eviSimulation: Expected Value of Information (EVI) Simulation.

Description

The Expected Value of Information (EVI) is calculated based on a Monte Carlo simulation of the expected welfare (or values or benefits) of two different decision alternatives. The expected welfare is calculated for the current estimate of variables determining welfare and a prospective estimate of these variables. The prospective estimate resembles an improvement in information.

Usage

eviSimulation(
  welfare,
  currentEstimate,
  prospectiveEstimate,
  numberOfModelRuns,
  randomMethod = "calculate",
  functionSyntax = "data.frameNames",
  relativeTolerance = 0.05,
  verbosity = 0
)

Value

An object of class eviSimulation with the following elements:

$current: welfareDecisionAnalysis object for currentEstimate
$prospective: welfareDecisionAnalysis object for single prospectiveEstimate or a list of welfareDecisionAnalysis objects for prospectiveEstimate being a list of estimates.
$evi: Expected Value of Information(s) (EVI)(s) gained by the prospective estimate(s) w.r.t. the current estimate.

Arguments

welfare: either a function or a list with two functions, i.e. list(p1,p2). In the first case the function is the net benefit (or welfare) of project approval (PA) vs. the status quo (SQ). In the second case the element p1 is the function valuing the first project and the element p2 valuing the second project, viz. the welfare function of p1 and p2 respectively.
currentEstimate: estimate: describing the distribution of the input variables as currently being estimated.
prospectiveEstimate: estimate or list of estimate objects: describing the prospective distribution of the input variables which could hypothetically be achieved by collecting more information, viz. improving the measurement.
numberOfModelRuns: integer: The number of running the welfare model for the underlying Monte Carlo simulation.
randomMethod: character: The method to be used to sample the distribution representing the input estimate. For details see option method in random.estimate.
functionSyntax: character: function syntax used in the welfare function(s). For details see mcSimulation.
relativeTolerance: numeric: the relative tolerance level of deviation of the generated confidence interval from the specified interval. If this deviation is greater than relativeTolerance a warning is given.
verbosity: integer: if 0 the function is silent; the larger the value the more verbose is output information.

Details

The Expected Value of Information (EVI)

The Expected Value of Information is the decrease in the $\textrm{EOL}$ for an information improvement from the current ($\rho_X^{current}$) to a better prospective (hypothetical) information ($\rho_X^{prospective}$): $$ \textrm{EVI} := \textrm{EOL}(\rho_X^{current}) - \textrm{EOL}(\rho_X^{prospective}). $$

References

Hubbard, Douglas W., How to Measure Anything? - Finding the Value of "Intangibles" in Business, John Wiley & Sons, Hoboken, New Jersey, 2014, 3rd Ed, https://www.howtomeasureanything.com/.

Gravelle, Hugh and Ray Rees, Microeconomics, Pearson Education Limited, 3rd edition, 2004.

Examples

Run this code

#############################################################
# Example 1 Only one prospective estimate:
#############################################################
numberOfModelRuns=10000
# Create the estimate object:
variable=c("revenue","costs")
distribution=c("posnorm","posnorm")
lower=c(10000,  5000)
upper=c(100000, 50000)
currentEstimate<-as.estimate(variable, distribution, lower, upper)
prospectiveEstimate<-currentEstimate
revenueConst<-mean(c(currentEstimate$marginal["revenue","lower"],
                     currentEstimate$marginal["revenue","upper"]))
prospectiveEstimate$marginal["revenue","distribution"]<-"const"
prospectiveEstimate$marginal["revenue","lower"]<-revenueConst 
prospectiveEstimate$marginal["revenue","upper"]<-revenueConst 
# (a) Define the welfare function without name for the return value:
profit<-function(x){
	x$revenue-x$costs
}

# Calculate the Expected Value of Information:
eviSimulationResult<-eviSimulation(welfare=profit,
                                   currentEstimate=currentEstimate,
                                   prospectiveEstimate=prospectiveEstimate,
                                   numberOfModelRuns=numberOfModelRuns,
                                   functionSyntax="data.frameNames")
# Show the simulation results:
print(summary(eviSimulationResult))
#############################################################
# (b) Define the welfare function with a name for the return value:
profit<-function(x){
	list(Profit=x$revenue-x$costs)
}
# Calculate the Expected Value of Information:
eviSimulationResult<-eviSimulation(welfare=profit,
                                   currentEstimate=currentEstimate,
                                   prospectiveEstimate=prospectiveEstimate,
                                   numberOfModelRuns=numberOfModelRuns,
                                   functionSyntax="data.frameNames")
# Show the simulation results:
print(summary((eviSimulationResult)))
#############################################################
# (c) Two decision variables:
decisionModel<-function(x){
 list(Profit=x$revenue-x$costs,
      Costs=-x$costs)
}
# Calculate the Expected Value of Information:
eviSimulationResult<-eviSimulation(welfare=decisionModel,
                                   currentEstimate=currentEstimate,
                                   prospectiveEstimate=prospectiveEstimate,
                                   numberOfModelRuns=numberOfModelRuns,
                                   functionSyntax="data.frameNames")
# Show the simulation results:
print(summary((eviSimulationResult)))
#############################################################
# Example 2 A list of prospective estimates:
#############################################################
numberOfModelRuns=10000
#  Define the welfare function with a name for the return value:
profit<-function(x){
 list(Profit=x$revenue-x$costs)
}
# Create the estimate object:
variable=c("revenue","costs")
distribution=c("posnorm","posnorm")
lower=c(10000,  5000)
upper=c(100000, 50000)
currentEstimate<-as.estimate(variable, distribution, lower, upper)
perfectInformationRevenue<-currentEstimate
revenueConst<-mean(c(currentEstimate$marginal["revenue","lower"],
                     currentEstimate$marginal["revenue","upper"]))
perfectInformationRevenue$marginal["revenue","distribution"]<-"const"
perfectInformationRevenue$marginal["revenue","lower"]<-revenueConst 
perfectInformationRevenue$marginal["revenue","upper"]<-revenueConst
# (a) A list with one element
prospectiveEstimate<-list(perfectInformationRevenue=perfectInformationRevenue)
# Calculate the Expected Value of Information:
eviSimulationResult<-eviSimulation(welfare=profit,
                                   currentEstimate=currentEstimate,
                                   prospectiveEstimate=prospectiveEstimate,
                                   numberOfModelRuns=numberOfModelRuns,
                                   functionSyntax="data.frameNames")
# Show the simulation results:
print(summary(eviSimulationResult))
#############################################################
# (b) A list with two elements
perfectInformationCosts<-currentEstimate
costsConst<-mean(c(currentEstimate$marginal["costs","lower"], 
                   currentEstimate$marginal["costs","upper"]))
perfectInformationCosts$marginal["costs","distribution"]<-"const"
perfectInformationCosts$marginal["costs","lower"]<-costsConst 
perfectInformationCosts$marginal["costs","upper"]<-costsConst
prospectiveEstimate<-list(perfectInformationRevenue=perfectInformationRevenue,
                          perfectInformationCosts=perfectInformationCosts)
# Calculate the Expected Value of Information:
eviSimulationResult<-eviSimulation(welfare=profit,
                                   currentEstimate=currentEstimate,
                                   prospectiveEstimate=prospectiveEstimate,
                                   numberOfModelRuns=numberOfModelRuns,
                                   functionSyntax="data.frameNames")
# Show the simulation results:
print(summary(eviSimulationResult))
#############################################################
# Example 3 A list of prospective estimates and two decision variables:
#############################################################
numberOfModelRuns=10000
# Create the current estimate object:
variable=c("revenue","costs")
distribution=c("posnorm","posnorm")
lower=c(10000,  5000)
upper=c(100000, 50000)
currentEstimate<-as.estimate(variable, distribution, lower, upper)
# Create a list of two prospective estimates:
perfectInformationRevenue<-currentEstimate
revenueConst<-mean(c(currentEstimate$marginal["revenue","lower"],
                     currentEstimate$marginal["revenue","upper"]))
perfectInformationRevenue$marginal["revenue","distribution"]<-"const"
perfectInformationRevenue$marginal["revenue","lower"]<-revenueConst 
perfectInformationRevenue$marginal["revenue","upper"]<-revenueConst
perfectInformationCosts<-currentEstimate
costsConst<-mean(c(currentEstimate$marginal["costs","lower"], 
                   currentEstimate$marginal["costs","upper"]))
perfectInformationCosts$marginal["costs","distribution"]<-"const"
perfectInformationCosts$marginal["costs","lower"]<-costsConst 
perfectInformationCosts$marginal["costs","upper"]<-costsConst
prospectiveEstimate<-list(perfectInformationRevenue=perfectInformationRevenue,
                          perfectInformationCosts=perfectInformationCosts)
# Define the welfare function with two decision variables:
decisionModel<-function(x){
 list(Profit=x$revenue-x$costs,
      Costs=-x$costs)
}
# Calculate the Expected Value of Information:
eviSimulationResult<-eviSimulation(welfare=decisionModel,
                                   currentEstimate=currentEstimate,
                                   prospectiveEstimate=prospectiveEstimate,
                                   numberOfModelRuns=numberOfModelRuns,
                                   functionSyntax="data.frameNames")
# Show the simulation results:
print(sort(summary(eviSimulationResult)),decreasing=TRUE,along="Profit")

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