kristrom: The Kristr\"om's nonparametric approach to analyze...
In DCchoice: Analyzing Dichotomous Choice Contingent Valuation Data

Description Usage Arguments Details Value References See Also Examples

This function analyzes single-bounded dichotomous choice contingent valuation (CV) data on the basis of the Kristr\"om's nonparametric method.

kristrom(formula, data, subset)

## S3 method for class 'kristrom'
print(x, digits = 4, ...)

`formula`	a formula specifying the model structure.
`data`	a data frame containing the variables in the model formula.
`subset`	an optional vector specifying a subset of observations.
`x`	an object of class `"kristrom"`.
`digits`	a number of digits to display.
`...`	optional arguments. Currently not in use.

The function kristrom() analyzes single-bounded dichotomous choice contingent valuation (CV) data on the basis of Kristr\"om's nonparametric method (Kristr\"om 1990).

The argument formula defines the response variables and bid variables. The argument data is set as a data frame containing the variables in the model.

A typical structure of the formula for kristrom() is defined as follows:

R1 ~ BD1

The formula consists of two parts. The first part, the left-hand side of the tilde sign (~), must contain the response variable (e.g., R1) for the suggested prices in the CV questions. The response variable contains "Yes" or "No" to the bid or 1 for "Yes" and 0 for "No". The other part, which starts after the tilde sign, must contain a bid variable (e.g., BD1) containing suggested prices in the CV question.

The structure of data set which assigned to the argument data is the same as that in case of dbchoice(). See dbchoice for details in the data set structure.

The function kristrom() returns an object of S3 class "kristrom". An object of "kristrom" is a list with the following components.

`tab.dat`	a matrix describing the number of respondents who answered `"yes"` to CV question, total number of respondents, and ratio of respondents who answered `"yes"` among the total number of respondents for each value of the suggested bids.
`M`	the number of rows of `tab.dat`.
`adj.p`	a vector describing the probability of a yes-answer to the suggested bid, which is the same as the last column of `tab.dat`.
`nobs`	the number of observations.
`unq.bid`	a vector of the unique bids.
`estimates`	a matrix of the estimated Kristr\"om's survival probabilities.

The generic function print() is available for fitted model object of class "kristrom" and displays the estimated Kristr\"om's survival probabilities.

The extractor function summary() is used to display the estimated Kristr\"om's survival probabilities as well as three types of WTP estimates (Kaplan-Meier and Spearman-Karber mean, and median estimates). Note that the Spearman-Karber mean estimate is computed upto the X-intercept.

A graph of the estimated empirical survival function is depicted by plot(). See plot.kristrom for details.

turnbull.sb is an alternative nonparametric method for analyzing single-bounded dichotomous choice data. A parametric analysis can be done by sbchoice.

Croissant Y (2011). Ecdat: Data Sets for Econometrics, R package version 0.1-6.1, http://CRAN.R-project.org/package=Ecdat.

Kristr\"om B (1990). “A Non-Parametric Approach to the Estimation of Welfare Measures in Discrete Response Valuation Studies.” Land Economics, 66(2), 135–139.

plot.kristrom, NaturalPark, turnbull.sb, sbchoice

## Examples for kristrom() are also based on a data set NaturalPark in the package 
## Ecdat (Croissant 2011): so see the section Examples in the dbchoice() for details.
data(NaturalPark, package = "Ecdat")

## The variable answers are converted into a format that is suitable for the function 
## kristrom() as follows:
NaturalPark$R1 <- ifelse(substr(NaturalPark$answers, 1, 1) == "y", 1, 0)

## The formula is defined as follows:
fmks <- R1 ~ bid1

## The function kristrom() with the function fmks and the data frame NP 
## is executed as follows:
NPks <- kristrom(fmks, data = NaturalPark)
NPks
NPkss <- summary(NPks)
NPkss
plot(NPks)

Loading required package: MASS
Loading required package: interval
Loading required package: survival
Loading required package: perm
Loading required package: Icens
Loading required package: MLEcens
Loading required package: Formula

Probability: 
  Upper  Prob.
1     0 1.0000
2     6 0.6579
3    12 0.5584
4    24 0.5122
5    48 0.4675
6   Inf 0.0000
Survival probability: 
   Upper   Prob.
1      0  1.0000
2      6  0.6579
3     12  0.5584
4     24  0.5122
5     48  0.4675
6    Inf  0.0000

WTP estimates:
 Mean: 24.665138  (Kaplan-Meier)
 Mean: 85.533280  (Spearman-Karber)
 Median: 30.553191