n\), and \(S(t|\theta_P)\) is the survivor function for the PM accumulator.
\(f(t|\theta_{i,inh})\) refers to the probability density of ongoing task accumulator \(i\) reaching
threshold at time \(t\), given possible inhibition from PM stimulus inputs, and \(S(t|\theta_{j,inh})\)
refers to the survivor function for any alternative ongoing task accumulators \(j\) in \(j… n\) ,
given possible inhibition from PM stimulus inputs. On non-PM trials,
inhibition from PM stimulus inputs is fixed at 0.