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Using logistic regression to estimate delay-discounting functions.

E Paul Wileyto1, Janet Audrain-McGovern, Leonard H Epstein

  • 1Tobacco Use Research Center, University of Pennsylvania, 3535 Market Street, Suite 4100, Philadelphia, PA 19104, USA. epw@mail.med.upenn.edu

Behavior Research Methods, Instruments, & Computers : a Journal of the Psychonomic Society, Inc
|June 12, 2004
PubMed
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This study introduces a new logistic regression method to directly estimate the hyperbolic parameter k from monetary choice questionnaire (MCQ) responses. This approach accurately models delayed reward preferences in adolescents.

Area of Science:

  • Behavioral Economics
  • Psychology
  • Neuroscience

Background:

  • The monetary choice questionnaire (MCQ) assesses indifference between immediate and delayed rewards.
  • Indifference data are typically fitted using a hyperbolic function to model value decline over time.

Purpose of the Study:

  • To present a novel fitting method for estimating the hyperbolic parameter k directly from survey responses.
  • To validate this logistic regression method against standard scoring techniques for the MCQ.

Main Methods:

  • Modeled binary preferences using logistic regression with time (X2) and reward ratio (X1) as predictors.
  • Derived the hyperbolic parameter k as the ratio of logistic regression coefficients (k = beta 2/beta 1).
  • Administered the MCQ to 1,073 adolescents and compared standard and logistic scoring methods.

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Main Results:

  • The logistic regression method yielded results highly correlated with the standard method (rho = 0.973).
  • Means for the natural logarithm of k were similar between methods (standard: -4.53, logistic: -4.51).
  • Simulated data indicated the logistic method provides an unbiased estimate of k, except for vague responses.

Conclusions:

  • The logistic regression approach offers a direct and reliable method for estimating hyperbolic discounting from MCQ data.
  • This method is validated for use with adolescent populations and provides accurate parameter estimation.