adopy.tasks.cra

The choice under risk and ambiguity task (CRA; Levy et al., 2010) involves preferential choice decisions in which the participant is asked to indicated his/her preference between two options:

1. A fixed (or reference) option of either winning a fixed amount of reward (\(R_F\), r_fix) with a fixed probability of 0.5 or winning none otherwise; and

2. A variable option of either winning a varying amount of reward (\(R_V\), r_var) with a varying probability (\(p_V\), p_var) and a varying level of ambiguity (\(A_V\), a_var) or winning none otherwise.

Further, the variable option comes in two types:

1. risky type in which the winning probabilities are fully known to the participant; and

2. ambiguous type in which the winning probabilities are only partially known to the participant.

The level of ambiguity (\(A_V\)) is varied between 0 (no ambiguity and thus fully known) and 1 (total ambiguity and thus fully unknown).

References

Levy, I., Snell, J., Nelson, A. J., Rustichini, A., & Glimcher, P. W. (2010). Neural Representation of Subjective Value Under Risk and Ambiguity. Journal of Neurophysiology, 103 (2), 1036-1047.

Task

class adopy.tasks.cra.TaskCRA

Bases: adopy.base._task.Task

The Task class for the choice under risk and ambiguity task (Levy et al., 2010).

Design variables

• p_var (\(p_V\)) - probability to win of a variable option

• a_var (\(A_V\)) - level of ambiguity of a variable option

• r_var (\(R_V\)) - amount of reward of a variable option

• r_fix (\(R_F\)) - amount of reward of a fixed option

Responses

0 (choosing a fixed option) or 1 (choosing a variable option)

Examples

>>> from adopy.tasks.cra import TaskCRA
>>> task = TaskCRA()
>>> task.designs
['p_var', 'a_var', 'r_var', 'r_fix']
>>> 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

class adopy.tasks.cra.ModelLinear

Bases: adopy.base._model.Model

The linear model for the CRA task (Levy et al., 2010).

\[\begin{split}\begin{align} U_F &= 0.5 \cdot (R_F)^\alpha \\ U_V &= \left[ p_V - \beta \cdot \frac{A_V}{2} \right] \cdot (R_V)^\alpha \\ P(V\, over \, F) &= \frac{1}{1 + \exp [-\gamma (U_V - U_F)]} \end{align}\end{split}\]

Model parameters

• alpha (\(\alpha\)) - risk attitude parameter (\(\alpha > 0\))

• beta (\(\beta\)) - ambiguity attitude parameter

• gamma (\(\gamma\)) - inverse temperature (\(\gamma > 0\))

References

Levy, I., Snell, J., Nelson, A. J., Rustichini, A., & Glimcher, P. W. (2010). Neural Representation of Subjective Value Under Risk and Ambiguity. Journal of Neurophysiology, 103 (2), 1036-1047.

Examples

>>> from adopy.tasks.cra import ModelExp
>>> model = ModelExp()
>>> model.task
Task('CRA', designs=['p_var', 'a_var', 'r_var', 'r_fix'], responses=[0, 1])
>>> model.params
['alpha', 'beta', 'gamma']

compute(p_var, a_var, r_var, r_fix, alpha, beta, gamma)

Compute the probability of choosing a certain response given values of design variables and model parameters.

class adopy.tasks.cra.ModelExp

Bases: adopy.base._model.Model

The exponential model for the CRA task (Hsu et al., 2005).

\[\begin{split}\begin{align} U_F &= 0.5 \cdot (R_F)^\alpha \\ U_V &= (p_V) ^ {(1 + \beta \cdot A_V)} \cdot (R_V)^\alpha \\ P(V\, over \, F) &= \frac{1}{1 + \exp [-\gamma (U_V - U_F)]} \end{align}\end{split}\]

Model parameters

• alpha (\(\alpha\)) - risk attitude parameter (\(\alpha > 0\))

• beta (\(\beta\)) - ambiguity attitude parameter

• gamma (\(\gamma\)) - inverse temperature (\(\gamma > 0\))

References

Hsu, Y.-F., Falmagne, J.-C., and Regenwetter, M. (2005). The tuning in-and-out model: a randomwalk and its application to presidential election surveys. Journal of Mathematical Psychology, 49, 276–289.

Examples

>>> from adopy.tasks.cra import ModelLinear
>>> model = ModelLinear()
>>> model.task
Task('CRA', designs=['p_var', 'a_var', 'r_var', 'r_fix'], responses=[0, 1])
>>> model.params
['alpha', 'beta', 'gamma']

compute(p_var, a_var, r_var, r_fix, alpha, beta, gamma)

Compute the probability of choosing a certain response given values of design variables and model parameters.

Engine

class adopy.tasks.cra.EngineCRA(model, grid_design, grid_param)

Bases: adopy.base._engine.Engine

The Engine class for the CRA task. It can be only used for TaskCRA.