Parallel probability density approximation

Lin, Yi-Shin; Heathcote, Andrew; Holmes, William R.

doi:10.3758/s13428-018-1153-1

Cited by 15 publications

(16 citation statements)

References 46 publications

(93 reference statements)

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“…The ggdmc package is ready to assist applied researchers to exploit the advantages of hierarchical evidence accumulation modeling. Our software is built upon an earlier suite of R functions, Dynamic Models of Choice (Heathcote et al, 2019). We have provided a convenient interface to incorporate experimental designs.…”

Section: Discussionmentioning

confidence: 99%

“…For example, we have recently fitted the piecewise LBA model (Holmes et al, 2016) with ggdmc to explore the method of using massive par-allel computation in likelihood simulations. This example shows ggdmc can accommodate cognitive models without analytic likelihood functions (Holmes, 2015;Lin, Heathcote, & Holmes, 2019;Turner & Sederberg, 2012). When this combined with approximate Bayesian computation (Beaumont, Zhang, & Balding, 2002), it can empower researchers to estimate model parameters with only process descriptions in hand.…”

Section: Discussionmentioning

confidence: 99%

“…To facilitate working with Bayesian evidence accumulation models, we present a new, highly efficient R package, ggdmc, that incorporates a user-friendly interface for entering various factorial designs (Heathcote et al, 2019;Vandekerckhove & Tuerlinckx, 2007). Below we provide a general overview of the steps for researchers to apply ggdmc.…”

Section: Bayesian Estimationmentioning

confidence: 99%

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Evidence accumulation models with R: A practical guide to hierarchical Bayesian methods

Lin¹,

Strickland²

2020

TQMP

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Evidence accumulation models are a useful tool to allow researchers to investigate the latent cognitive variables that underlie response time and response accuracy. However, applying evidence accumulation models can be difficult because they lack easily computable forms. Numerical methods are required to determine the parameters of evidence accumulation that best correspond to the fitted data. When applied to complex cognitive models, such numerical methods can require substantial computational power which can lead to infeasibly long compute times. In this paper, we provide efficient, practical software and a step-by-step guide to fit evidence accumulation models with Bayesian methods. The software, written in C++, is provided in an R package: 'ggdmc'. The software incorporates three important ingredients of Bayesian computation, (1) the likelihood functions of two common response time models, (2) the Markov chain Monte Carlo (MCMC) algorithm (3) a population-based MCMC sampling method. The software has gone through stringent checks to be hosted on the Comprehensive R Archive Network (CRAN) and is free to download. We illustrate its basic use and an example of fitting complex hierarchical Wiener diffusion models to four shooting-decision data sets.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Bayesian Estimationmentioning

confidence: 99%

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Evidence accumulation models with R: A practical guide to hierarchical Bayesian methods

Lin¹,

Strickland²

2020

TQMP

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“…Response time is then given by the distance to the threshold (θ) divided by the rate of accumulation toward the corresponding response option (δ all • v i ), plus a fixed non-decision time (τ). The likelihood of the data for a particular trial was obtained by generating 1000 simulated trials for every real trial and calculating the predicted accuracy (% correct) and distribution of response times by passing a kernel density estimator over the RT data to perform probability density approximation (Turner & Sederberg, 2014;Holmes, 2015;Lin et al, 2019).…”

Section: Figure 13mentioning

confidence: 99%

A unified theory of discrete and continuous responding

Kvam¹,

Marley²,

Heathcote³

2021

Preprint

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Understanding the cognitive processes underlying choice requires theories that can disentangle the representation of stimuli from the processes that map these representations onto observed responses. We develop a dynamic theory of how stimuli are mapped onto discrete (choice) and continuous response scales. It proposes that the mapping from stimuli to the input to an evidence accumulation process is accomplished using multiple reference points or "anchors". Evidence is accumulated until a threshold amount for a particular response is obtained, with the relative balance of support for each anchor at that time determining the response. We tested this Multiple Anchored Accumulation Theory (MAAT) using the results of two experiments requiring discrete or continuous responses to line length and color stimuli. We manipulated the number of options for discrete responses, the number of different stimuli, and the similarity amongst them, and compared the outcomes to continuous response conditions. We show that MAAT accounts for several key phenomena: more accurate choices and more skewed response distributions near the ends of a response scale; a decrease in accuracy and response speed as the number of discrete choice options increases; and longer response times and lower accuracy when discrete responses were more similar to one another. Our empirical and modeling results suggest that discrete and continuous response tasks can share a common evidence representation, and that the decision process is sensitive to the perceived similarity among the response options.

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“…Instead, we use an approach for model fitting based on kernel density estimation to turn the simulated data into a truly continuous, 2-dimensional distribution of responses and response times. This method has been effectively used to approximate the likelihoods of several types of simulation-based models (Palestro et al, 2018;Turner & Van Zandt, 2012;Turner & Sederberg, 2014), is reasonably efficient especially with the addition of signal processing methods (Holmes, 2015;Lin et al, 2019), and can be easily adapted to a two-dimensional joint distribution like the one produced by the SCDM and GDM. For these models, we can simulate a large number of trials from the model, use the kernel density method to generate an approximate likelihood, and then impute the likelihood of each combination of response and response time in the observed data set.…”

Section: Model Likelihoodsmentioning

confidence: 99%

Reconciling similarity across models of continuous selections

Kvam¹,

Turner²

2019

Preprint

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Recently-developed models of decision behavior have provided richer accounts of the cognitive processes underlying choice by examining performance on tasks where responses can fall along a continuum, such as identifying the color or orientation of a stimulus. While these have laudably expanded models beyond simple binary and multi-alternative choice paradigms, critical concerns remain about the models' lack of completeness, poor computational tractability, or inability to capture important characteristics of choice responses. Specifically, no model is yet able to predict a truly continuous distribution of responses that exhibit multimodality, where responses have more than one central tendency. This property appears frequently in real data where there is conflict between decision information favoring responses at different locations, such as a predecision cue that indicates a different response than the stimulus. These patterns of data are informative to psychological theory, making it critical to develop a better account of continuous response tasks. In this theoretical note, we use a geometric approach developed by Kvam (2019) to provide a solution to this issue and to reconcile the different existing models under a common framework. The resulting geometric diffusion model (GDM) yields a truly continuous joint distribution of responses and response times, produces multimodal distributions of responses, and offers much greater computational efficiency than models producing discrete approximations of continuous responses. We demonstrate that this model can be extended to account for behavior when alternatives are not arranged in a circle, including a case where responses can fall along a 2-dimensional plane such as identifying the location of an item on a computer screen.

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Parallel probability density approximation

Cited by 15 publications

References 46 publications

Evidence accumulation models with R: A practical guide to hierarchical Bayesian methods

Evidence accumulation models with R: A practical guide to hierarchical Bayesian methods

A unified theory of discrete and continuous responding

Reconciling similarity across models of continuous selections

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