PS918: Psychological Models of Choice
Modeling Asignment
The Data
Thirty participants each made 180 choices to give a data file with one row for each of 5,400
choices. Each row is for a choice betwen "a p1 chance of x1 otherwise a (1-p1) chance of y1" vs "a
p2 chance of x2 otherwise a (1-p2) chance of y2". Here are the first few rows of the data file:
subject choice
pair
p1 x1 y1 p2 x2 y2 choice EV1 EV2
1 1 0.29 88 78 0.29 53 91 0 80.9 79.98
1 2 0.82 26 34 0.49 18 31 1 27.44 24.63
1 3 0.59 31 63 0.89 92 20 0 44.12 84.08
For example, the second choice is betwen "an 82% chance of winning 26 otherwise an 18% chance
of winning 34" and a "49% chance of winning 18 otherwise a 51% chance of winning 31".
The choice column indicates the participants' decisions, with 1 indicating a choice of the gamble
"p1 chance of x1 otherwise a (1-p1) chance of y1" and 0 indicating a choice of the gamble "p2
chance of x2 otherwise a (1-p2) chance of y2".
The Modeling
Use a simplified version of cumulative prospect theory (CPT, Tversky & Kahneman, 1992).
Specificaly asume b=α in Equation 5, and δ=γ in Equation 6. Asume a softmax function.
1. For each participant, estimate the best-fiting values for value function curvature α, loss aversion
λ, probability weighting curvature γ, and the inverse temperature parameter in the softmax equation.
Report these values for each individual in a table. Do we se "clasic" prospect-theory behaviour
with risk aversion, loss aversion, and overweighting of smal probabilities and under-weighting of
large probabilities?
2. For each participant, is the extra complexity in CPT necesary compared to a simpler model with
no loss aversion and no probability weighting? HINT: Use a likelihood ratio test.
3. Make scater plots for each pairing of parameters, with dots for each participant. You'll se that
parameters are correlated over participants. For example, the curvature of the utility function
correlates with the softmax inverse temperature parameter. Why is this? How might the model be
altered to avoid this problem?
The Coding
Implement the models in either R or Matlab. Think about how best to represent risky choices in the
language you choose, and think about the best way to expres the psychology in code. Credit wil be
given for producing readable, simple, and clear code. Write the model as a function to which the
choice atributes and model parameters are pased. The function should return choice probabilities.
The example from Wek 5 shows how to do this for a Fechner expected utility model.
The Report
Your report should include a brief description of the model as it would appear, for example, in a
modeling paper comparing the fits of several models (e.g., Glöckner & Pachur, 2012). It should be
sufficient for someone to be able to replicate your calculations and to give a brief intuition about the
psychology involved. You should take care to explain the answers to the thre modeling questions
above and explain what these answers mean in terms of the psychology of the model.
Include the source code as an appendix in your report. Be sure to include comments in your code,
explaining how the code relates to your description. The code should be runnable as a complete,
stand-alone script. That is, I should be able to copy and paste your code into R or Matlab in one
chunk and have it reproduce your analysis.
The main body of your report, excluding the source code, should be fewer than 3,000 words. A
good report might be much shorter.
References
Glöckner, A., & Pachur, T. (2012). Cognitive models of risky choice: Parameter stability and
predictive acuracy of prospect theory. Cognition, 123, 21–32.
Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of
uncertainty. Journal of Risk and Uncertainty, 5, 297–323.
Marking Guidelines
Papers wil be asesed along the following criteria:
- Correctnes of solutions.
- Quality of answers to thre questions.
- Completenes, clarity, and concision of
- Background and context
- Model description and details
- Results, including visuals (Figures and Tables)
- Discussion of implications and limitations
- Simple, Readable Code
Marking Scale
95: Perfect paper. Correct answers. Clearly writen. No mistakes. Answers that go beyond the
question in sensible and creative ways, including possibly novel analysis or analytic techniques.
85: Near-perfect paper. Al answers correct. Some creative additions beyond the question. Minor
omisions only.
75: Excelent paper. Al answers correct. Some mild clarity or conceptual isues.
67: Very good paper. Almost al correct, but some significant erors. Some clarity isues and often
limited context and analysis.
62: Good paper. Mostly correct, but several erors. Some significant clarity isues with some
important mising details and very limited context and analysis
57: Fair paper. Mix of correct and incorect answers. Several smal to significant isues in
implementing and/or presenting the model and results.
52: Passable paper. Some correct answers, but multiple key erors in answering the questions and
executing the modeling works. Limited clarity and mising important details.
45: Poor paper. Answers mostly incorrect or irelevant. Hard to read with confusing or incorrect
background, model exposition, and results.
35: Very poor paper. Almost no correct or relevant information. Failed to answer the core
questions. Litle to no evidence of engagement with the asigned task.