adopy.tasks.dd¶
Delay discounting refers to the well-established finding that humans tend to discount the value of a future reward such that the discount progressively increases as a function of the receipt delay (Green & Myerson, 2004; Vincent, 2016). In a typical delay discounting (DD) task, the participant is asked to indicate his/her preference between two delayed options: a smaller-sooner (SS) option (e.g., 8 dollars now) and a larger-longer (LL) option (e.g., 50 dollars in 1 month).
References
Green, L. and Myerson, J. (2004). A discounting framework for choice with delayed and probabilistic rewards. Psychological Bulletin, 130, 769–792.
Vincent, B. T. (2016). Hierarchical Bayesian estimation and hypothesis testing for delay discounting tasks. Behavior Research Methods, 48, 1608–1620.
Task¶
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class
adopy.tasks.dd.TaskDD¶ Bases:
adopy.base._task.TaskThe Task class for the delay discounting task.
- Design variables
t_ss(\(t_{SS}\)) - delay of a SS optiont_ll(\(t_{LL}\)) - delay of a LL optionr_ss(\(R_{SS}\)) - amount of reward of a SS optionr_ll(\(R_{LL}\)) - amount of reward of a LL option
- Responses
0 (choosing a SS option) or 1 (choosing a LL option)
Examples
>>> from adopy.tasks.ddt import TaskDD >>> task = TaskDD() >>> task.designs ['t_ss', 't_ll', 'r_ss', 'r_ll'] >>> task.responses [0, 1]
A task object stores information for a specific experimental task, including labels of design variables (
designs), possible responses (responses) and its name (name).- Parameters
designs – Labels of design variables in the task.
responses – Possible values for the response variable of the task.
name – Name of the task.
Examples
>>> task = Task(name='Task A', designs=['d1', 'd2'], responses=[0, 1]) >>> task Task('Task A', designs=['d1', 'd2'], responses=[0, 1]) >>> task.name 'Task A' >>> task.designs ['d1', 'd2'] >>> task.responses [0, 1]
Model¶
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class
adopy.tasks.dd.ModelExp¶ Bases:
adopy.base._model.ModelThe exponential model for the delay discounting task (Samuelson, 1937).
\[\begin{split}\begin{align} D(t) &= e^{-rt} \\ V_{LL} &= R_{LL} \cdot D(t_{LL}) \\ V_{SS} &= R_{SS} \cdot D(t_{SS}) \\ P(LL\, over \, SS) &= \frac{1}{1 + \exp [-\tau (V_{LL} - V_{SS})]} \end{align}\end{split}\]- Model parameters
r(\(r\)) - discounting parameter (\(r > 0\))tau(\(\tau\)) - inverse temperature (\(\tau > 0\))
References
Samuelson, P. A. (1937). A note on measurement of utility. The review of economic studies, 4 (2), 155–161.
Examples
>>> from adopy.tasks.ddt import ModelExp >>> model = ModelExp() >>> model.task Task('DDT', designs=['t_ss', 't_ll', 'r_ss', 'r_ll'], responses=[0, 1]) >>> model.params ['r', 'tau']
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compute(t_ss, t_ll, r_ss, r_ll, r, tau)¶ Compute the probability of choosing a certain response given values of design variables and model parameters.
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class
adopy.tasks.dd.ModelHyp¶ Bases:
adopy.base._model.ModelThe hyperbolic model for the delay discounting task (Mazur, 1987).
\[\begin{split}\begin{align} D(t) &= \frac{1}{1 + kt} \\ V_{LL} &= R_{LL} \cdot D(t_{LL}) \\ V_{SS} &= R_{SS} \cdot D(t_{SS}) \\ P(LL\, over \, SS) &= \frac{1}{1 + \exp [-\tau (V_{LL} - V_{SS})]} \end{align}\end{split}\]- Model parameters
k(\(k\)) - discounting parameter (\(k > 0\))tau(\(\tau\)) - inverse temperature (\(\tau > 0\))
References
Mazur, J. E. (1987). An adjusting procedure for studying delayed reinforcement. Commons, ML.;Mazur, JE.; Nevin, JA, 55–73.
Examples
>>> from adopy.tasks.ddt import ModelHyp >>> model = ModelHyp() >>> model.task Task('DDT', designs=['t_ss', 't_ll', 'r_ss', 'r_ll'], responses=[0, 1]) >>> model.params ['k', 'tau']
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compute(t_ss, t_ll, r_ss, r_ll, k, tau)¶ Compute the probability of choosing a certain response given values of design variables and model parameters.
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class
adopy.tasks.dd.ModelHPB¶ Bases:
adopy.base._model.ModelThe hyperboloid model for the delay discounting task (Green & Myerson, 2004).
\[\begin{split}\begin{align} D(t) &= \frac{1}{(1 + kt)^s} \\ V_{LL} &= R_{LL} \cdot D(t_{LL}) \\ V_{SS} &= R_{SS} \cdot D(t_{SS}) \\ P(LL\, over \, SS) &= \frac{1}{1 + \exp [-\tau (V_{LL} - V_{SS})]} \end{align}\end{split}\]- Model parameters
k(\(k\)) - discounting parameter (\(k > 0\))s(\(s\)) - scale parameter (\(s > 0\))tau(\(\tau\)) - inverse temperature (\(\tau > 0\))
References
Green, L. and Myerson, J. (2004). A discounting framework for choice with delayed and probabilistic rewards. Psychological Bulletin, 130, 769–792.
Examples
>>> from adopy.tasks.ddt import ModelHPB >>> model = ModelHPB() >>> model.task Task('DDT', designs=['t_ss', 't_ll', 'r_ss', 'r_ll'], responses=[0, 1]) >>> model.params ['k', 's', 'tau']
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compute(t_ss, t_ll, r_ss, r_ll, k, s, tau)¶ Compute the probability of choosing a certain response given values of design variables and model parameters.
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class
adopy.tasks.dd.ModelCOS¶ Bases:
adopy.base._model.ModelThe constant sensitivity model for the delay discounting task (Ebert & Prelec, 2007).
\[\begin{split}\begin{align} D(t) &= \exp[-(rt)^s] \\ V_{LL} &= R_{LL} \cdot D(t_{LL}) \\ V_{SS} &= R_{SS} \cdot D(t_{SS}) \\ P(LL\, over \, SS) &= \frac{1}{1 + \exp [-\tau (V_{LL} - V_{SS})]} \end{align}\end{split}\]- Model parameters
r(\(r\)) - discounting parameter (\(r > 0\))s(\(s\)) - scale parameter (\(s > 0\))tau(\(\tau\)) - inverse temperature (\(\tau > 0\))
References
Ebert, J. E. and Prelec, D. (2007). The fragility of time: Time-insensitivity and valuation of thenear and far future. Management science, 53 (9), 1423–1438.
Examples
>>> from adopy.tasks.ddt import ModelCOS >>> model = ModelCOS() >>> model.task Task('DDT', designs=['t_ss', 't_ll', 'r_ss', 'r_ll'], responses=[0, 1]) >>> model.params ['r', 's', 'tau']
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compute(t_ss, t_ll, r_ss, r_ll, r, s, tau)¶ Compute the probability of choosing a certain response given values of design variables and model parameters.
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class
adopy.tasks.dd.ModelQH¶ Bases:
adopy.base._model.ModelThe quasi-hyperbolic model (or Beta-Delta model) for the delay discounting task (Laibson, 1997).
\[\begin{split}\begin{align} D(t) &= \begin{cases} 1 & \text{if } t = 0 \\ \beta \delta ^ t & \text{if } t > 0 \end{cases} \\ V_{LL} &= R_{LL} \cdot D(t_{LL}) \\ V_{SS} &= R_{SS} \cdot D(t_{SS}) \\ P(LL\, over \, SS) &= \frac{1}{1 + \exp [-\tau (V_{LL} - V_{SS})]} \end{align}\end{split}\]- Model parameters
beta(\(\beta\)) - constant rate (\(0 < \beta < 1\))delta(\(\delta\)) - constant rate (\(0 < \delta < 1\))tau(\(\tau\)) - inverse temperature (\(\tau > 0\))
References
Laibson, D. (1997). Golden eggs and hyperbolic discounting. The Quarterly Journal of Economics, 443–477
Examples
>>> from adopy.tasks.ddt import ModelQH >>> model = ModelQH() >>> model.task Task('DDT', designs=['t_ss', 't_ll', 'r_ss', 'r_ll'], responses=[0, 1]) >>> model.params ['beta', 'delta', 'tau']
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compute(t_ss, t_ll, r_ss, r_ll, beta, delta, tau)¶ Compute the probability of choosing a certain response given values of design variables and model parameters.
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class
adopy.tasks.dd.ModelDE¶ Bases:
adopy.base._model.ModelThe double exponential model for the delay discounting task (McClure et al., 2007).
\[\begin{split}\begin{align} D(t) &= \omega e^{-rt} + (1 - \omega) e^{-st} \\ V_{LL} &= R_{LL} \cdot D(t_{LL}) \\ V_{SS} &= R_{SS} \cdot D(t_{SS}) \\ P(LL\, over \, SS) &= \frac{1}{1 + \exp [-\tau (V_{LL} - V_{SS})]} \end{align}\end{split}\]- Model parameters
omega(\(r\)) - weight parameter (\(0 < \omega < 1\))r(\(r\)) - discounting rate (\(r > 0\))s(\(s\)) - discounting rate (\(s > 0\))tau(\(\tau\)) - inverse temperature (\(\tau > 0\))
References
McClure, S. M., Ericson, K. M., Laibson, D. I., Loewenstein, G., and Cohen, J. D. (2007). Time discounting for primary rewards. Journal of neuroscience, 27 (21), 5796–5804.
Examples
>>> from adopy.tasks.ddt import ModelDE >>> model = ModelDE() >>> model.task Task('DDT', designs=['t_ss', 't_ll', 'r_ss', 'r_ll'], responses=[0, 1]) >>> model.params ['omega', 'r', 's', 'tau']
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compute(t_ss, t_ll, r_ss, r_ll, omega, r, s, tau)¶ Compute the probability of choosing a certain response given values of design variables and model parameters.