dual.valueMatrix: Returns a Value Matrix using two reference points

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

Description

This function is based on the value function of the dual reference point (dual-rp) models, as seen in reference 1 (Golman, Loewenstein). It first builds a desicion matrix for each user and then applys the 'utility function' over each value using two given reference points (SQ, G). It does so by calling the function smallerThanZero. The dual-rp utility function works in two steps, much like prospect theory's value function overallPV,pvMatrix See details and references.

Usage

dual.valueMatrix(dataset, userid = NULL, attr = NULL, rounds = NULL,
  cost_ids = NULL, dual.refps = NULL, lambda = 2.25, delta = 0.8,
  consumption_fun = NULL)

Arguments

dataset	data.frame with the user generated data from a product configurator. See decisionMatrix for specifications of the dataset.
userid	a vector of integers that gives the information of which users the matrix should be calculated. Vectorised.
attr	attributes IDs, vector of integer numbers corresponding to the attributes you desire to use; attr are assumed to be 1-indexed.
rounds	integer vector or text option. Which steps of the configuration process should be shown? Defaults are first and last step. Text options are all, first, last.
cost_ids	argument used to convert selected cost attributes into benefit attributes. Integer vector.
dual.refps	numeric matrix or vector - two numbers indicating the status-quo and the aspiration level(goal) for the given attributes. This function is an improvement over dualValueMatrix.oneAttr since it allows a matrix to be given through dual.refps. The matrix should have two columns, first column is the Status-Quo and the second should be the Goal. It should have as many rows as attributes, i.e. one set of reference points for each attribute.
lambda	numeric - parameter of loss aversion for the value function as given by reference[1]. Default value is 2.25 as in [2] and should be lambda > 1.
delta	numeric - expresses the relative importance of the aspiration level to other factors. Default is 0.8 and it should satisfy 0 < delta <1.
consumption_fun	non-working parameter for future developments. Leave at NULL.

Details

Note that since the dual-rp value function uses a logarithmic function, attribute values and reference points should be larger than zero. Nontheless, if this function detects a zero or negative value it will monotonically scale your data and your reference points so that for all values applies x > 0. The transformation does not have an impact on the absolute differences between attribute values and reference points.

This function is an improvement over dualValueMatrix.oneAttr since it allows a matrix to be given through dual.refps. The matrix should have two columns, first column is the Status-Quo and the second should be the Goal. It should have as many rows as attributes, i.e. one set of reference points for each attribute.

dataset We assume the input data.frame has following columns usid = User IDs, round = integers indicating which round the user is in (0-index works best for 'round'), atid = integer column for referring the attribute ID (1 indexed), selected = numeric value of the attribute for a specific, given round, selectable = amount of options the user can chose at a given round, with the current configuration.

userid is a necessary parameter, without it you'll get a warning. Default is NULL.

attr Default calculates with all attributes. Attributes are automatically read from provided dataset, it is important you always provide the complete data so that the package functions properly. Moreover, userid and attr will not be sorted and will appear in the order you input them.

rounds Default calculates with first and last rounds (initial and final product configuration). You can give a vector of arbitrarily chosen rounds as well.

cost_ids Default assumes all your attributes are of benefit type, that is a higher value in the attribute means the user is better off than with a lower value. If one or more of the attributes in your data is of cost type, e.g. price, so that lower is better then you should identify this attributes as such, providing their id, they'll be converted to benefit type (higher amount is better).

delta [1] Initially called alpha, we chose delta to avoid confusion with prospect theory's parameter for concavity, such as seen in overallPV

Note: When converting a cost attribute to a benefit attribute its two reference points change as well, enter the unconverted dual.refps, the function transforms them automatically when it detects a cost_ids != NULL. Also, since for cost attributes, lower is better, unconverted they should follow (G < SQ).

Value

a list of value matrices for each user.

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

#Not runnable yet
dualValueMatrix(pc_config_data, 9:10, dual.refps = c(1, 3.5))
dualValueMatrix(aDataFrame, userid = 100, rounds = "all", dual.refps = c(1, 2))
dualValueMatrix(myData, userid = 11, attr =  1, cost_ids = 1, dual.refps = c(8, 2)) # Note that for cost attributes:  SQ > G
dualValueMatrix(data1, 2) # Returns an error since no reference points given

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