adopy.tasks.dd
¶
Delay discounting refers to the wellestablished 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 smallersooner (SS) option (e.g., 8 dollars now) and a largerlonger (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¶

class
adopy.tasks.dd.
TaskDD
¶ Bases:
adopy.base._task.Task
The 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
choice
 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 ['choice']
Model¶

class
adopy.tasks.dd.
ModelExp
¶ Bases:
adopy.base._model.Model
The 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']

compute
(choice, t_ss, t_ll, r_ss, r_ll, r, tau)¶ Compute log likelihood of obtaining responses with given designs and model parameters. The function provide the same result as the argument
func
given in the initialization. If the likelihood function is not given for the model, it returns the log probability of a random noise.Warning
Since the version 0.4.0,
compute()
function should compute the log likelihood, instead of the probability of a binary response variable. Also, it should include the response variables as arguments. These changes might break existing codes using the previous versions of ADOpy.Changed in version 0.4.0: Provide the log likelihood instead of the probability of a binary response.

class
adopy.tasks.dd.
ModelHyp
¶ Bases:
adopy.base._model.Model
The 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']

compute
(choice, t_ss, t_ll, r_ss, r_ll, k, tau)¶ Compute log likelihood of obtaining responses with given designs and model parameters. The function provide the same result as the argument
func
given in the initialization. If the likelihood function is not given for the model, it returns the log probability of a random noise.Warning
Since the version 0.4.0,
compute()
function should compute the log likelihood, instead of the probability of a binary response variable. Also, it should include the response variables as arguments. These changes might break existing codes using the previous versions of ADOpy.Changed in version 0.4.0: Provide the log likelihood instead of the probability of a binary response.

class
adopy.tasks.dd.
ModelHPB
¶ Bases:
adopy.base._model.Model
The 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']

compute
(choice, t_ss, t_ll, r_ss, r_ll, k, s, tau)¶ Compute log likelihood of obtaining responses with given designs and model parameters. The function provide the same result as the argument
func
given in the initialization. If the likelihood function is not given for the model, it returns the log probability of a random noise.Warning
Since the version 0.4.0,
compute()
function should compute the log likelihood, instead of the probability of a binary response variable. Also, it should include the response variables as arguments. These changes might break existing codes using the previous versions of ADOpy.Changed in version 0.4.0: Provide the log likelihood instead of the probability of a binary response.

class
adopy.tasks.dd.
ModelCOS
¶ Bases:
adopy.base._model.Model
The 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: Timeinsensitivity 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']

compute
(choice, t_ss, t_ll, r_ss, r_ll, r, s, tau)¶ Compute log likelihood of obtaining responses with given designs and model parameters. The function provide the same result as the argument
func
given in the initialization. If the likelihood function is not given for the model, it returns the log probability of a random noise.Warning
Since the version 0.4.0,
compute()
function should compute the log likelihood, instead of the probability of a binary response variable. Also, it should include the response variables as arguments. These changes might break existing codes using the previous versions of ADOpy.Changed in version 0.4.0: Provide the log likelihood instead of the probability of a binary response.

class
adopy.tasks.dd.
ModelQH
¶ Bases:
adopy.base._model.Model
The quasihyperbolic model (or BetaDelta 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']

compute
(choice, t_ss, t_ll, r_ss, r_ll, beta, delta, tau)¶ Compute log likelihood of obtaining responses with given designs and model parameters. The function provide the same result as the argument
func
given in the initialization. If the likelihood function is not given for the model, it returns the log probability of a random noise.Warning
Since the version 0.4.0,
compute()
function should compute the log likelihood, instead of the probability of a binary response variable. Also, it should include the response variables as arguments. These changes might break existing codes using the previous versions of ADOpy.Changed in version 0.4.0: Provide the log likelihood instead of the probability of a binary response.

class
adopy.tasks.dd.
ModelDE
¶ Bases:
adopy.base._model.Model
The 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']

compute
(choice, t_ss, t_ll, r_ss, r_ll, omega, r, s, tau)¶ Compute log likelihood of obtaining responses with given designs and model parameters. The function provide the same result as the argument
func
given in the initialization. If the likelihood function is not given for the model, it returns the log probability of a random noise.Warning
Since the version 0.4.0,
compute()
function should compute the log likelihood, instead of the probability of a binary response variable. Also, it should include the response variables as arguments. These changes might break existing codes using the previous versions of ADOpy.Changed in version 0.4.0: Provide the log likelihood instead of the probability of a binary response.