Package ‘pt’

Package ‘pt’July 2, 2014

Type Package

Title Computational models for prospect theory and other theories of risky decision making

Version 1.0

Author Gary Au

Date 2014-03-01

Maintainer Gary Au <[email protected]>

Description Implements (cumulative) prospect theory and othertheories of risky decision making. A practically unlimited number ofchoices can be specified. The package allows for different probabilityweighting functions and utility functions to be specified, as well as theirparameters. Other features include the ability to plot individualprobability weighting curves and families of these curves, as well asindividual utility function curves. Single-stage decision trees can bedrawn. The probability simplex can also be drawn. Certainty equivalents andrisk premiums can be plotted. Theoretical predictions for different riskydecision making theories can be compared against each other and empirical data.

License GPL-3

VignetteBuilder knitr

Suggests methods, grid, knitr, roxygen2

BugReports https://github.com/gary-au/pt/issues

NeedsCompilation no

Repository CRAN

Date/Publication 2014-03-10 17:23:31

1

https://github.com/gary-au/pt/issues

2 R topics documented:

R topics documented:pt-package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Choices-class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5choicesFromFile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5compareEU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7compareEV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8compareGDU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9comparePRT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10comparePT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12compareRAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13compareRDU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15compareSWAU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16compareSWU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18compareTAX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19compound_invariance_pwf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21constant_relative_sensitivity_pwf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22drawChoices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22drawSimplex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24exponential_power_pwf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27exponential_uf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28expo_power_uf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28general_linear_uf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29general_power_uf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30hyperbolic_logarithm_pwf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31kt_pwf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32linear_in_log_odds_pwf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32linear_pwf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33linear_uf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34logarithmic_uf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34neo_additive_pwf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35normalized_exponential_uf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36normalized_logarithmic_uf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36normalized_power_uf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37plotOneParProbWFam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38plotProbW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39plotRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40plotTwoParProbWFam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42plotUtility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43power_pwf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45power_uf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45ProbWeight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46ProbWeight-class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47quadratic_uf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48saveChoices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Utility-class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

pt-package 3

vsdChoices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Index 54

pt-package An R package for Prospect Theory

Description

A package for computational prospect theory (PT) and comparing PT to other risky decision makingtheories. Choice visualisation capabilities are also provided.

Details

The pt package provides the ability to create, save and visualise choices. The results for differentrisky decision making theories can be calculated for these choice situations.

The fastest way to get started is to either create choices directly from the command line usingthe Choices function or load in choices from previously prepared external text files using thechoicesFromFile function.

Once the choices are in R, it is possible to visualise them using drawChoices. Newly createdchoices can be saved to text files using saveChoices.

The predictions of various risky decision making theories can then be run on choices using thefollowing functions:

compareEV (for expected value)

compareEU (expected utility)

compareRDU (rank-dependent utility)

comparePT (prospect theory)

compareSWU (subjectively weighted utility)

compareSWAU (subjectively weighted average utility)

compareRAM (rank-affected multiplicative weights utility)

compareTAX ((special) transfer of attention exchange utility)

compareGDU ((lower) gains decomposition utility)

comparePRT (prospective reference theory utility)

Visualisation functions include:

drawChoices (draws choices)

drawSimplex (draws the Marschak-Machina unit probability simplex)

plotProbW (draws a single probability weighting function)

plotOneParProbWFam (draws families of one parameter probability weighting functions)

plotTwoParProbWFam (draws families of two parameter probability weighting functions)

plotRP (draws the risk premium)

plotUtility (draws the utility function)

4 Choices

Author(s)

Gary Au <[email protected]>

Maintainer: Gary Au <[email protected]>

Choices Create a new instance of a Choices class.

Description

Create choices using five vectors.

Usage

Choices(choice_ids, gamble_ids, outcome_ids, objective_consequences, probability_strings)

Arguments

choice_ids vector, contains the choice_id of each objective_consequence.

gamble_ids vector, contains the gamble_id of each objective_consequence.

outcome_ids vector, contains the outcome_id of each objective_consequence.objective_consequences

vector, contains the objective consequences.probability_strings

vector, contains the probability_string of each objective consequence.

Details

This function creates a new instance of a Choices class. The inputs are five vectors, representingthe properties of each outcome.

Examples

choice_ids <- c(1, 1, 1, 1, 1, 1, 1, 1)

gamble_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)

outcome_ids <- c(1, 2, 3, 4, 1, 2, 3, 4)

objective_consequences <- c(7, 7, 84, 90,7, 10, 90, 90)

probability_strings <- c("0.1", "0.3", "0.3", "0.3","0.1", "0.3", "0.3", "0.3")

my_choices <- Choices(choice_ids=choice_ids,gamble_ids=gamble_ids,outcome_ids=outcome_ids,

Choices-class 5

objective_consequences=objective_consequences,probability_strings=probability_strings)

my_choices

Choices-class The Choices class.

Description

The Choices class contains choices for a decision maker. Each choice contains gambles.

Slots

choices: Object of class "vector", containing Gambles objects for decision makers to choosefrom.

Note

A function (also called Choices) has been defined to create instances of this class from the commandline. Another function (called choicesFromFile) reads in data from external text files to createinstances of the class.

See Also

Choices,choicesFromFile

choicesFromFile Create an instance of a Choices class using data from an external textfile.

Description

Create an instance of a Choices class using data from an external text file.

Usage

choicesFromFile(input_file, choice_id_header, gamble_id_header,outcome_id_header, objective_consequence_header, probability_header, DELIMITER)

6 choicesFromFile

Arguments

input_file text, the input_file.choice_id_header

text, the column name of the choice_id variable.gamble_id_header

text, the column name of the gamble_id variable.outcome_id_header

text, the column name of the outcome_id variable.objective_consequence_header

text, the column name of the objective_consequence variable.probability_header,

the column name of the probability_string variable.

DELIMITER text, the delimeter character separating the fields in the input file.

Details

This function is used to create a new instance of a Choices class from an external text file. This filehas at least 5 columns, delimited by the DELIMITER character string. Each row of the file containsan individual outcome. The last line of the file needs to be a blank row. An example input filedescribing the Allais constant ratio paradox looks like this, with the DELIMITER being a "\t".

choice_id gamble_id outcome_id probability objective_consequence

1 1 1 1 3000

1 2 1 0.8 4000

1 2 2 0.2 0

2 1 1 0.25 3000

2 1 2 0.75 0

2 2 1 0.2 4000

2 2 2 0.8 0

——

Note that the last line is a blank row.

Examples

# This example loads up the choices for the Allais constant ratio paradox, which# are available as text files in the pt package.

my_input_file <- system.file("external", "allais_constant_ratio_paradox.txt", package="pt")

my_choices <- choicesFromFile(input_file=my_input_file,choice_id_header="choice_id",gamble_id_header="gamble_id",outcome_id_header="outcome_id",objective_consequence_header="objective_consequence",probability_header="probability",DELIMITER="\t")

compareEU 7

my_choices

compareEU Compare the expected utility (EU) of choice gambles.

Description

Compare the expected utility (EU) of choice gambles.

Usage

compareEU(object, utility, digits)

## S4 method for signature 'Choices'compareEU(object, utility, digits)

Arguments

object Choices, an instance of a Choices class.

utility Utility, an instance of a Utility class.

digits numeric, the number of digits to display in the output.

References

von Neumann, J., & Morgenstern, O. (1947). Theory of games and economic behavior (2nd ed.).Princeton, NJ: Princeton University Press.

Bernoulli, D. (1954). Exposition of a new theory on the measurement of risk. Econometrica, 22(1),23-36.

Bernoulli, D. (1738). Specimen theoriae novae de mensura sortis. Commentarii Academiae Scien-tiarum Imperialis Petropolitanae, 5, 175-192.

Examples

# This example creates the two Allais common consequence paradox choices,# and computes the EU for each gamble in the choices.

choice_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)

gamble_ids <- c(1, 1, 1, 2, 1, 1, 2, 2)

outcome_ids <- c(1, 2, 3, 1, 1, 2, 1, 2)



8 compareEV

my_choices <- Choices(choice_ids=choice_ids,gamble_ids=gamble_ids,outcome_ids=outcome_ids,objective_consequences=objective_consequences,probability_strings=probability_strings)

my_choices

my_utility <- Utility(fun="power",par=c(alpha=1.0, beta=1.0, lambda=1.0))

compareEU(my_choices, utility=my_utility, digits=4)

compareEV Compare the expected value (EV) of choice gambles.

Description

Compare the expected value (EV) of choice gambles.

Usage

compareEV(object, digits)

## S4 method for signature 'Choices'compareEV(object, digits)

Arguments



References

Montgomery, H., & Adelbratt, T. (1982). Gambling decisions and information about expectedvalue. Organizational Behavior and Human Performance, 29(1), 39-57.

Lichtenstein, S., Slovic, P., & Zink, D. (1969). Effect of instruction in expected value on optimalityof gambling decisions. Journal of Experimental Psychology, 79(2, Pt.1), 236-240.

Li, S. (2003). The role of Expected Value illustrated in decision-making under risk: Single-play vsmultiple-play. Journal of Risk Research, 6(2), 113-124.

Colbert, G., Murray, D., & Nieschwietz, R. (2009). The use of expected value in pricing judgments.Journal of Risk Research, 12(2), 199-208.

Yates, J. F. (1990). Judgment and decision making. Englewood Cliffs, NJ: Prentice Hall.

compareGDU 9

Examples

# This example creates the two Allais common consequence paradox choices,# and computes the EV for each gamble in the choices.

choice_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)

gamble_ids <- c(1, 1, 1, 2, 1, 1, 2, 2)

outcome_ids <- c(1, 2, 3, 1, 1, 2, 1, 2)




my_choices

compareEV(my_choices, digits=4)

compareGDU Compare choice gambles under Luce’s (2000) (Lower) Gains-decompositions utility (GDU) theory.

Description

Compare choice gambles under Luce’s (2000) (Lower) Gains-decompositions utility (GDU) theory.

Usage

compareGDU(object, prob_weight, utility, digits)

## S4 method for signature 'Choices'compareGDU(object, prob_weight, utility, digits)

Arguments


prob_weight ProbWeight, an instance of a ProbWeight class.



10 comparePRT

References

Luce, R. D. (2000). Utility of gains and losses: Measurement-theoretical and experimental ap-proaches. Mahwah, NJ: Lawrence Erlbaum Associates.

Examples

# This example creates the two Allais common consequence paradox choices,# and computes the GDU for each gamble in the choices.

choice_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)

gamble_ids <- c(1, 1, 1, 2, 1, 1, 2, 2)

outcome_ids <- c(1, 2, 3, 1, 1, 2, 1, 2)




my_choices

my_pwf <-ProbWeight(fun="compound_invariance",par=c(alpha=0.542, beta=1.382))

my_utility <- Utility(fun="power",par=c(alpha=1, beta=1, lambda=1))

compareGDU(my_choices,prob_weight=my_pwf,utility=my_utility,digits=4)

comparePRT Compare choice gambles under Viscusi’s (1989) Prospective referencetheory (PRT).

Description

Compare choice gambles under Viscusi’s (1989) Prospective reference theory (PRT).

comparePRT 11

Usage

comparePRT(object, utility, gamma, digits)

## S4 method for signature 'Choices'comparePRT(object, utility, gamma, digits)

Arguments



gamma numeric, the gamma parameter in Viscusi’s theory.


References

Viscusi, W. K. (1989). Prospective reference theory: Toward an explanation of the paradoxes.Journal of Risk and Uncertainty, 2(3), 235-263.

Examples

# This example creates the two Allais common consequence paradox choices,# and computes the PRT for each gamble in the choices.

choice_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)

gamble_ids <- c(1, 1, 1, 2, 1, 1, 2, 2)

outcome_ids <- c(1, 2, 3, 1, 1, 2, 1, 2)




my_choices

my_utility <- Utility(fun="power",par=c(alpha=0.631, beta=0.631, lambda=1))

gamma <- 0.676

comparePRT(my_choices,utility=my_utility,

12 comparePT

gamma=gamma,digits=4)

comparePT Compare choice gambles under Tversky and Kahneman’s (1992) (Cu-mulative) prospect theory (PT).

Description

Compare choice gambles under Tversky and Kahneman’s (1992) (Cumulative) prospect theory(PT).

Usage

comparePT(object, prob_weight_for_positive_outcomes,prob_weight_for_negative_outcomes, utility, digits)

## S4 method for signature 'Choices'comparePT(object, prob_weight_for_positive_outcomes,prob_weight_for_negative_outcomes, utility, digits)

Arguments

object Choices, an instance of a Choices class.prob_weight_for_positive_outcomes

ProbWeight, an instance of a ProbWeight class.prob_weight_for_negative_outcomes

ProbWeight, an instance of a ProbWeight class.



References

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

Wakker, P. P. (2010). Prospect theory: For risk and ambiguity. Cambridge, UK: Cambridge Uni-versity Press.

Examples

# This example creates the two Allais common consequence paradox choices,# and computes the PT for each gamble in the choices.

choice_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)

gamble_ids <- c(1, 1, 1, 2, 1, 1, 2, 2)

compareRAM 13

outcome_ids <- c(1, 2, 3, 1, 1, 2, 1, 2)




my_choices

tk_1992_utility <- Utility(fun="power",par=c(alpha=0.88, beta=0.88, lambda=2.25))

tk_1992_positive_probWeight <-ProbWeight(fun="Tversky_Kahneman_1992",par=c(alpha=0.61))

tk_1992_negative_probWeight <-ProbWeight(fun="Tversky_Kahneman_1992",par=c(alpha=0.69))

comparePT(my_choices,prob_weight_for_positive_outcomes=tk_1992_positive_probWeight,prob_weight_for_negative_outcomes=tk_1992_negative_probWeight,utility=tk_1992_utility,digits=4)

compareRAM Compare choice gambles under Birnbaum’s (2008) configural weightRAM theory.

Description

Compare choice gambles under Birnbaum’s (2008) configural weight RAM theory.

Usage

compareRAM(object, branch_weight_list, prob_weight, utility, digits)

## S4 method for signature 'Choices'

14 compareRAM

compareRAM(object, branch_weight_list, prob_weight, utility,digits)

Arguments

object Choices, an instance of a Choices class.branch_weight_list

list, a list of branch weighting vectors.




References

Birnbaum, M. H. (2008). New paradoxes of risky decision making. Psychological Review, 115(2),463-501.

Examples

# This example creates the two Allais common consequence paradox choices,# and computes the RAM for each gamble in the choices.

choice_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)

gamble_ids <- c(1, 1, 1, 2, 1, 1, 2, 2)

outcome_ids <- c(1, 2, 3, 1, 1, 2, 1, 2)




my_choices

# note that the maximum number of outcomes in the gambles is 3,# so branch weights for 3 outcomes need to be provided.

branch_weight_list <- list(c(1),c(0.3738, 0.6262),c(0.16, 0.33, 0.51))

my_utility <- Utility(fun="linear",par=c(lambda=1))

compareRDU 15

power_probability_weighting <-ProbWeight(fun="power",par=c(alpha=0.7, beta=1))

compareRAM(my_choices,branch_weight_list=branch_weight_list,prob_weight=power_probability_weighting,utility=my_utility,digits=4)

compareRDU Compare choice gambles under Quiggin’s (1993) Rank-dependentutility (RDU).

Description

Compare choice gambles under Quiggin’s (1993) Rank-dependent utility (RDU).

Usage

compareRDU(object, prob_weight, utility, digits)

## S4 method for signature 'Choices'compareRDU(object, prob_weight, utility, digits)

Arguments





References

Quiggin, J. (1982). A theory of anticipated utility. Journal of Economic Behavior & Organization,3(4), 323-343.

Quiggin, J. (1985). Subjective utility, anticipated utility, and the Allais paradox. OrganizationalBehavior and Human Decision Processes, 35(1), 94-101.

Quiggin, J. (1993). Generalized expected utility theory: The rank-dependent model. Boston, MA:Kluwer Academic Publishers.

16 compareSWAU

Examples

# This example creates the two Allais common consequence paradox choices,# and computes the RDU for each gamble in the choices.

choice_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)

gamble_ids <- c(1, 1, 1, 2, 1, 1, 2, 2)

outcome_ids <- c(1, 2, 3, 1, 1, 2, 1, 2)




my_choices


tk_1992_positive_probWeight <-ProbWeight(fun="Tversky_Kahneman_1992",par=c(alpha=0.61))

compareRDU(my_choices,prob_weight=tk_1992_positive_probWeight,utility=tk_1992_utility,digits=4)

compareSWAU Compare choices under Subjectively weighted average utility (SWAU).

Description

Compare choices under Subjectively weighted average utility (SWAU).

Usage

compareSWAU(object, prob_weight, utility, digits)

compareSWAU 17

## S4 method for signature 'Choices'compareSWAU(object, prob_weight, utility, digits)

Arguments





References

Karmarkar, U. S. (1978). Subjectively weighted utility: A descriptive extension of the expectedutility model. Organizational Behavior & Human Performance, 21(1), 61-72.

Karmarkar, U. S. (1979). Subjectively weighted utility and the Allais Paradox. OrganizationalBehavior & Human Performance, 24(1), 67-72.

Viscusi, W. K. (1989). Prospective reference theory: Toward an explanation of the paradoxes.Journal of Risk and Uncertainty, 2(3), 235-263.

Lattimore, P. K., Baker, J. R., & Witte, A. D. (1992). The influence of probability on risky choice:A parametric examination. Journal of Economic Behavior and Organization, 17(3), 377-400.

Birnbaum, M. H. (1999). The paradoxes of Allais, stochastic dominance, and decision weights. InJ. Shanteau, B. A. Mellers & D. A. Schum (Eds.), Decision science and technology: Reflections onthe contributions of Ward Edwards (pp. 27-52). Norwell, MA: Kluwer Academic Publishers.

Examples

# This example creates the two Allais common consequence paradox choices,# and computes the SWAU for each gamble in the choices.

choice_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)

gamble_ids <- c(1, 1, 1, 2, 1, 1, 2, 2)

outcome_ids <- c(1, 2, 3, 1, 1, 2, 1, 2)




my_choices

18 compareSWU


my_pwf <-ProbWeight(fun="linear_in_log_odds",par=c(alpha=0.4, beta=0.4))

compareSWAU(my_choices,prob_weight=my_pwf,utility=my_utility,digits=4)

compareSWU Compare choice gambles under Edwards’ (1954, 1962) SubjectiveWeighted Utility (SWU).

Description

Compare choice gambles under Edwards’ (1954, 1962) Subjective Weighted Utility (SWU).

Usage

compareSWU(object, prob_weight, utility, digits)

## S4 method for signature 'Choices'compareSWU(object, prob_weight, utility, digits)

Arguments





References

Edwards, W. (1954). The theory of decision making. Psychological Bulletin, 51(4), 380-417.

Edwards, W. (1962). Subjective probabilities inferred from decisions. Psychological Review, 69(2),109-135.

Birnbaum, M. H. (1999). The paradoxes of Allais, stochastic dominance, and decision weights. InJ. Shanteau, B. A. Mellers & D. A. Schum (Eds.), Decision science and technology: Reflections onthe contributions of Ward Edwards (pp. 27-52). Norwell, MA: Kluwer Academic Publishers.

compareTAX 19

Examples

# This example creates the two Allais common consequence paradox choices,# and computes the SWU for each gamble in the choices.

choice_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)

gamble_ids <- c(1, 1, 1, 2, 1, 1, 2, 2)

outcome_ids <- c(1, 2, 3, 1, 1, 2, 1, 2)




my_choices


my_pwf <-ProbWeight(fun="linear_in_log_odds",par=c(alpha=0.4, beta=0.4))

compareSWU(my_choices,prob_weight=my_pwf,utility=my_utility,digits=4)

compareTAX Compare choice gambles under Birnbaum’s (2008) configural weight(special) TAX theory.

Description

Compare choice gambles under Birnbaum’s (2008) configural weight (special) TAX theory.

Usage

compareTAX(object, prob_weight, utility, delta, digits)

## S4 method for signature 'Choices'compareTAX(object, prob_weight, utility, delta, digits)

20 compareTAX

Arguments




delta numeric, the delta parameter in Birnbaum’s TAX theory.


References


Examples

# This example creates the two Allais common consequence paradox choices,# and computes the TAX for each gamble in the choices.

choice_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)

gamble_ids <- c(1, 1, 1, 2, 1, 1, 2, 2)

outcome_ids <- c(1, 2, 3, 1, 1, 2, 1, 2)




my_choices

my_utility <- Utility(fun="linear",par=c(lambda=1))

power_probability_weighting <-ProbWeight(fun="power",par=c(alpha=0.7, beta=1))

compareTAX(my_choices,prob_weight=power_probability_weighting,utility=my_utility,delta=-1,digits=4)

compound_invariance_pwf 21

compound_invariance_pwf

The compound invariance probability weighting function.

Description

The compound invariance probability weighting function is given by

w(p) = (exp(-beta * (-log(x))âlpha)),

where p is the probability constrained by

w(0) = 0, w(1) = 1, 0 0, beta > 0.

Usage

compound_invariance_pwf(par, p)

Arguments

par vector, contains the alpha and beta parameters for the pwf

p numeric, the probability

References

Prelec, D. (1998). The probability weighting function. Econometrica, 60(3), 497-528.

al-Nowaihi, A., & Dhami, S. (2006). A simple derivation of Prelec’s probability weighting function.Journal of Mathematical Psychology, 50(6), 521-524.

p. 179, 207, Wakker, P. P. (2010). Prospect theory: For risk and ambiguity. Cambridge, UK:Cambridge University Press.

See Also

plotProbW, plotTwoParProbWFam

22 drawChoices

constant_relative_sensitivity_pwf

The constant relative sensitivity probability weighting function.

Description

Constant relative sensitivity probability weighting function is given by

w(p) = beta^(1-alpha)*pâlpha,


w(0) = 0, w(1) = 1, 0 0, 0 <= beta <= 1.

Usage

constant_relative_sensitivity_pwf(par, p)

Arguments

par vector, contains the alpha and beta parameters for the probability weightingfunction.


References

p. 52, Abdellaoui, M., L’Haridon, O., & Zank, H. (2010). Separating curvature and elevation: Aparametric probability weighting function. Journal of Risk and Uncertainty, 41(1), 39-65.

See Also


drawChoices Draw a one-stage decision tree.

Description

Draws choices.

drawChoices 23

Usage

drawChoices(choices, decision_square_x, decision_square_edge_length,circle_radius, y_split_gap, x_split_offset, probability_text_digits,y_probability_text_offset, y_value_text_offset, x_value_text_offset,probability_text_font_colour, probability_text_font_size,objective_consequence_text_font_colour, objective_consequence_text_font_size,label, label_font_colour, label_font_size, label_positions, line_positions,line_colours, line_styles, line_arrows, line_widths)

Arguments

choices, an instance of class Choicesdecision_square_x

numeric, the decision_square_x positiondecision_square_edge_length

numeric, the decision_square_edge_length

circle_radius numeric, the circle_radius

y_split_gap numeric, the vertical gap between outcomes

x_split_offset numeric, the horizontal gap between the decision square and decision circlesprobability_text_digits

numeric, the digits to use for probability texty_probability_text_offset

numeric, the y offset between an outcome line and the probability texty_value_text_offset

numeric, the vertical offset between an outcome line and the objective_consequencetext

x_value_text_offset

numeric, the horizontal offset between an outcome line and the objective_consequencetext

probability_text_font_colour

character, the colour of the probability_textprobability_text_font_size

numeric, the font size of the probability_textobjective_consequence_text_font_colour

character, the colour of the objective_consequence_textobjective_consequence_text_font_size

numeric, the font size of the objective_consequence_text_font_size

label vector, extra text labelslabel_font_colour

vector, label_font_colourlabel_font_size

vector, label_font_sizelabel_positions

list, a list of label coordinates of the form (x,y)

24 drawSimplex

line_positions list, a list of line coordinates of the form (x1,y1,x2,y2)

line_colours vector, line_colours

line_styles vector, line_styles

line_arrows vector, line_arrows

line_widths vector, line_widths

Examples

# This example creates the Allais common consequence paradox choices, and# draws them.

choice_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)gamble_ids <- c(1, 1, 1, 2, 1, 1, 2, 2)outcome_ids <- c(1, 2, 3, 1, 1, 2, 1, 2)objective_consequences <- c(2500, 2400, 0, 2400,2500, 0, 2400, 0)probability_strings <- c("0.33", "0.66", "0.01", "1.0","0.33", "0.67", "0.34", "0.66")my_choices <- Choices(choice_ids=choice_ids,gamble_ids=gamble_ids,outcome_ids=outcome_ids,objective_consequences=objective_consequences,probability_strings=probability_strings)my_choices

drawChoices(my_choices, decision_square_x=0.2, decision_square_edge_length=0.05,circle_radius=0.025, y_split_gap=0.1, x_split_offset=0.03,probability_text_digits=4, y_probability_text_offset=0.015,y_value_text_offset=0.005, x_value_text_offset=0.025,probability_text_font_colour="red", probability_text_font_size=11,objective_consequence_text_font_colour="blue",objective_consequence_text_font_size=11, label=c("A","B","C", "D"),label_font_colour=c("orange","magenta","green","blue"),label_font_size=c(11,11,11,11),label_positions=list(c(0.26,0.85),c(0.26,0.55),c(0.26,0.4),c(0.26,0.1)))

drawSimplex Draw the probability simplex.

Description

Draws the probability simplex.

drawSimplex 25

Usage

drawSimplex(x1, x2, x3, line_dot_density, draw_ev_flag, ev_colour, draw_pt_flag,alpha, beta, pt_colour, draw_utility_flag, utility, eu_colour, start_points,labels, label_positions, label_colours, label_font_sizes, label_font_faces,label_rotations, circle_radii, circle_outline_colours, circle_fill_colours,circle_positions, lines, line_widths, line_styles, line_colours, arrows,arrow_widths, arrow_styles, arrow_colours)

Arguments

x1 numeric, x1

x2 numeric, x2

x3 numeric, x3line_dot_density

numeric, the number of dots to use when drawing lines

draw_ev_flag logical, flag to tell whether to draw expected value indifference lines

ev_colour, the colour of the expected value indifference lines

draw_pt_flag logical, flag to tell whether to draw prospect theory indifference curves

alpha numeric, the alpha parameter in the linear_in_log_odds pwf

beta numeric, beta parameter in the linear_in_log_odds pwf

pt_colour character, the colour of the prospect theory indifference curvesdraw_utility_flag

logical, flag to tell whether to draw expected utility indifference lines

utility Utility, utility

eu_colour character, the colour of the expected utility indifference lines

start_points list, start_points for the family of indifference lines or curves

labels vector, a vector of text labelslabel_positions

vector, a vector of label_positions

label_colours vector, a vector of label_colourslabel_font_sizes

vector, a vector of label_font_sizeslabel_font_faces

vector, a vector of label_font_faceslabel_rotations

vector, a vector of label_rotations

circle_radii vector, a vector of circle_radiicircle_outline_colours

vector, a vector of circle_outline_colourscircle_fill_colours

vector, a vector of circle_fill_colourscircle_positions

vector, a vector of circle_positions

26 drawSimplex

lines vector, a vector of lines

line_widths vector, a vector of line_widths

line_styles vector, a vector of line_styles

line_colours vector, a vector of line_colours

arrows vector, a vector of arrows

arrow_widths vector, a vector of arrow_widths

arrow_styles vector, a vector of arrow_styles

arrow_colours vector, a vector of arrow_colours

Details

Iso-expected value lines, expected utility indifference lines and prospect theory indifference curves(based on a linear in log odds probability weighting function) can be drawn.

References

Marschak, J. (1950). Rational behavior, uncertain prospects, and measurable utility. Econometrica,18(2), 111-141.

Machina, M. J. (1987). Choice under uncertainty: Problems solved and unsolved. Journal ofEconomic Perspectives, 1(1), 121-154.

Examples

my_utility <- Utility(fun="power",par=c(alpha=0.88, beta=0.88, lambda=2.25))

drawSimplex(x1=0, x2=100, x3=200,line_dot_density=100,draw_ev_flag=TRUE, ev_colour="black",draw_pt_flag=TRUE, alpha=0.61, beta=0.724, pt_colour="red",draw_utility_flag=TRUE, utility=my_utility, eu_colour="purple",start_points=list(c(0.1,0.9),c(0.2,0.8),c(0.3,0.7),c(0.4,0.6),c(0.5,0.5),c(0.6,0.4),c(0.7,0.3),c(0.8,0.2),c(0.9,0.1)),labels=c("A","B","C","D","increasing preference"),label_positions=list(c(0.05,0.02),c(0.07,0.12),c(0.92,0.02),c(0.95,0.10),c(0.7,0.7)),label_colours=c("red","green","blue","orange","red"),label_font_sizes=c(12,12,12,12,16),label_font_faces=c("plain","plain","plain","plain","bold"),label_rotations=c(0,0,0,0,-45),circle_radii=c(0.005,0.005,0.005,0.005),circle_outline_colours=c("black","black","black","black"),circle_fill_colours=c("red","green","blue","orange"),circle_positions=list(c(0,0),c(0.01,0.1),c(0.89,0),c(0.9,0.1)),lines=list(c(0,0,0.01,0.1),c(0.89,0,0.9,0.1),c(0.01,0.1,0.9,0.1),c(0,0,0.89,0)),line_widths=c(1, 1, 1, 1),line_styles=c("dashed", "dashed", "dashed", "dashed"),line_colours=c("red","red","red","red"),

exponential_power_pwf 27

arrows=list(c(0.8,0.5,0.5,0.8)),arrow_widths=c(2),arrow_styles=c("solid"),arrow_colours=c("red"))

exponential_power_pwf The exponential-power probability weighting function.

Description

The exponential-power probability weighting function is given by

w(p) = exp(-alpha/beta * (1-p^beta))


w(0) = 0, w(1) = 1, 0 0.

Usage

exponential_power_pwf(par, p)

Arguments



References


p. 176, Luce, R. D. (2001). Reduction invariance and Prelec’s weighting functions. Journal ofMathematical Psychology, 45(1), 167-179.

Footnote 3, p. 105, Stott, H. P. (2006). Cumulative prospect theory’s functional menagerie. Journalof Risk and Uncertainty, 32(2), 101-130.

See Also


28 expo_power_uf

exponential_uf The exponential utility function.

Description

Exponential utility function is given by

U(oc) = 1 - exp(-alpha * oc), if alpha > 0,

U(oc) = oc, if alpha == 0, and

U(oc) = exp(-alpha * oc) - 1, if alpha < 0.

U is the utility and oc is the objective consequence of a gamble outcome. lambda is the loss aversioncoefficient. alpha is an index of concavity. This function is defined on the entire real line (seeWakker, p. 80).

Usage

exponential_uf(par, oc)

Arguments

par vector, parameter alpha for the utility function.

oc numeric, the objective consequence

References

p. 309 Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representa-tion of uncertainty. Journal of Risk and Uncertainty, 5(4), 297-323.

p. 466 Eqn. 2, 469, Birnbaum, M. H. (2008). New paradoxes of risky decision making. Psycholog-ical Review, 115(2), 463-501.

p. 80 Wakker, P. P. (2008). Explaining the characteristics of the power (CRRA) utility family.Health Economics, 17(12), 1329-1344.

expo_power_uf The expo-power utility function.

Description

The expo-power utility function is given by

U(oc) = gamma - exp(-beta * ocâlpha), if oc >= 0 and

U(oc) = -lambda * gamma - exp(-beta * (-oc)âlpha), if oc < 0.

U is the utility and oc is the objective consequence of a gamble outcome. lambda is the loss aversioncoefficient. The Tversky & Kahneman (1992) assumption has also been made, namely

U(-oc) = -lambda * U(oc) where oc >= 0.

general_linear_uf 29

Parameter restrictions from Saha (1993) are:

gamma > 1,

alpha != 0,

beta != 0, and

alpha * beta > 1.

Usage

expo_power_uf(par, oc)

Arguments

par vector, parameters alpha, beta, gamma and lambda for the utility function.


References

Saha, A. (1993). Expo-power utility: A ’flexible’ form for absolute and relative risk aversion.American Journal of Agricultural Economics, 75(4), 905-913.

Peel, D. A., & Zhang, J. (2009). The expo-power value function as a candidate for the work-horsespecification in parametric versions of cumulative prospect theory. Economics Letters, 105(3), 326-329.

general_linear_uf The general linear utility function.

Description

The general linear utility function is given by

U(oc) = alpha * oc, if oc >= 0 and

U(oc) = -lambda * (beta * -oc), if oc < 0.



Usage

general_linear_uf(par, oc)

Arguments

par vector, parameter lambda for the utility function.

oc numeric, the objective consequence.

30 general_power_uf

References



general_power_uf The general power utility function.

Description

The general power utility function is given by

U(oc) = beta * ocâlpha, if oc >= 0 and

U(oc) = -lambda * (delta * -oc)^gamma, if oc < 0.



Usage

general_power_uf(par, oc)

Arguments

par vector, parameters alpha, beta and lambda for the utility function.


References



hyperbolic_logarithm_pwf 31

hyperbolic_logarithm_pwf

The hyperbolic-logarithm probability weighting function.

Description

The hyperbolic-logarithm probability weighting function is given by

w(p) = (1 - alpha * log(p))^(-beta/alpha)


w(0) = 0, w(1) = 1, 0 0, beta > 0.

Usage

hyperbolic_logarithm_pwf(par, p)

Arguments



References


p. 176, Luce, R. D. (2001). Reduction invariance and Prelec’s weighting functions. Journal ofMathematical Psychology, 45(1), 167-179.

Footnote 3, p. 105, Stott, H. P. (2006). Cumulative prospect theory’s functional menagerie. Journalof Risk and Uncertainty, 32(2), 101-130.

See Also


32 linear_in_log_odds_pwf

kt_pwf The Tversky and Kahneman (1992) probability weighting function.

Description

Tversky and Kahneman’s (1992) probability weighting function is given by

w(p) = pâlpha / ((pâlpha + (1 - p)âlpha)^(1/alpha))


w(0) = 0, w(1) = 1, 0 = 0.28 as the function is not strictlyincreasing for alpha < 0.28.

Usage

kt_pwf(par, p)

Arguments

par vector, contains the alpha parameter for the pwf


References


p. 206, Wakker, P. P. (2010). Prospect theory: For risk and ambiguity. Cambridge, UK: CambridgeUniversity Press.

See Also

plotProbW, plotOneParProbWFam

linear_in_log_odds_pwf

The linear in log odds probability weighting function.

Description

The linear in log odds probability weighting function is given by

w(p) = beta * pâlpha / (beta * pâlpha + (1 - p)âlpha),


w(0) = 0, w(1) = 1, 0 < p < 1.

linear_pwf 33

Usage

linear_in_log_odds_pwf(par, p)

Arguments



References

p. 139, Gonzalez, R., & Wu, G. (1999). On the shape of the probability weighting function.Cognitive Psychology, 38, 129-166.

p. 208, Wakker, P. P. (2010). Prospect theory: For risk and ambiguity. Cambridge, UK: CambridgeUniversity Press.

See Also


linear_pwf The linear probability weighting function.

Description

Linear probability weighting function.

Usage

linear_pwf(p)

Arguments


See Also

plotProbW

34 logarithmic_uf

linear_uf The linear utility function.

Description

The linear utility function is given by

U(oc) = oc, if oc >= 0 and

U(oc) = -lambda * (-oc), if oc < 0.



Usage

linear_uf(par, oc)

Arguments

par vector, parameter lambda for the utility function.

oc numeric, the objective consequence.

References



logarithmic_uf The logarithmic utility function.

Description

The logarithmic utility function is given by

U(oc) = log(alpha + oc), if oc >= 0 and

U(oc) = -lambda * (log(beta + (-oc)), if oc < 0.



Usage

logarithmic_uf(par, oc)

neo_additive_pwf 35

Arguments

par vector, parameters alpha and lambda for the utility function.


neo_additive_pwf The neo-additive probability weighting function.

Description

The neo-additive probability weighting function is given by

w(p) = beta + alpha * p,


w(0) = 0, w(1) = 1, 0 = 0,

beta >= 0, and

alpha + beta <= 1.

Usage

neo_additive_pwf(par, p)

Arguments



References

Eqn. 7.2.5, p. 208-209 Wakker, P. P. (2010). Prospect theory: For risk and ambiguity. Cambridge,UK: Cambridge University Press.

See Also


36 normalized_logarithmic_uf

normalized_exponential_uf

The normalized exponential utility function.

Description

The normalized exponential utility function is given by

U(oc) = 1/alpha * (1 - exp(-alpha * oc)), if oc >= 0 and

U(oc) = -lambda/beta * (1-exp(-beta*(-oc))), if oc < 0.



Usage

normalized_exponential_uf(par, oc)

Arguments



References

Scholten, M., & Read, D. (2014). Prospect theory and the “forgotten" fourfold pattern of riskpreferences. Journal of Risk and Uncertainty, DOI 10.1007/s11166-014-9183-2.

normalized_logarithmic_uf

The normalized logarithmic utility function.

Description

The normalized logarithmic utility function is given by

U(oc) = log(1-alpha*x), if oc >= 0 and

U(oc) = -lambda/beta * log(1-alpha*x), if oc < 0.



Usage

normalized_logarithmic_uf(par, oc)

normalized_power_uf 37

Arguments



References



normalized_power_uf The normalized power utility function.

Description

The normalized power utility function is given by

U(oc) = ((1+alpha)*oc)^(1+alpha), if oc >= 0 and

U(oc) = -(-(1+beta)*oc/lambda)^(1+beta), if oc < 0.



Usage

normalized_power_uf(par, oc)

Arguments



References


38 plotOneParProbWFam

plotOneParProbWFam Plot a family of one parameter probability weighting functions.

Description

Plot a family of one parameter probability weighting functions using base graphics.

Usage

plotOneParProbWFam(my_title, my_title_colour, my_title_font_size, my_x_label,my_y_label, pwf, par, draw_reference_line_flag, reference_line_colour,reference_line_style, my_labels, my_label_positions, font_scaling,arrow_positions)

Arguments

my_title text, the titlemy_title_colour

text, the title colourmy_title_font_size

numeric, the title font size

my_x_label text, my_x_label

my_y_label text, the my_y_label

pwf function, the pwf

par vector, the pwf_parametersdraw_reference_line_flag

logical, draw_reference_line_flagreference_line_colour

text, reference_line_colourreference_line_style

text, reference_line_style

my_labels vector, labelsmy_label_positions

vector, the coordinates for the labels

font_scaling numeric, the scaling factor for the labelsarrow_positions

vector, the positions of arrow lines

References

p. 207, Fig. 7.2.1 from Wakker, P. P. (2010). Prospect theory: For risk and ambiguity. Cambridge,UK: Cambridge University Press.

plotProbW 39

Examples

plotOneParProbWFam(my_title="Tversky & Kahneman (1992) family",my_title_colour="black", my_title_font_size=4,my_x_label = "p", my_y_label = "w(p)", pwf=kt_pwf,par=c(0.3, 0.61, 0.8, 1.0, 1.3),draw_reference_line_flag=TRUE, reference_line_colour="red",reference_line_style="dotted",my_labels=c(expression(paste(alpha == 0.3)),expression(paste(alpha == 0.61)),expression(paste(alpha == 0.8)),expression(paste(alpha == 1.0)),expression(paste(alpha == 1.3)),expression(paste(w(italic(p)) == frac(italic(p)âlpha,(italic(p)âlpha + (1-italic(p))âlpha)^(1/alpha))))),my_label_positions=list(c(0.9,0.15),c(0.7,0.45),c(0.15,0.5),c(0.31,0.62),c(0.5,0.7),c(0.42, 0.9)),font_scaling=1.0,arrow_positions = list(c(0.3,0.5,0.39,0.41),c(0.42,0.58,0.52,0.51),c(0.59,0.66,0.66,0.66)))

plotProbW Plot a probability weighting function.

Description

Plot a probability weighting function using base graphics.

Usage

plotProbW(my_title, my_title_colour, my_title_font_size, my_x_label, my_y_label,pwf, par, draw_reference_line_flag, reference_line_colour,reference_line_style, my_labels, my_label_positions, font_scaling,arrow_positions)

Arguments








logical, draw_reference_line_flag

40 plotRP

reference_line_colour

text, reference_line_colourreference_line_style




font_scaling numeric, the scaling factor for the labelsarrow_positions


Examples

plotProbW(my_title=expression(paste("Kahneman & Tversky (1992), ",c==0.61)),my_title_colour="black", my_title_font_size=4,my_x_label = "p", my_y_label = "w(p)",pwf=kt_pwf, par=c(c=0.61),draw_reference_line_flag=TRUE, reference_line_colour="red",reference_line_style="dotted",my_labels=c(expression(paste(w(italic(p)) == frac(italic(p)^c,(italic(p)^c + (1-italic(p))^c)^(1/c))))),my_label_positions=list(c(0.4,0.8)),font_scaling=1.0)

plotRP Plot the risk premium.

Description

Plot the risk premium.

Usage

plotRP(my_title, my_title_colour, my_title_font_size, my_x_label, xmin, xmax,my_y_label, my_color, fun, par, ev, eu, ce, my_labels, my_label_colors,my_label_positions, font_scaling)

Arguments





plotRP 41

xmin numeric, the xmin

xmax numeric, the xmax


my_color text, the line color

fun function, the utility function

par vector, the uf_parameters

ev numeric, the expected value

eu numeric, the expected utility

ce numeric, the certainty equivalent

my_labels vector, text labelsmy_label_colors

vector, colors of the text labelsmy_label_positions

vector, positions of the text labels

font_scaling numeric, the scaling of the text labels

Examples

choice_ids <- c(1, 1, 1, 2, 2, 2, 2)

gamble_ids <- c(1, 1, 2, 1, 1, 2, 2)

outcome_ids <- c(1, 1, 2, 1, 2, 1, 2)

objective_consequences <- c(4000, 0, 3000,4000, 0, 3000, 0)

probability_strings <- c("0.8", "0.2", "1.0","0.2", "0.8", "0.25", "0.75")


my_choices

my_utility <- Utility(fun="power",par=c(alpha=0.88, beta=0.88, lambda=1))eu_df <- compareEU(my_choices, utility=my_utility, digits=4)eu_df

ev <- as.numeric(eu_df$ev[1])eu <- as.numeric(eu_df$eu[1])ce <- as.numeric(eu_df$ce[1])

plotRP(my_title = "risk premium",

42 plotTwoParProbWFam

my_title_colour="black",my_title_font_size=4,my_x_label = "objective consequence",my_y_label = "subjective value",xmin = 2500, xmax = 3500,my_color="violet",fun=power_uf,par=c(alpha=0.88, beta=0.88, lambda=1),ev=ev, eu=eu, ce=ce,my_labels=c(expression(paste(U(x)==xâlpha, ",", x>=0)),expression(paste(plain()==-lambda * (-x)^beta, ", ", x<0)),"ev","eu","ce","rp"),my_label_colors=c("violet","violet","black","red","orange","blue"),my_label_positions=list(c(2700,1275),c(2740,1250),c(3250,1075),c(2800,1170),c(3050,1075),c(3150,1170)),font_scaling=1)

plotTwoParProbWFam Plot a family of two parameter probability weighting functions.

Description

Plot a family of two parameter probability weighting functions using base graphics.

Usage

plotTwoParProbWFam(my_title, my_title_colour, my_title_font_size, my_x_label,my_y_label, pwf, par, draw_reference_line_flag, reference_line_colour,reference_line_style, my_labels, my_label_positions, font_scaling,arrow_positions)

Arguments








logical, draw_reference_line_flagreference_line_colour

text, reference_line_colour

plotUtility 43

reference_line_style




font_scaling numeric, the scaling factor for the labels

arrow_positions


References

p. 140, Fig. 4 from Gonzalez, R., & Wu, G. (1999). On the shape of the probability weightingfunction. Cognitive Psychology, 38, 129-166.

Examples

plotTwoParProbWFam(my_title=expression(paste("linear in log odds, ",gamma == 0.6)),my_title_colour="black", my_title_font_size=4,my_x_label = "p", my_y_label = "w(p)", pwf=linear_in_log_odds_pwf,par=list(a_list=c(0.6), b_list=seq(from=0.2, to=1.8, by=0.06)),draw_reference_line_flag=TRUE, reference_line_colour="red",reference_line_style="dotted",my_labels=c(expression(paste(delta == 0.2)),expression(paste(delta == 1.8)),expression(paste(w(italic(p)) == frac(delta * italic(p)^gamma,delta * italic(p)^gamma + (1-italic(p))^gamma)))),my_label_positions=list(c(0.7,0.09),c(0.2,0.6),c(0.42, 0.9)),font_scaling=1.0,arrow_positions = list(c(0.28,0.56,0.35,0.53),c(0.7,0.23,0.75,0.35)))

plotUtility Plot a utility function.

Description

Plot the utility function.

Usage

plotUtility(my_title, my_title_colour, my_title_font_size, my_x_label, xmin,xmax, my_y_label, fun, par, fun_colour, draw_reference_line_flag,reference_line_colour, reference_line_style, my_labels, my_label_positions,my_label_colours, my_label_font_sizes)

44 plotUtility

Arguments

my_title text, the title of the chart.

my_title_colour

text, the title colour.

my_title_font_size

numeric, the title font size.

my_x_label text, the x-axis label.

xmin numeric, the xmin on the x-axis.

xmax numeric, the xmax on the x-axis.

my_y_label text, the y-axis label.

fun Utility, an instance of the Utility class.

par vector, the parameters for the utility function.

fun_colour text, the colour of the utility function line.

draw_reference_line_flag

logical, a boolean flag determining whether or not to draw a y=x reference line.

reference_line_colour

text, the reference line colour.

reference_line_style

numeric, the reference line style.

my_labels vector, a vector of text labels to draw.

my_label_positions

list, a list of coordinates for the text labels.

my_label_colours

vector, stores the colours for each text label.

my_label_font_sizes

vector, stores the font size of each text label.

Examples

plotUtility(my_x_label = "objective consequence",my_y_label = "subjective value",xmin = -10, xmax = 10,fun=power_uf,par=c(alpha = 0.88, beta = 0.88, lambda = 2.25),fun_colour = "purple",draw_reference_line_flag = TRUE,reference_line_colour = "red",reference_line_style = 1)

power_pwf 45

power_pwf The power probability weighting function.

Description

The power probability weighting function is given by

w(p) = beta * pâlpha,


w(0) = 0, w(1) = 1, 0 < p < 1.

Usage

power_pwf(par, p)

Arguments



References

Stott, H. P. (2006). Cumulative prospect theory’s functional menagerie. Journal of Risk and Uncer-tainty, 32(2), 101-130.

See Also


power_uf The power utility function.

Description

The power utility function is given by

U(oc) = ocâlpha, if oc >= 0 and

U(oc) = -lambda * (-oc)^beta, if oc < 0.



Usage

power_uf(par, oc)

46 ProbWeight

Arguments



References



p. 1336 Wakker, P. P. (2008). Explaining the characteristics of the power (CRRA) utility family.Health Economics, 17(12), 1329-1344.

ProbWeight Create an instance of a ProbWeight class.

Description

Creates an instance of the ProbWeight class.

Usage

ProbWeight(fun, par)

Arguments

fun text, the probability function string

par vector, parameters for the probability function

Details

This function creates an instance of a ProbWeight class. The following functional forms are cur-rently implemented:

linear

Tversky_Kahneman_1992 (requires 1 parameter > 0.28)

linear_in_log_odds (requires 2 parameters)

power (requires 2 parameters)

neo_additive (requires 2 parameters)

hyperbolic_logarithm (requires 2 parameters)

exponential_power (requires 2 parameters)

compound_invariance (requires 2 parameters)

constant_relative_sensitivity (requires 2 parameters)

ProbWeight-class 47

References



Wu, G., & Gonzalez, R. (1996). Curvature of the probability weighting function. ManagementScience, 42(12), 1676-1690.



Examples

# This example creates a linear in log odds# probability weighting function.

linear_in_log_odds_prob_weight <-ProbWeight(fun="linear_in_log_odds",par=c(alpha=0.61, beta=0.724))

# These examples create the probability weighting functions# used by Tversky and Kahneman (1992).

tk_1992_positive_prob_weight <-ProbWeight(fun="Tversky_Kahneman_1992",par=c(alpha=0.61))

tk_1992_negative_prob_weight <-ProbWeight(fun="Tversky_Kahneman_1992",par=c(alpha=0.69))

ProbWeight-class The ProbWeight class.

Description

The ProbWeight class stores both the form and parameter specification for a probability weightingfunction.

Slots

fun: Object of class "text", containing a text string that specifies the functional form of the prob-ability weighting function.

par: Object of class "vector", containing the parameter specifications for the probability weight-ing function.

48 saveChoices

Note

A function (also called ProbWeight) has been defined to create an instance of this class.

See Also

ProbWeight

quadratic_uf The quadratic utility function.

Description

The quadratic utility function is given by

U(oc) = alpha * oc - oc^2, if oc >= 0 and

U(oc) = -lambda * (beta * (-oc) - (-oc)^2), if oc < 0.



Usage

quadratic_uf(par, oc)

Arguments



saveChoices Saves a Choices object to an external text file.

Description

Saves a Choices object to an external text file.

Usage

saveChoices(object, output_file, choice_id_header, gamble_id_header,outcome_id_header, probability_header, objective_consequence_header,DELIMITER)

## S4 method for signature 'Choices'saveChoices(object, output_file, choice_id_header,gamble_id_header, outcome_id_header, probability_header,objective_consequence_header, DELIMITER)

saveChoices 49

Arguments


output_file text, the output file for saving my_choices.choice_id_header

text, the column name for the choice_id field in the output file.gamble_id_header

text, the column name for the gamble_id field in the output file.outcome_id_header

text, the column name for the outcome_id field in the output file.probability_header

text, the column name for the probability field in the output file.objective_consequence_header

text, the column name for the objective_consequence field in the output file.

DELIMITER text, the delimiter character used to separate the columns in the output file.

Examples

# This example creates the two Allais common consequence paradox choices,# and saves them to an external text file.

choice_ids <- c(1, 1, 1, 1, 2, 2, 2, 2)

gamble_ids <- c(1, 1, 1, 2, 1, 1, 2, 2)

outcome_ids <- c(1, 2, 3, 1, 1, 2, 1, 2)




my_choices

my_output_file <- paste(tempdir(), "\\", "saved_choices.txt", sep="")

saveChoices(my_choices,output_file=my_output_file,choice_id_header="choice_id",gamble_id_header="gamble_id",outcome_id_header="outcome_id",probability_header="probability",objective_consequence_header="objective_consequence",

50 Utility

DELIMITER="\\t")

# after finishing with the file, delete to keep the workspace tidyunlink(my_output_file)# remove the object from the global environmentrm(my_output_file)

Utility Create an instance of a Utility class.

Description

This function creates an instance of a Utility class.

Usage

Utility(fun, par)

Arguments

fun text, a string selecting the utility function

par vector, parameters for the utility function

Details

This function creates an instance of a Utility class object. Two arguments need to be provided tocreate this object. The first argument is a text string that defines the functional form of a utilityfunction stored by the Utility class object. The second argument is a vector of parameters neededfor the selected utility function.

The following functional forms are currently implemented:

linear (requires 1 parameter)

power (requires 3 parameters)

exponential (requires 2 parameters)

normalized_exponential_uf (requires 3 parameters)

normalized_logarithmic_uf (requires 3 parameters)

normalized_power_uf (requires 3 parameters)

quadratic_uf (requires 3 parameters)

logarithmic_uf (requires 3 parameters)

expo_power_uf (requires 4 parameters)

general_linear_uf (requires 3 parameters)

general_power_uf (requires 5 parameters)

Utility-class 51

References





Examples

# This example creates the power utility function with parameters# used in the Tversky & Kahneman (1992) paper.


# This example creates a linear utility function.

my_linear_utility <- Utility(fun="linear",par=c(lambda=1))

Utility-class The Utility class.

Description

The Utility class stores both the functional form and parameter specifications for a utility function.

Slots

fun: Object of class "text", containing a text string that specifies the functional form of the utilityfunction.

par: Object of class "vector", containing the parameter specifications for the utility function.

Note

A wrapper function (also called Utility) can be used to create an instance of this class.

See Also

Utility

52 vsdChoices

vsdChoices Create choice situations that can elicit violations of (first-order)stochastic dominance in decision makers, using Birbaum’s (1997)recipe.

Description

Create choice situations that can elicit violations of (first-order) stochastic dominance in decisionmakers, using Birbaum’s (1997) recipe.

Usage

vsdChoices(x, y, p, q, x_plus, y_minus, r)

Arguments

x numeric, x is one of the objective consequences in the original binary gambleG0.

y numeric, y is the other objective consequences in the original binary gamble G0.

p text, p is a probability string associated with the objective consequence x.

q text, q is a probability string associated with the objective consequence y.

x_plus numeric, x_plus

y_minus numeric, y_minus

r numeric, r the g_minus probability offset

Details

Given a binary gamble G0, this function creates a pair of three outcome gambles G+ and G- and apair of four outcome gambles GS+, GS- that can elicit vsd behaviour in decision makers. e.g.

G0 = (96, 0.9; 12, 0.1)

G+ = (12, 0.05; 14, 0.05; 96, 0.9) and G- = (12, 0.1; 90, 0.05; 96, 0.85)

where G+ dominates G0 and G- is dominated by G0.

GS+ = (12, 0.05; 14, 0.05; 96, 0.05; 96, 0.85) and GS- = (12, 0.05; 12, 0.05; 90, 0.05; 96, 0.85)

References

Figure 5, p. 475 from Birnbaum, M. H. (2008). New paradoxes of risky decision making. Psycho-logical Review, 115(2), 463-501.

Birnbaum, M. H. (1997). Violations of monotonicity in judgment and decision making. In A.A. J. Marley (Ed.), Choice, decision, and measurement: Essays in honor of R. Duncan Luce (pp.73-100). Mahwah, NJ: Erlbaum.

vsdChoices 53

Examples

my_choices_list <- vsdChoices(x=12, y=96, p="0.1", q="0.9", x_plus=14, y_minus=90, r="0.05")

original_choice <- my_choices_list[[1]]

original_choice

pair_of_three_outcome_choices <- my_choices_list[[2]]

pair_of_three_outcome_choices

pair_of_four_outcome_choices <- my_choices_list[[3]]

pair_of_four_outcome_choices

Index

∗Topic packagept-package, 3

Choices, 3, 4, 5Choices-class, 5choicesFromFile, 3, 5, 5compareEU, 3, 7compareEU,Choices-method (compareEU), 7compareEV, 3, 8compareEV,Choices-method (compareEV), 8compareGDU, 3, 9compareGDU,Choices-method (compareGDU),

9comparePRT, 3, 10comparePRT,Choices-method (comparePRT),

10comparePT, 3, 12comparePT,Choices-method (comparePT), 12compareRAM, 3, 13compareRAM,Choices-method (compareRAM),

13compareRDU, 3, 15compareRDU,Choices-method (compareRDU),

15compareSWAU, 3, 16compareSWAU,Choices-method

(compareSWAU), 16compareSWU, 3, 18compareSWU,Choices-method (compareSWU),

18compareTAX, 3, 19compareTAX,Choices-method (compareTAX),

19compound_invariance_pwf, 21constant_relative_sensitivity_pwf, 22

drawChoices, 3, 22drawSimplex, 3, 24

expo_power_uf, 28

exponential_power_pwf, 27exponential_uf, 28

general_linear_uf, 29general_power_uf, 30

hyperbolic_logarithm_pwf, 31

kt_pwf, 32

linear_in_log_odds_pwf, 32linear_pwf, 33linear_uf, 34logarithmic_uf, 34

neo_additive_pwf, 35normalized_exponential_uf, 36normalized_logarithmic_uf, 36normalized_power_uf, 37

plotOneParProbWFam, 3, 32, 38plotProbW, 3, 21, 22, 27, 31–33, 35, 39, 45plotRP, 3, 40plotTwoParProbWFam, 3, 21, 22, 27, 31, 33,

35, 42, 45plotUtility, 3, 43power_pwf, 45power_uf, 45ProbWeight, 46, 48ProbWeight-class, 47pt (pt-package), 3pt-package, 3

quadratic_uf, 48

saveChoices, 3, 48saveChoices,Choices-method

(saveChoices), 48

Utility, 50, 51Utility-class, 51

vsdChoices, 52

54

Documents

Package ‘pt’