Parametric supplements to systems factorial analysis: Identifying interactive parallel processing using systems of accumulators

Gregory E. Cox, Amy Criss

Research output: Contribution to journalReview article

1 Citation (Scopus)

Abstract

Systems Factorial Technology (SFT; Townsend and Nozawa (1995)) gains much of its power from finding tight nonparametric links between theory and data. But this power comes at a price: Applying SFT typically requires low error rates, many observations, and a guarantee of selective influence of experimental manipulations, conditions that cannot be satisfied in many fields of psychology. We present a set of parametric methods that, while lacking the full power of traditional SFT, allow its logic to be applied to situations that do not adhere to those conditions. These methods are based around building different parallel architectures from systems of Linear Ballistic Accumulators (Brown and Heathcote (2008)), including architectures that involve interactions between processes. The primary output of these methods is an estimate of the probabilities that a participant is best described by each of these architectures. In an example and set of simulations, we show that these methods are accurate and robust at identifying the processing architectures employed by a set of participants, may be estimated in maximum a posteriori or fully Bayesian fashion, and that hierarchical estimation allowing accurate identification with as few as three trials per participant per condition. We provide code that allows researchers to apply these methods to their own data at https://osf.io/m6ubq/.

Original languageEnglish (US)
JournalJournal of Mathematical Psychology
DOIs
StatePublished - Jan 1 2019

Fingerprint

Parallel architectures
Factorial
Parallel processing systems
Ballistics
Parallel Processing
Processing
Maximum a Posteriori
Parallel Architectures
Error Rate
Manipulation
Research Personnel
Logic
Psychology
Technology
Output
Interaction
Estimate
Architecture
Power (Psychology)
Simulation

Keywords

  • Accumulator models
  • Bayesian statistics
  • Hierarchical models
  • Systems factorial technology

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics

Cite this

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abstract = "Systems Factorial Technology (SFT; Townsend and Nozawa (1995)) gains much of its power from finding tight nonparametric links between theory and data. But this power comes at a price: Applying SFT typically requires low error rates, many observations, and a guarantee of selective influence of experimental manipulations, conditions that cannot be satisfied in many fields of psychology. We present a set of parametric methods that, while lacking the full power of traditional SFT, allow its logic to be applied to situations that do not adhere to those conditions. These methods are based around building different parallel architectures from systems of Linear Ballistic Accumulators (Brown and Heathcote (2008)), including architectures that involve interactions between processes. The primary output of these methods is an estimate of the probabilities that a participant is best described by each of these architectures. In an example and set of simulations, we show that these methods are accurate and robust at identifying the processing architectures employed by a set of participants, may be estimated in maximum a posteriori or fully Bayesian fashion, and that hierarchical estimation allowing accurate identification with as few as three trials per participant per condition. We provide code that allows researchers to apply these methods to their own data at https://osf.io/m6ubq/.",
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AB - Systems Factorial Technology (SFT; Townsend and Nozawa (1995)) gains much of its power from finding tight nonparametric links between theory and data. But this power comes at a price: Applying SFT typically requires low error rates, many observations, and a guarantee of selective influence of experimental manipulations, conditions that cannot be satisfied in many fields of psychology. We present a set of parametric methods that, while lacking the full power of traditional SFT, allow its logic to be applied to situations that do not adhere to those conditions. These methods are based around building different parallel architectures from systems of Linear Ballistic Accumulators (Brown and Heathcote (2008)), including architectures that involve interactions between processes. The primary output of these methods is an estimate of the probabilities that a participant is best described by each of these architectures. In an example and set of simulations, we show that these methods are accurate and robust at identifying the processing architectures employed by a set of participants, may be estimated in maximum a posteriori or fully Bayesian fashion, and that hierarchical estimation allowing accurate identification with as few as three trials per participant per condition. We provide code that allows researchers to apply these methods to their own data at https://osf.io/m6ubq/.

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