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Randomly stopped sums: models and psychological applications.

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  • 1Research School of Psychology, The Australian National University Canberra, ACT, Australia.

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This study introduces new statistical models for analyzing random sums, particularly useful for psychological research on decision-making time. The models enhance understanding of total decision time in information search tasks.

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accumulation models of decision-makingdecision modelingfinancial loss modelingrandom sumsresponse time modeling

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Area of Science:

  • Psychology
  • Statistics
  • Decision Science

Background:

  • Randomly stopped sums are common in financial statistics but underutilized in psychology.
  • Modeling total decision time in information search tasks presents unique statistical challenges.

Purpose of the Study:

  • To develop and evaluate statistical models for sums of continuous random variables where the number of observations is also random.
  • To adapt financial statistics techniques for randomly stopped sums to psychological research, specifically decision-making processes.

Main Methods:

  • Modeling randomly stopped sums using life distributions (e.g., gamma, log-normal).
  • Conducting a simulation study to assess Type I error rates and statistical power.
  • Employing a Bayesian hierarchical approach for general linear modeling of sums.
  • Discussing model diagnostics and applying models to real-world datasets.

Main Results:

  • The proposed gamma and log-normal models demonstrate accurate Type I error rates and adequate power in simulations.
  • The Bayesian hierarchical approach provides a flexible framework for analyzing complex sum data.
  • Illustrations show the practical applicability of the models to psychological data.

Conclusions:

  • The developed statistical models offer a robust framework for analyzing randomly stopped sums in psychological research.
  • These methods can advance the understanding of decision-making processes and information processing in psychology.
  • The study bridges a gap between financial statistics and psychological modeling techniques.