9.84. 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.

9.84.1. History

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

9.84.2. Source

  • From Kirby et al. (1999) as above.

9.84.3. Calculations

Hyperbolic delay discounting. The principle is to judge the value V of two options, V_1 and V_2. Each has an amount A_1, A_2 and a delay D_1, D_2. Hyperbolic delay discounting is assumed, according to the discounting parameter k:

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): D_1 = 0. One has a delay (the large delayed reward or LDR – call it option 2).

The values are therefore:

V_1 = \frac{A_1}{1 + k D_1} = A_1

V_2 = \frac{A_2}{1 + k D_2}

At indifference:

V_1 = V_2

so at indifference:

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 k can be calculated in various ways.

Kirby’s method (Kirby et al. 1999; Kirby, 2000). For each question, at indifference, k_{\text{indiff}} can be calculated from the equations above via k_{\text{indiff}} = \frac{A_2 - A_1}{A_1 D_2}. Kirby’s method compares subject’s choices against these indifference k values: if the subject chooses the delayed option, then k < k_{\text{indiff}}, and if the subject chooses the immediate option, then k > k_{\text{indiff}}. For a consistent series of choices, the geometric mean of the tested k values straddling the subject’s indifference point is taken as the subject’s k value. If the subject’s 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 k is used. Where choices are not consistent, then the subject’s value of k is taken as the k value with which the subject’s choices were most consistent (i.e. the most choices were as predicted by that value of k) or, if there is no clear winner, the geometric mean of multiple possible tested 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 R = \frac{A_1}{A_2}, and then predicts the probability p of choosing the delayed response using a logistic regression, p = \frac{e^y}{1 + e^y} = \frac{1}{1 + e^{–y}} where y =
\beta_1(1 – \frac{1}{R}) + \beta_2 D_2. That is, 1 – \frac{A_2}{A_1} and D_2 are used as predictors, obtaining the coefficients \beta_1 and \beta_2. At indifference, where y = 0, this gives R = \frac{1}{1 + \frac{\beta_2}{\beta_1} D_2}, and hence k is estimated by \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.

\frac{1}{k} is the delay at which a prospective reward has decayed to half its original value.

9.84.4. Intellectual property rights

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

9.84.5. 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.