discounting: Temporal discounting models to understand affect dynamics

This project revolves around the comparison of several temporal discounting models when applied to affect, following up on the call for such a comparison mentioned in Vanhasbroeck et al. (2024). The code within this project combines the structure of an R package alongside scripts that call upon the functions used within that package, providing its own ecosystem in which functions evolve together with our research purposes. While in-principle the discounting package can be used by others, it is not necessarily meant to and may, therefore, feel user-unfriendly.

Installation

To install the package and use its functions, one can use the remotes package:

remotes::intall_github("ndpvh/discounting-affect")

One can then call the library() function to load the package’s functions:

library(discounting)

Getting Started

Most of the package’s functionality depends on the definition of an instance of a model, namely of the exponential discounting model (exponential(); Samuelson, 1937, Rutledge et al., 2014), the quasi-hyperbolic discounting model (quasi_hyperbolic(); Laibson, 1997), or the double-exponential discounting model (double_exponential(); van den Bos & McClure, 2013). For example, we can create a one-dimensional exponential discounting model as follows:

my_model <- exponential(
  parameters = list(
      "alpha" = 1, 
      "beta" = as.matrix(1),
      "gamma" = as.matrix(0.5)
  ),
  covariance = as.matrix(1)
)
my_model
#> Model of class "exponential":
#> 
#> Dimension: 1
#> Number of predictors: 1
#> Number of parameters: 4
#> 
#> Parameters:
#>   alpha: |  1.00  |
#> 
#>   beta: | 1.00 |
#> 
#>   gamma: | 0.50 |
#> 
#> 
#> Covariance: | 1.00 |

Simulating from this model can be achieved through the simulate() function:

data <- simulate(
  my_model,
  X = runif(100, min = -1, max = 1)
)
data
#> An object of class "dataset"
#> 
#> Slot "Y": 100x1matrix
#>             [,1]
#> [1,]  0.06461276
#> [2,]  1.36331527
#> [3,]  0.38434100
#> [4,]  0.58480309
#> [5,]  1.23406025
#> [6,] -0.40797861
#> 
#> Slot "X": 100x1matrix
#>             [,1]
#> [1,] -0.19391610
#> [2,] -0.34337644
#> [3,] -0.96389265
#> [4,]  0.25205182
#> [5,]  0.92311981
#> [6,]  0.03515012

To estimate parameters of a model based on observed data, we have to transform our dataset to an instance of the dataset class and can then call the function fit() for a particular instance of the models denoted above:

# Define the model you wish to fit
fit_model <- quasi_hyperbolic(d = 1, k = 1)

# Fit the model to the previously simulated data
result <- fit(
  fit_model,
  data,
  trace = FALSE
)
result$model 
#> Model of class "quasi_hyperbolic":
#> 
#> Dimension: 1
#> Number of predictors: 1
#> Number of parameters: 5
#> 
#> Parameters:
#>   alpha: |  0.9929598  |
#> 
#>   beta: | 0.9340197 |
#> 
#>   nu: | 0.8361718 |
#> 
#>   kappa: | 0.4134251 |
#> 
#> 
#> Covariance: | 0.8733049 |

Analyses

For those who wish to reproduce or otherwise inspect our analyses, they can find the analysis scripts in the folder scripts. Currently, we provide the following analyses:

• recovery.R: Recovery study, providing a sanity check of being able to estimate the models provided by the package.

Further Reading

One can consult the package’s vignettes for more information on the project, the models, and the package.

References

Laibson, D. (1997). Golden eggs and hyperbolic discounting. The Quarterly Journal of Economics, 112(2), 443-477.

Samuelson, P. A. (1937). A note on measurement of utility. The Review of Economic Studies, 4(2), 155-161.

Rutledge, R. B., Skandali, N., Dayan, P., & Dolan, R. J. (2014). A computational and neural model of momentary subjective well-being. Proceedings of the National Academy of Sciences of the United States of America, 111(33), 12252–12257. doi: 10.1073/pnas.1407535111

van den Bos, W. & McClure, S. M. (2013). Towards a general model of temporal discounting. Journal of the Experimental Analysis of Behavior, 99, 58–73. doi: 10.1002/jeab.6

Vanhasbroeck, N., Loossens, T., & Tuerlinckx, F. (2024). Two peas in a pod: Discounting models as a special case of the VARMAX. Journal of Mathematical Psychology, Article 102856. doi: 10.1016/j.jmp.2024.102856