# 9.86. 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.

## 9.86.1. History¶

• Kirby et al. (1999) [27-item version].
• Based on the earlier 21-item version: Kirby & Maraković (1996).

## 9.86.2. Source¶

• From Kirby et al. (1999) as above.

## 9.86.3. Calculations¶

Hyperbolic delay discounting. The principle is to judge the value of two options, and . Each has an amount , and a delay , . Hyperbolic delay discounting is assumed, according to the discounting parameter :

In the case of the Kirby MCQ, one option has zero delay (the small immediate reward or SIR – call it option 1): . One has a delay (the large delayed reward or LDR – call it option 2).

The values are therefore:

At indifference:

so at indifference:

Given a set of trials, a subject’s indifference point can be calculated in various ways.

Kirby’s method (Kirby et al. 1999; Kirby, 2000). For each question, at indifference, can be calculated from the equations above via . Kirby’s method compares subject’s choices against these indifference values: if the subject chooses the delayed option, then , and if the subject chooses the immediate option, then . For a consistent series of choices, the geometric mean of the tested values straddling the subject’s indifference point is taken as the subject’s value. If the subject’s 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 is used. Where choices are not consistent, then the subject’s value of is taken as the value with which the subject’s choices were most consistent (i.e. the most choices were as predicted by that value of ) or, if there is no clear winner, the geometric mean of multiple possible tested 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 , and then predicts the probability of choosing the delayed response using a logistic regression, where . That is, and are used as predictors, obtaining the coefficients and . At indifference, where , this gives , and hence is estimated by . However, it is possible for such estimates to be negative under conditions of inconsistent choice.

Todo

Reference RNC new method when published.

is the delay at which a prospective reward has decayed to half its original value.

## 9.86.4. Intellectual property rights¶

Believed to contain no significant intellectual property, aside from the code, which is part of CamCOPS.

## 9.86.5. 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.