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

## Description

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

## Usage

 ```1 2 3 4``` ```kristrom(formula, data, subset) ## S3 method for class 'kristrom' print(x, digits = 4, ...) ```

## Arguments

 `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.

## Details

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.

## Value

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`.

## References

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`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```## 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) ```