We demonstrate how to add a custom distribution into the general-purpose, open-source, cross-platform graphical modeling package JAGS ("Just Another Gibbs Sampler"). JAGS is intended to be modular and extensible, and modules written in the way laid out here can be loaded at runtime as needed and do not interfere with regular JAGS functionality when not loaded. Writing custom extensions requires knowledge of C++, but installing a new module can be highly automatic, depending on the operating system. As a basic example, we implement a Bernoulli distribution in JAGS. We further present our implementation of the Wiener diffusion first-passage time distribution, which is freely available at https://sourceforge.net/projects/jags-wiener/.

We present the RWiener package that provides R functions for the Wiener diffusion model. The core of the package are the four distribution functions dwiener, pwiener, qwiener and rwiener, which use up-to-date methods, implemented in C, and provide fast and accurate computation of the density, distribution, and quantile function, as well as a random number generator for the Wiener diffusion model. We used the typical Wiener diffusion model with four parameters: boundary separation, non-decision time, initial bias and drift rate parameter. Beyond the distribution functions, we provide extended likelihood-based functions that can be used for parameter estimation and model selection. The package can be obtained via CRAN.A. Voss and J. Voss. fast-dm: A free program for efficient diffusion model analysis. Behavior Research Methods, 39(4):767-775, 2007. [p49] E.-J. Wagenmakers. Methodological and empirical developments for the Ratcliff diffusion model of response times and accuracy.

The article presents Bayesian hierarchical modeling frameworks for two measurement models for visual working memory. The models can be applied to the distributions of responses on a circular feature dimension, as obtained with the continuous reproduction (a.k.a. delayed estimation) task. The first measurement model is a mixture model that describes the response distributions as a mixture of one (Zhang & Luck, 2008) or several (Bays, Catalao, & Husain, 2009) von-Mises distribution(s) and a uniform distribution. The second model is a novel, interference-based measurement model. We present parameter recovery simulations for both models, demonstrating that the hierarchical framework enables precise parameter estimates when a small number of trials are compensated by a large number of subjects. Simulations with the mixture model show that the Bayesian hierarchical framework minimizes the previously observed estimation bias for memory precision in conditions of low performance. Unbiased and reasonably precise parameter estimates can also be obtained from the interference measurement model, though some parameters of this model demand a relatively large amount of data for precise measurement. Both models are applied to two experimental data sets. Experiment 1 measures the effect of memory set size on the model parameters. Experiment 2 provides evidence for the assumption in the interference model that the target feature tends to be confused with features of those nontargets that are close to the target on the dimension used as retrieval cue.

The shifted-Wald model is a popular analysis tool for one-choice reaction-time tasks. In its simplest version, the shifted-Wald model assumes a constant trial-independent drift rate parameter. However, the presence of endogenous processes—fluctuation in attention and motivation, fatigue and boredom—suggest that drift rate might vary across experimental trials. Here we show how across-trial variability in drift rate can be accounted for by assuming a trial-specific drift rate parameter that is governed by a positive-valued distribution. We consider two candidate distributions: the truncated normal distribution and the gamma distribution. For the resulting distributions of first-arrival times, we derive analytical and sampling-based solutions, and implement the models in a Bayesian framework. Recovery studies and an application to a data set comprised of 1469 participants suggest that (1) both mixture distributions yield similar results; (2) all model parameters can be recovered accurately except for the drift variance parameter; (3) despite poor recovery, the presence of the drift variance parameter facilitates accurate recovery of the remaining parameters; (4) shift, threshold, and drift mean parameters are correlated.