Using logistic regression to estimate delay-discounting functions |
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Authors: | Email author" target="_blank">E?Paul?WileytoEmail author Janet?Audrain-Mcgovern Leonard?H?Epstein Caryn?Lerman |
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Institution: | 1.Tobacco Use Research Center,University of Pennsylvania,Philadelphia;2.State University of New York,Buffalo;3.University of Pennsylvania,Philadelphia |
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Abstract: | The monetary choice questionnaire (MCQ) and similar computer tasks ask preference questions in order to ascertain indifference,
the perceived equivalence of immediate versus larger delayed rewards. Indifference data are then fitted with a hyperbolic
function, summarizing the decline in perceived value with delay time. We present a fitting method that estimates the hyperbolic
parameterk directly from survey responses. Binary preferences are modeled as a function of time (X2) and a transformed reward ratio (X
1), yielding logistic regression coefficients β2 and β1. The hyperbolic parameter emerges ask = β2/β1, where the logistic predictedp = .5 (the definition of indifference). The MCQ was administered to 1,073 adolescents and was scored using both standard and
logistic methods. The means for ln(k) were similar (standard, −4.53; logistic, −4.51), and the results were highly correlated (ρ = .973). Simulated MCQ data showed
thatk was unbiased, except where β1 ≥ −1, indicating a vague survey response. Jackknife standard errors provided excellent coverage. |
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