Simple matrix methods for analyzing diffusion models of choice probability, choice response time, and simple response time

Diederich, Adele; Busemeyer, Jerome R.

doi:10.1016/s0022-2496(03)00003-8

Cited by 134 publications

(134 citation statements)

References 35 publications

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“…In addition, error rates tend to be higher in our study than in those to which SFT is typically applied. We therefore obtained predictions for the SFT measures using a combination of simulations (Diederich & Busemeyer, 2003;Fific et al, 2008;Eidels et al, 2011) and analytic methods (Townsend & Thomas, 1994), as described in Appendix A. The resulting predictions allow for both a large proportion of errors (from near 0% to 96%) and violations of selective influence; while we lose the statistical power available with low error rates and selective influence, we can be confident that we have provided a fair qualitative characterization of each possible retrieval architecture.…”

Section: Systems Factorial Analysismentioning

confidence: 99%

“…Analytic simulation results were obtained via matrix methods (Diederich & Busemeyer, 2003). While the precise implementation depended on the simulated architecture, as described below, the general idea is to define the state space X of the accumulators and use the increment probabilities u 1 and u 2 and stopping rule (self-terminating or exhaustive) to determine the probability of transitioning from one part of the state space x i ∈ X to another x j ∈ X, expressed via a transition matrix Q.…”

Section: A1 Simulationsmentioning

confidence: 99%

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Parallel interactive retrieval of item and associative information from event memory

Cox

Criss

2017

Cognitive Psychology

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Memory contains information about individual events (items) and combinations of events (associations). Despite the fundamental importance of this distinction, it remains unclear exactly how these two kinds of information are stored and whether different processes are used to retrieve them. We use both model-independent qualitative properties of response dynamics and quantitative modeling of individuals to address these issues. Item and associative information are not independent and they are retrieved concurrently via interacting processes. During retrieval, matching item and associative information mutually facilitate one another to yield an amplified holistic signal. Modeling of individuals suggests that this kind of facilitation between item and associative retrieval is a ubiquitous feature of human memory.

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Section: Systems Factorial Analysismentioning

confidence: 99%

Section: A1 Simulationsmentioning

confidence: 99%

Parallel interactive retrieval of item and associative information from event memory

Cox

Criss

2017

Cognitive Psychology

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“…The more complex methods for solving SDEs yielded no improvement in accuracy over the Euler method. However, the matrix method proposed by Diederich and Busemeyer (2003) yielded significant improvements. The accuracy of all methods depended critically on the size of the approximating time step.…”

mentioning

confidence: 99%

“…One is the matrix algebra method of Diederich and Busemeyer (2003;see also Busemeyer & Townsend, 1993), referred to hereafter as the BDT matrix method. The other solution method is actually a large class of differential equation "tracking" algorithms combined with Monte Carlo integration over sources of variability.…”

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confidence: 99%

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Evaluating methods for approximating stochastic differential equations

Brown

Ratcliff

Smith

2006

Journal of Mathematical Psychology

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Models of decision making and response time (RT) are often formulated using stochastic differential equations (SDEs). Researchers often investigate these models using a simple Monte Carlo method based on Euler's method for solving ordinary differential equations. The accuracy of Euler's method is investigated and compared to the performance of more complex simulation methods. The more complex methods for solving SDEs yielded no improvement in accuracy over the Euler method. However, the matrix method proposed by Diederich and Busemeyer (2003) yielded significant improvements. The accuracy of all methods depended critically on the size of the approximating time step. The large (∼10 ms) step sizes often used by psychological researchers resulted in large and systematic errors in evaluating RT distributions.Over the past 40 years, models of response time (RT) for simple decision making have become very successful at capturing the details of observed data (Audley & Pike, 1965;Brown & Heathcote, 2005;Busemeyer & Townsend, 1993;Diederich, 1997;Heath, 1981;LaBerge, 1962;Lacouture and Marley, 1991;Laming, 1966;Link & Heath, 1975;Ratcliff, 1978; Ratcliff & Smith, 2004, Appendix;Ratcliff, Van Zandt, & McKoon, 1999;Smith, 1995;Vickers, 1970;Vickers & Lee, 2000). More recently, the same models have also become quite successful at explaining decision making at a neural level (Carpenter & Reddi, 2001;Cook & Maunsell, 2002;Glimcher 2003;Gold & Shadlen, 2001;Ratcliff, Cherian & Seagraves, 2003;Reddi & Carpenter, 2000;Roitman & Shadlen, 2002;Sato, Murthy, Thompson & Schall, 2001;Sato & Schall, 2003;Shadlen, Britten, Newsome & Movshon, 1996;Wang, 2002). The most successful models of decision making in both cognitive and neural domains are the sequential sampling models. These models are based on the idea that noisy stimulus information is accumulated progressively over time until sufficient information for one of the response alternatives has been obtained. The predicted decision time in such models is obtained mathematically by solving a first-passage-time (FPT) problem, that is, the time taken for the accumulated information to reach a criterion and trigger a response. For some models, there exist explicit analytic methods or highly accurate numerical methods for solving the FPT problem (see Ratcliff & Smith, Appendix, for a survey). For other models, this problem may be complex or intractable. In such situations, researchers must resort to Monte Carlo simulation techniques to obtain predicted RT distributions and choice probabilities. We investigate the properties of such simulation techniques in this article.One of the best-known sequential sampling models, and one that has been applied to a wide range of experimental data, is the diffusion model of Ratcliff (1978;Ratcliff & Rouder, 1998). This model assumes that evidence accumulation begins at some initial value (z) and

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Computational Models of Decision Making

Busemeyer¹,

Johnson²

2004

Blackwell Handbook of Judgment and Decision Making

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107

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This chapter presents a connectionist or artificial neural network approach to decision making. An essential idea of this approach is that decisions are based on the accumulation of the affective evaluations produced by each action until a threshold criterion is reached. This type of sequential sampling process forms the basis for decision making in a wide variety of other cognitive tasks such as perception, categorization, and memory. We apply these concepts to several important preferential choice phenomena, including similarity effects, attraction effects, compromise effects, loss aversion effects, and preference reversals. These analyses indicate that a relatively complex model of an individual's choice process reveals a relatively simple representation of the individual's underlying value structure.

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Simple matrix methods for analyzing diffusion models of choice probability, choice response time, and simple response time

Cited by 134 publications

References 35 publications

Parallel interactive retrieval of item and associative information from event memory

Parallel interactive retrieval of item and associative information from event memory

Evaluating methods for approximating stochastic differential equations

Computational Models of Decision Making

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