# The Kristr\"om's nonparametric approach to analyze single-bounded 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 |

### 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 |

`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 |

`M` |
the number of rows of |

`adj.p` |
a vector describing the probability of a yes-answer to the suggested bid, which is the same
as the last column of |

`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.

### See Also

`plot.kristrom`

, `NaturalPark`

,
`turnbull.sb`

, `sbchoice`

### Examples

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)
``` |

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