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.

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

discounting: Temporal discounting models to understand affect dynamics

Installation

Getting Started

Analyses

Further Reading

References