smallerThanZero: Outputs a value matrix from a decision matrix

In avilesd/productConfig: Tools to analyze behavioral patterns from Product Configurators

Description

This function is called within dualValueMatrix, but it is the function that actually does the work of producing the value matrix.It works in three steps. The first step checks if the matrix or the reference points have a value smaller or equal to 0. If this is the case it monotonically scales all values so that they are all larger than zero*. The second step calculates a gain-loss matrix using both reference points and a function given by [1]. The third step normalizes the gain-loss matrix to make all attributes comparable.

Usage

smallerThanZero(aMatrix, dual.refps, lambda = 2.25, delta = 0.8)

Arguments

aMatrix	the decision matrix, with attr as columns and rounds as rows.
dual.refps	two numeric reference points (status-quo, goal).
lambda	numeric - parameter of loss aversion for the value function as given by reference[1]. Default value is 2.25 as given by [2].
delta	numeric - expresses the relative importance of the aspiration level to other factors. Default is 0.8 and it should satisfy 0 < delta <1.

Details

*The transformation changes all values, but keeps the differences between them as they were.

Value

a value matrix with equal dimensions as the input aMatrix

References

[1] Golman, R., & Loewenstein, G. (2011). Explaining Nonconvex Preferences with Aspirational and Status Quo Reference Dependence. Mimeo, Carnegie Mellon University.

[2] Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and uncertainty, 5(4), 297-323.

Examples

#Runnable
smallerThanZero(matrix(16:31, 4, 4), dual.refps= c(22, 28))
smallerThanZero(matrix(16:31, 4, 4), dual.refps= c(22, 28), delta= 0.6)
smallerThanZero(matrix(1:100, 5, 20, byrow= T), dual.refps= c(sq=45, g=88))

#Not runnable yet
smallerThanZero <- function(decisionMatrix(myData, 9, rounds="all"), c(1.5, 2.5), lambda = 5, delta = 0.8)

avilesd/productConfig documentation built on May 11, 2019, 4:08 p.m.