.. docs/source/tasks/kirby.rst .. Copyright (C) 2012, University of Cambridge, Department of Psychiatry. Created by Rudolf Cardinal (rnc1001@cam.ac.uk). . This file is part of CamCOPS. . CamCOPS is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. . CamCOPS is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. . You should have received a copy of the GNU General Public License along with CamCOPS. If not, see . .. _kirby_mcq: Kirby Monetary Choice Questionnaire (MCQ) ----------------------------------------- Series of hypothetical choices pitting an immediate amount of money against a delayed amount of money, to measure delay discounting. History ~~~~~~~ - Kirby et al. (1999) [27-item version]. - Based on the earlier 21-item version: Kirby & Maraković (1996). Source ~~~~~~ - From Kirby et al. (1999) as above. Calculations ~~~~~~~~~~~~ .. math markup: see ftp://ftp.ams.org/ams/doc/amsmath/short-math-guide.pdf **Hyperbolic delay discounting.** The principle is to judge the value :math:V of two options, :math:V_1 and :math:V_2. Each has an amount :math:A_1, :math:A_2 and a delay :math:D_1, :math:D_2. Hyperbolic delay discounting is assumed, according to the discounting parameter :math:k: .. math:: V = \frac{A}{1 + k D} In the case of the Kirby MCQ, one option has zero delay (the small immediate reward or SIR -- call it option 1): :math:D_1 = 0. One has a delay (the large delayed reward or LDR -- call it option 2). The values are therefore: .. math:: V_1 = \frac{A_1}{1 + k D_1} = A_1 V_2 = \frac{A_2}{1 + k D_2} At indifference: .. math:: V_1 = V_2 so at indifference: .. math:: A_1 = \frac{A_2}{1 + k D_2} \frac{A_2}{A_1} = 1 + k D_2 k = \frac{\frac{A_2}{A_1} - 1}{D_2} = \frac{A_2 - A_1}{A_1 D_2} Given a set of trials, a subject's indifference point :math:k can be calculated in various ways. **Kirby’s method (Kirby et al. 1999; Kirby, 2000).** For each question, at indifference, :math:k_{\text{indiff}} can be calculated from the equations above via :math:k_{\text{indiff}} = \frac{A_2 - A_1}{A_1 D_2}. Kirby’s method compares subject’s choices against these indifference :math:k values: if the subject chooses the delayed option, then :math:k < k_{\text{indiff}}, and if the subject chooses the immediate option, then :math:k > k_{\text{indiff}}. For a consistent series of choices, the geometric mean of the tested :math:k values straddling the subject’s indifference point is taken as the subject’s :math:k value. If the subject’s :math:k value falls outside the tested range (i.e. all choices were for the immediate, or all for the delayed, option), then the most extreme assessed :math:k is used. Where choices are not consistent, then the subject’s value of :math:k is taken as the :math:k value with which the subject’s choices were most consistent (i.e. the most choices were as predicted by that value of :math:k) or, if there is no clear winner, the geometric mean of multiple possible tested :math:k values that were equally and maximally consistent with the subject’s choice. This geometric mean approach reduces to the simple ‘consistent’ approach for consistent choices, and thus may be used throughout. **Wileyto et al.’s method (Wileyto et al., 2004).** This method defines the reward ratio :math:R = \frac{A_1}{A_2}, and then predicts the probability :math:p of choosing the delayed response using a logistic regression, :math:p = \frac{e^y}{1 + e^y} = \frac{1}{1 + e^{–y}} where :math:y = \beta_1(1 – \frac{1}{R}) + \beta_2 D_2. That is, :math:1 – \frac{A_2}{A_1} and :math:D_2 are used as predictors, obtaining the coefficients :math:\beta_1 and :math:\beta_2. At indifference, where :math:y = 0, this gives :math:R = \frac{1}{1 + \frac{\beta_2}{\beta_1} D_2}, and hence :math:k is estimated by :math:\frac{\beta_2}{\beta_1}. However, it is possible for such estimates to be negative under conditions of inconsistent choice. .. todo:: Reference RNC new method when published. :math:\frac{1}{k} is the delay at which a prospective reward has decayed to half its original value. Intellectual property rights ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Believed to contain no significant intellectual property, aside from the code, which is part of CamCOPS. References ~~~~~~~~~~ Kirby KN, Petry NM, Bickel WK (1999). Heroin addicts have higher discount rates for delayed rewards than non-drug-using controls. *Journal of Experimental Psychology: General* 128: 78-87. https://www.ncbi.nlm.nih.gov/pubmed/10100392 Kirby KN, Maraković NN (1996). Delay-discounting probabilistic rewards: Rates decrease as amounts increase. *Psychon. Bull. Rev.* 3: 100-104. https://www.ncbi.nlm.nih.gov/pubmed/24214810; https://doi.org/10.3758/BF03210748. Kirby KN (2000) Instructions for inferring discount rates from choices between immediate and delayed rewards. Unpublished, Williams College. Wileyto EP, Audrain-McGovern J, Epstein LH, Lerman C (2004). Using logistic regression to estimate delay-discounting functions. *Behav Res Methods Instrum Comput J Psychon Soc Inc* 36: 41–51. https://www.ncbi.nlm.nih.gov/pubmed/15190698.