| Title: | Analyzing Dichotomous Choice Contingent Valuation Data |
|---|---|
| Description: | Functions for analyzing dichotomous choice contingent valuation (CV) data. It provides functions for estimating parametric and nonparametric models for single-, one-and-one-half-, and double-bounded CV data. For details, see Aizaki et al. (2022) <doi:10.1007/s42081-022-00171-1>. |
| Authors: | Tomoaki Nakatani [aut, cph] (original developer), Hideo Aizaki [aut, cre], Kazuo Sato [ctb] (theoretical part of the manual) |
| Maintainer: | Hideo Aizaki <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.2.0 |
| Built: | 2024-11-24 06:48:26 UTC |
| Source: | CRAN |
The package provides functions for analyzing single-, one-and-one-half-, and double-bounded dichotomous choice contingent valuation (CV) data
This package provides functions for analyzing single-, one-and-one-half-, and double-bounded dichotomous choice contingent valuation (CV) data.
In the single-bounded dichotomous choice (SBDC) CV that was first proposed by Bishop and Heberlein (1979) respondents are requested to answer a question like the following:
If the environmental policy burdens you with USD annually, would you agree or disagree to it?
This format, respondents only states "yes (I agree)" or "no (I disagree)," meaning whether their
willingness to pay (WTP) is greater or lower than the bid (USD ) they are offered.
The double-bounded dichotomous choice (DBDC) CV was proposed by Hanemann (1985)
and Carson (1985) to improve the efficiency of SBDC-CV.
In the CV format, respondents are requested to answer the second (follow-up) question
just after they answer the SBDC-CV style question
(the first/initial question). An example of DBDC-CV
questions is as follows ():
First question
If the environmental policy burdens you with USD annually, would you agree or disagree to it?
Second question for the respondents who agree to the policy in the first question
If the amount of tax is USD , would you agree or disagree to it?
Second question for the respondents who disagree to the policy in the first question
If the amount of tax is USD , would you agree or disagree to it?
In the DBDC-CV question, there are four possible response
outcomes: (yes, yes); (yes, no); (no, yes); and (no, no). If the respondent 's answer
is (yes, yes), the analyst can tell ( is the WTP of the
respondent ). Similarly, (yes, no) means , (no, yes) means
, and (no, no) means .
One-and-one-half-bound dichotomous choice (OOHBDC) CV, which was developed by Cooper et al. (2002), is an intermediate CV format between SBDC-CV format and DBDC-CV format.
In the OOHBDC-CV survey, after answering the first SBDC-CV style question (the first stage), only respondents who satisfy certain conditions are requested to answer an additional SBDC-CV style question (the second stage). Details in the OOHBDC-CV survey are as follows:
Step 1) A list of bid ranges [BLj, BHj] (j = 1, 2, ..., J), where BLj < BHj, are decided: i.e., [BL1, BH1], [BL2, BH2], ..., and [BLJ, BHJ].
Step 2) One of the bid ranges is randomly presented to respondents (e.g., a bid range of [BL3, BH3] for j = 3).
Step 3) One of the two bids presented to the respondents is selected randomly (i.e., BL3 or BH3 in the case of step 2 example) and then the respondents are asked whether they would be willing to pay the amount of the bid selected (the first stage).
Step 4) The respondents are asked to answer the second stage if they satisfy either condition: (a) their answer in the first stage is "yes" when the lower bid is presented in the first stage, or (b) their answer in the first stage is "no" when the higher bid is presented in the first stage.
Therefore, there are six possible responses to the OOHBDC-CV survey: "no", "yes-no", and "yes-yes" when the lower bid is shown in the first stage; and "yes", "no-yes", and "no-no" when the higher bid is shown in the first stage. Refer to Cooper et al. (2002) for detailed explanation of OOHBDC-CV, including the example CV questions.
There are two ways of estimating WTP from the SBDC-, OOHBDC-, and DBDC-CV:
parametric and nonparametric approaches. In this package, the functions sbchoice,
oohbchoice, and dbchoice, which are based on the utility difference
approach (Hanemann, 1984), are developed for the parametric approach to SBDC, OOHBDC, and DBDC data,
respectively.
Confidence intervals for the estimates of WTPs are constructed by two methods.
These are the Krinsky and Robb (1986, 1990)'s method and the bootstrap one.
The former is implemented by krCI while the latter by bootCI.
Both of the methods rely on simulation techniques with different settings. Usually, a bootstrap method takes much longer time than the Krinsky and Robb's method does. It has been pointed out that each method has both advantages and disadvantages, see, for instance, the discussions in Hole (2007) and the references therein.
Functions for nonparametric approaches are also included in the package. kristrom
(Kristrom, 1990) and turnbull.sb (Carson and Steinberg, 1990) are designed for
analyses for SBDC data, whereas turnbull.oohb and turnbull.db
(Carson and Hanemann, 2005) for OOHBDC and DBDC ones, respectively.
This work was supported by JSPS KAKENHI Grant Number JP20K06251.
DCchoice depends on interval (Fay and Shaw, 2010) package. It further depends on several packages, among which Icens (Gentleman and Vandal, 2011) package may not be installed by the GUI Package Installer accessible from the menu bar (Windows and Mac OS) because it is available only from Bioconductor.
To install DCchoice and other dependent packages simultaneously, use the
install.packages function instead. See the Examples section for the
code.
Aizaki H, Nakatani T, Sato K (2014). Stated Preference Methods Using R. CRC Press, Boca Raton FL.
Aizaki H, Nakatani T, Sato K, Fogarty J (2022). “R package DCchoice for dichotomous choice contingent valuation: a contribution to open scientific software and its impact” Japanese Journal of Statistics and Data Science, 5, 871–884. https://link.springer.com/article/10.1007/s42081-022-00171-1.
Bishop RC, Heberlein TA (1979). “Measuring Values of Extra-Market Goods: Are Indirect Measures Biased?” American Journal of Agricultural Economics, 61(5), 926–930.
Carson RT (1985). “Three Essays on Contingent Valuation”. Dissertation, University of California Berkeley.
Carson RT, Hanemann WM (2005). “Contingent Valuation.” in KG M\"aler, JR Vincent (eds.), Handbook of Environmental Economics. Elsevier, New York.
Carson RT, Steinberg D (1990). “Experimental Design for Discrete Choice Voter Preference Surveys.” in 1989 Proceeding of the Survey Methodology Section of the American Statistical Association, 821–822.
Cooper JC, Hanemann M, Signorello G (2002). “One-and-one-half-bound dichotomous choice contingent valuation”, The Review of Economics and Statistics, 84, 742–750.
Croissant Y (2011). Ecdat: Data Sets for Econometrics, R package version 0.1-6.1, https://CRAN.R-project.org/package=Ecdat.
Fay MP, Shaw PA (2010). “Exact and Asymptotic Weighted Logrank Tests for Interval Censored Data: The interval R Package”, Journal of Statistical Software, 36(2), 1-34. https://www.jstatsoft.org/v36/i02/.
Gentleman R, Vandal A (2011). Icens: NPMLE for Censored and Truncated Data. R package version 1.24.0, https://CRAN.R-project.org/package=Icens.
Hanemann, WM (1984). “Welfare Evaluations in Contingent Valuation Experiments with Discrete Responses”, American Journal of Agricultural Economics, 66(2), 332–341.
Hanemann WM (1985). “Some Issues in Continuous- and Discrete-Response Contingent Valuation Studies.” Northeastern Journal of Agricultural Economics, 14, 5–13.
Hole AR (2007). “A Comparison of Approaches to Estimating Confidence Intervals for Willingness to Pay Measure.” Health Economics, 16, 827–840.
Krinsky I, Robb AL (1986). “On Approximating the Statistical Properties of Elasticities.” The Review of Economics and Statistics, 68, 715–719.
Krinsky I, Robb AL (1990). “On Approximating the Statistical Properties of Elasticities: A Correction.” The Review of Economics and Statistics, 72, 189–190.
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.
## Installation of DCchoice along with dependent packages is carried out ## by the following lines of code: ## Not run: install.packages("DCchoice", repos = c("@CRAN@", "http://www.bioconductor.org/packages/release/bioc"), dep = TRUE) ## End(Not run) ## You may select a CRAN mirror a few times. ## For Mac and Unix/Linux users, add the option argument 'type="source"'.## Installation of DCchoice along with dependent packages is carried out ## by the following lines of code: ## Not run: install.packages("DCchoice", repos = c("@CRAN@", "http://www.bioconductor.org/packages/release/bioc"), dep = TRUE) ## End(Not run) ## You may select a CRAN mirror a few times. ## For Mac and Unix/Linux users, add the option argument 'type="source"'.
Double-bounded dichotomous choice survey data for quality inprovements in the Albemarle-Pamlico sounds, North Carolina.
data(AP)data(AP)
a data frame containing 721 observations.
a vector of bids expressd in USD.
a vector of bids expressd in USD.
a vector of binary dummies equal to 1 if the bid is accepted and 0 otherwise.
a vector of binary dummies equal to 1 if the bid is accepted and 0 otherwise.
a numeric vrector containing the annual household income in 1995 USD of the respondent
a vector of binary dummies equal to 1 if the respondent is employed in fulltime and 0 otherwise.
a numeric vector containing the age of the respondent.
a vector of binary dummies equal to 1 if the respondent is female and 0 otherwise.
a vector of binary dummies equal to 1 if the respondent is married and 0 otherwise.
The original data are based on a telephone survey regarding quality improvements in the Albemarle-Pamlico sounds, North Carolina. The data were intensively analyzed, for instance, in Whitehead (1995) and Whitehead, et. al. (1998) in different contexts. Details of the survey can be found in the web site (see Source for the URL).
The original data have $1077$ observations and include the bids and the responses of the double-bounded dichotomous choice survey. Various socio-demographic characteristics are also collected by the survey.
A subset of the data consisting of the responses to the CVM questions as well as minimum number of socio-demographic characteristics. In addition, observations with missing values were removed from the subset.
The complete data and details can be obtained in the online version of Whitehead (2015).
The data are included here under kind permission from Professor John Whitehead, Appalachian State University.
Whitehead JC (1995). “Willingness to Pay for Quality Improvements: Comparative Statics and Interpretation of Contingent Valuation Results.” Land Economics, 71(2), 207–215.
Whitehead JC (2015). “Albemarle-Pamlico Sounds Revealed and Stated Preference Data.” Data in Brief, 3, 90–94.
Whitehead JC, Haab TC, Huang JC (1998). “Part-Whole Bias in Contingent Valuation: Will Scope Effects be Detected with Inexpensive Survey Methods?” Southern Economic Journal, 65(1), 160–168.
This function calculates confidence intervals for WTP using the nonparametric bootstrap method.
bootCI(obj, nboot = 1000, CI = 0.95, individual = NULL) ## S3 method for class 'bootCI' print(x, ...)bootCI(obj, nboot = 1000, CI = 0.95, individual = NULL) ## S3 method for class 'bootCI' print(x, ...)
obj |
an S3 class object |
nboot |
the number of bootstrap resampling. |
CI |
a percentile of the confidence intervals to be estimated. |
individual |
a data frame containing covariates that show an individual of which to estimate WTP. |
x |
an object of class |
... |
optional arguments. Currently not in use. |
The bootstrap method resamples the data at our hands and repeatedly estimates the model with the bootstrapped data to formulate an empirical distribution of the associated WTP. This is a clear contrast with the method of Krinsky and Robb (1986, 1990) where the parameters are directly drawn from the multivariate normal distribution.
The upper and the lower bound of the interval is determined similarly to the case of
the function krCI.
Hole (2007) conducted simulation experiments to compare the performance of the method of Krinsky and Robb (1986, 1990) with the bootstrap one.
A WTP of a specific individual (e.g., a representative respondent) can be estimated
when assigning covariates to individual. See Example for details.
The function bootCI() returns an object of S3 class "bootCI".
An object of "bootCI" is a list with the following components.
out |
the output table with simulated confidence intervals as well as the four type of WTP estimates (mean, truncated mean, truncated mean with adjustment and median) from the ML estimation. |
mWTP |
a vector of simulated mean WTP. When |beta| < 1, this item is set
to |
tr.mWTP |
a vector of simulated mean WTP truncated at the maximum bid. |
adj.tr.mWTP |
a vector of simulated mean WTP truncated at the maximum bid with the adjustment. |
medWTP |
a vector of simulated median WTP. |
When the parameter estimate on the bid does not satisfy the condition for the existence
of the finite mean WTP (|beta|>1), the values of the lower and the upper bound of the
confidence interval are coerced to set to -999.
The generic function print() is available for the object of class
"bootCI" and displays the table of simulated confidence intervals.
The table contains the confidence intervals for the four types (mean, truncated mean, truncated mean with adjustment and median) of WTP from the ML estimation. The adjustment for the truncated mean WTP is implemented by the method of Boyle et~al.(1988).
It is time consuming (usually takes several minutes) to implement this function.
Boyle KJ, Welsh MP, Bishop RC (1988). “Validation of Empirical Measures of Welfare Change: Comment.” Land Economics, 64(1), 94–98.
Hole AR (2007). “A Comparison of Approaches to Estimating Confidence Intervals for Willingness to Pay Measure.” Health Economics, 16, 827–840.
Krinsky I, Robb AL (1986). “On Approximating the Statistical Properties of Elasticities.” The Review of Economics and Statistics, 68, 715–719.
Krinsky I, Robb AL (1990). “On Approximating the Statistical Properties of Elasticities: A Correction.” The Review of Economics and Statistics, 72, 189–190.
## See Examples in dbchoice and sbchoice.## See Examples in dbchoice and sbchoice.
Contingency tables for the suggested bids and the number of respondents saying yes or no to the bids in the Exxon Valdez Oil Spill CVM survey.
data(CarsonSB) data(CarsonDB)data(CarsonSB) data(CarsonDB)
Both CarsonSB and CarsonDB are data frame objects
of contingency tables.
For CarsonSB,
a bid expressd in USD.
a number of respondents accepting the bid.
a number of respondents not accepting the bid.
For CarsonDB,
a first stage bid expressd in USD.
a second stage bid increased from the first one, expressd in USD.
a second stage bid decreased from the first one, expressd in USD.
a number of respondents accepting both the first and the second bids.
a number of respondents accepting only the first bid.
a number of respondents accepting only the second bid.
a number of respondents not accepting the first nor the second bids.
Out of CarsonSB and CarsonSB, one may reconstruct the original yes/no
type of data for 1043 observations. See the example for CarsonSB.
CarsonSB and CarsonDB are reproduced from Tables A-15,
A-16 and A-17 in Appendix C.1 of Carson et.al (1992).
The data are included under kind permission from Professor Richard T. Carson of University of California, San Diego.
Carson RT, Mitchell RC, Hanemann WM, Kopp RJ, Presser S, Ruud PA (1992). “A Contingent Valuation Study of Lost Passive Use Values Resulting from the Exxon Valdez Oil Spill.” Technical Report Report to the Attorney General of the State of Alaska, Natural Resource Damage Assessment Inc. https://mpra.ub.uni-muenchen.de/6984/.
## The following lines of code reconstruct the original yes/no type of data ## for 1043 observations. A data frame object sb.data consists of two variables, ## namely, bid1 and R1. The conversion into a simole data frame object can be ## done either manually or by using the \code{ct2df} function. data(CarsonSB) ## Using the \code{ct2df} function CarsonSB.dat <- ct2df( x = CarsonSB, bid1 = "T1", y = "Y", n = "N", type = "single") head(CarsonSB.dat) # Manual conversion n <- rowSums(CarsonSB[, -1]) sb.data <- data.frame( bid = c(rep(CarsonSB$T1[1], n[1]), rep(CarsonSB$T1[2], n[2]), rep(CarsonSB$T1[3], n[3]), rep(CarsonSB$T1[4], n[4])), R1 = c(rep(1, CarsonSB$Y[1]), rep(0, CarsonSB$N[1]), rep(1, CarsonSB$Y[2]), rep(0, CarsonSB$N[2]), rep(1, CarsonSB$Y[3]), rep(0, CarsonSB$N[3]), rep(1, CarsonSB$Y[4]), rep(0, CarsonSB$N[4])) ) dim(sb.data) head(sb.data) ## Double-bounded dichotomous choice CV format. data(CarsonDB) CarsonDB CarsonDB.dat <- ct2df( x = CarsonDB, bid1 = "T1", bid2h = "TU", bid2l = "TL", yy = "yy", yn = "yn", ny = "ny", nn = "nn", type = "double") head(CarsonDB.dat) ## An example of manual conversion is omitted. ## See Appendix 2.A of Aizaki, et. al. (2014).## The following lines of code reconstruct the original yes/no type of data ## for 1043 observations. A data frame object sb.data consists of two variables, ## namely, bid1 and R1. The conversion into a simole data frame object can be ## done either manually or by using the \code{ct2df} function. data(CarsonSB) ## Using the \code{ct2df} function CarsonSB.dat <- ct2df( x = CarsonSB, bid1 = "T1", y = "Y", n = "N", type = "single") head(CarsonSB.dat) # Manual conversion n <- rowSums(CarsonSB[, -1]) sb.data <- data.frame( bid = c(rep(CarsonSB$T1[1], n[1]), rep(CarsonSB$T1[2], n[2]), rep(CarsonSB$T1[3], n[3]), rep(CarsonSB$T1[4], n[4])), R1 = c(rep(1, CarsonSB$Y[1]), rep(0, CarsonSB$N[1]), rep(1, CarsonSB$Y[2]), rep(0, CarsonSB$N[2]), rep(1, CarsonSB$Y[3]), rep(0, CarsonSB$N[3]), rep(1, CarsonSB$Y[4]), rep(0, CarsonSB$N[4])) ) dim(sb.data) head(sb.data) ## Double-bounded dichotomous choice CV format. data(CarsonDB) CarsonDB CarsonDB.dat <- ct2df( x = CarsonDB, bid1 = "T1", bid2h = "TU", bid2l = "TL", yy = "yy", yn = "yn", ny = "ny", nn = "nn", type = "double") head(CarsonDB.dat) ## An example of manual conversion is omitted. ## See Appendix 2.A of Aizaki, et. al. (2014).
A convinience function converting a data frame object in contingency-table format of bid(s) and responses of dichotomous choice CV into a simple data frame of individual observations. The outcome is suitable for the analysis using functions in the package.
ct2df(x, bid1 = "bid1", bid2h = "bidh", bid2l = "bidl", bidl = "bidl", bidh = "bidh", nny = "nny", nnn = "nnn", yy = "yy", yn = "yn", ny = "ny", nn = "nn", y = "y", n = "n", n_y = "n_y", n_n = "n_n", nn_y = "nn_y", nn_n = "nn_n", type = "double", spike = FALSE)ct2df(x, bid1 = "bid1", bid2h = "bidh", bid2l = "bidl", bidl = "bidl", bidh = "bidh", nny = "nny", nnn = "nnn", yy = "yy", yn = "yn", ny = "ny", nn = "nn", y = "y", n = "n", n_y = "n_y", n_n = "n_n", nn_y = "nn_y", nn_n = "nn_n", type = "double", spike = FALSE)
x |
a data frame object in contingency-table format containing bid(s) and responses |
bid1 |
a character string showing the bid (for "single") or the bid in the first stage (for "double") |
bid2h |
a character string showing the second (higher) bid when respondents answer "Yes" in the first stage |
bid2l |
a character string showing the second (lower) bid when respondents answer "No" in the first stage |
bidh |
a character string showing the higher bid (for "oohb") |
bidl |
a character string showing the lower bid (for "oohb") |
nny |
a character string showing a number of respondents rejecting the first and the second bids and having a positive willingness-to-pay (WTP) (for a spike "double") |
nnn |
a character string showing a number of respondents rejecting the first and the second bids and having a zero WTP (for a spike "double") |
yy |
a character string showing a number of respondents accepting both the first and the second bids |
yn |
a character string showing a number of respondents accepting only the first bid |
ny |
a character string showing a number of respondents accepting only the second bid (for "double") or rejecting the first bid and having a positive WTP (for a spike "single") |
nn |
a character string showing a number of respondents rejecting the first and the second bids (for "double") or rejecting the first bid and having a zero WTP (for a spike "single") |
y |
a character string showing a number of respondents accepting the bid |
n |
a character string showing a number of respondents rejecting the bid |
n_y |
a character string showing a number of respondents rejecting the bid and having a positive WTP (for a spike "oohb") |
n_n |
a character string showing a number of respondents rejecting the bid and having a zero WTP (for a spike "oohb") |
nn_y |
a character string showing a number of respondents rejecting the first and second bids and having a positive WTP (for a spike "oohb") |
nn_n |
a character string showing a number of respondents rejecting the first and second bid and having a zero WTP (for a spike "oohb") |
type |
a character string setting the elicitation format, which takes one of "single" (single-bounded dichotomous choice format), "oohb" (one-and-one-half-bounded dichotomous choice format), or "double" (double-bounded dichotomous choice format) |
spike |
a logical code: |
The function ct2df implements a conversion of a data frame
containing bid(s) and responses regarding dichotomous choice CV in
contingency-table format into a data frame suitable for use by the functions
sbchoice, oohbchoice, dbchoice, sbspike, oohbspike, dbspike, kristrom,
turnbull.sb, and turnbull.db.
See CarsonSB and CarsonDB for dataset
in contingency-table format.
See the examples below and ones in spike-models, for usage in detail.
The function returns a data frame, in which each row shows a single respondent. It contains the following variables.
For "single",
R1 |
a response to a bid: 1 for "Yes", 0 for "No" |
bid1 |
the bid |
For "double",
B1 |
a bid in the first stage |
B2H |
a (higher) bid in the second stage when the response is "Yes" in the first stage |
B2L |
a (lower) bid in the second stage when the response is "No" in the first stage |
R |
a combination of responses in the first and second stages, which takes yy for "Yes" and "Yes", yn for "Yes" and "No", ny for "No" and "Yes", or nn for "No" and "No" |
R1 |
the response in the first stage, which takes 1 for "Yes", 0 for "No" |
R2 |
the response in the second stage, which takes 1 for "Yes", 0 for "No" |
bid1 |
the bid in the first stage |
bid2 |
the bid in the second stage the respondent faced |
For "oohb",
BH |
a higher bid |
BL |
a lower bid |
R |
a combination of responses in the first and second stages |
R1 |
the response in the first stage, which takes |
R2 |
the response in the second stage, which takes |
For spike models,
S |
the response in a simple spike question, which takes |
Aizaki H, Nakatani T, Sato K (2014). Stated Preference Methods Using R. CRC Press, Boca Raton, FL.
sbchoice, oohbchoice, dbchoice,
sbspike, oohbspike, dbspike,
kristrom, turnbull.sb, turnbull.db
# Single-bounded dichotomous choice CV format data(CarsonSB) CarsonSB CarsonSB.dat <- ct2df( x = CarsonSB, bid1 = "T1", y = "Y", n = "N", type = "single") head(CarsonSB.dat) summary(turnbull.sb(R1 ~ bid1, data = CarsonSB.dat)) # Double-bounded dichotomous choice CV format data(CarsonDB) CarsonDB CarsonDB.dat <- ct2df( x = CarsonDB, bid1 = "T1", bid2h = "TU", bid2l = "TL", yy = "yy", yn = "yn", ny = "ny", nn = "nn", type = "double") head(CarsonDB.dat) summary(turnbull.db(R1 + R2 ~ bid1 + bid2, data = CarsonDB.dat))# Single-bounded dichotomous choice CV format data(CarsonSB) CarsonSB CarsonSB.dat <- ct2df( x = CarsonSB, bid1 = "T1", y = "Y", n = "N", type = "single") head(CarsonSB.dat) summary(turnbull.sb(R1 ~ bid1, data = CarsonSB.dat)) # Double-bounded dichotomous choice CV format data(CarsonDB) CarsonDB CarsonDB.dat <- ct2df( x = CarsonDB, bid1 = "T1", bid2h = "TU", bid2l = "TL", yy = "yy", yn = "yn", ny = "ny", nn = "nn", type = "double") head(CarsonDB.dat) summary(turnbull.db(R1 + R2 ~ bid1 + bid2, data = CarsonDB.dat))
This function analyzes double-bounded dichotomous choice contingent valuation (CV) data on the basis of the utility difference approach.
dbchoice(formula, data, subset, na.action = na.omit, dist = "log-logistic", par = NULL, ...) ## S3 method for class 'dbchoice' print(x, digits = max(3, getOption("digits") - 1), ...) ## S3 method for class 'dbchoice' vcov(object, ...) ## S3 method for class 'dbchoice' logLik(object, ...)dbchoice(formula, data, subset, na.action = na.omit, dist = "log-logistic", par = NULL, ...) ## S3 method for class 'dbchoice' print(x, digits = max(3, getOption("digits") - 1), ...) ## S3 method for class 'dbchoice' vcov(object, ...) ## S3 method for class 'dbchoice' logLik(object, ...)
formula |
an object of S3 class |
data |
a data frame containing the variables in the model formula. |
subset |
an optional vector specifying a subset of observations. |
na.action |
a function which indicates what should happen when the data contains |
dist |
a character string setting the error distribution in the model, which
takes one of |
par |
a vector of initial parameters over which the optimization is carried out. |
x |
an object of class |
digits |
a number of digits to display. |
object |
an object of class |
... |
optional arguments. Currently not in use. |
The function dbchoice() implements an analysis of double-bounded dichotomous choice
contingent valuation (CV) data on the basis of the utility difference approach (Hanemann, 1984).
A generic call to dbchoice() is given by
dbchoice(formula, data, dist = "log-logistic", ...)
The extractor function summary() is available for a "dbchoice" class object.
See summary.dbchoice for details.
There are two functions available for computing the confidence intervals for the estimates of WTPs.
krCI implements simulations to construct empirical distributions of the WTP while
bootCI carries out nonparametric bootstrapping.
The argument formula defines the response variables and covariates. The argument data
is mandatory where the data frame containing the variables in the model is specified. The argument dist
sets the error distribution.
Currently, one of "logistic", "normal", "log-logistic", "log-normal",
or "weibull" is available.
The default value is dist = "log-logistic", so that it may be omitted if the user wants to estimate a model
with log-logistic error distribution.
The difference between normal and log-normal models or between logistic or log-logistic ones is how the bid variable is incorporated into the model to be estimated. For the Weibull model, the bid variable must be entered in the natural log. Therefore, the user must be careful in defining the model formula that is explained in details below.
A typical structure of the formula for dbchoice() is defined as follows:
R1 + R2 ~ (the names of the covariates) | BD1 + BD2
The formula is an object of class "formula" and specifies the model structure. It has to be written in a
symbolic expression in R.
The formula consists of three parts. The first part, the left-hand side of the tilde sign (~), must
contain the response variables for the suggested prices in the first and the second stage of CV questions.
In the example below, R1 denotes a binary or two-level factor response variable for a bid in the first
stage and R2 for a bid in the second stage. Each of R1 and R2 contains "Yes" or
"No" to the bid or 1 for "Yes" and 0 for "No".
The covariates are defined in the second part in the place of (the names of the covariates). Each covariate is
connected with the arithmetic operator + and (the names of the covariates) in the above syntax should be
replaced with var1 + var2 and the like. The plus sign is nothing to do with addition of the two variables
in the symbolic expression. When the covariate contains only a constant term, a value of 1 is set as the
covariate (that is, R1 + R2 ~ 1 | BD1 + BD2)
The last part starts after the vertical bar (|). The names of the two variables (BD1 and BD2)
containing suggested prices in the first and second stage of double-bounded dichotomous choice CV question are
specified in this part. The two variables are also connected with the arithmetic operator (+).
According to the structure of the formula, a data set (data frame) consists of three parts. An example of the
data set is as follows (sex, age, and income are respondents characteristics and assumed
to be covariates):
R1 |
R2 |
sex |
age |
income |
BD1 |
BD2
|
| Yes | Yes | Male | 20 | Low | 100 | 250 |
| Yes | No | Male | 30 | Low | 500 | 1000 |
| ... |
The second bid in the double-bounded dichotomous choice CV question is larger or lower than the first bit
according to the response to the first stage: if the response to the first stage is "Yes", the second bid is
larger than the first bid; if the response is "No", the second bid is lower than the first bid. In the example
above, BD2 is set as the second bid according to each respondent faced in the second stage. However,
the followings style of data set is frequently prepared:
R1 |
R2 |
sex |
age |
income |
BD1 |
BD2H |
BD2L
|
| Yes | Yes | Male | 20 | Low | 100 | 250 | 50 |
| Yes | No | Male | 30 | Low | 500 | 1000 | 250 |
| ... |
BD2H is the second (higher) bid when the respondent answers "Yes" in the first stage; BD2L
is the second (lower) bid when the respondent answers "No" in the first stage. In this case, the users
have to convert BD2H and BD2L into BD2 (see the section "Examples").
The function dbchoice() analyzes double-bounded dichotomous choice CV data using the function
optim on the basis of the initial coefficients that are estimated from a binary
logit model analysis of the first-stage CV responses (the binary logit model is estimated internally
by the function glm with the argument family = binomial(link = "logit")).
Nonparametric analysis of double-bounded dichotomous choice data can be done by turnbull.db.
A single-bounded analogue of dbchoice is called sbchoice.
This function returns an S3 class object "dbchoice" that is a list with the following components.
f.stage |
a list of components returned from the function |
dbchoice |
a list of components returned from the function |
coefficients |
a named vector of estimated coefficients. |
call |
the matched call. |
formula |
the formula supplied. |
Hessian |
an estimate of the Hessian. See also |
distribution |
a character string showing the error distribution used. |
loglik |
a value of the log likelihood at the estimates. |
convergence |
an logical code: |
niter |
a vector of two integers describing the number of calls to the object function and the
numerical gradient, respectively. See also |
nobs |
a number of observations. |
covariates |
a named matrix of the covariates used in the model. |
bid |
a named matrix of the bids used in the model. |
yn |
a named matrix of the responses to the initial and follow-up CV questions used in the model. |
data.name |
the data matrix. |
terms |
terms |
contrast |
contrasts used for factors |
xlevels |
levels used for factors |
Bateman IJ, Carson RT, Day B, Hanemann M, Hanley N, Hett T, Jones-Lee M, Loomes G, Mourato S, \"Ozdemiro\=glu E, Pearce DW, Sugden R, Swanson J (eds.) (2002). Economic Valuation with Stated Preference Techniques: A Manual. Edward Elger, Cheltenham, UK.
Carson RT, Hanemann WM (2005). “Contingent Valuation.” in KG M\"aler, JR Vincent (eds.), Handbook of Environmental Economics. Elsevier, New York.
Croissant Y (2011). Ecdat: Data Sets for Econometrics, R package version 0.1-6.1, https://CRAN.R-project.org/package=Ecdat.
Hanemann, WM (1984). “Welfare Evaluations in Contingent Valuation Experiments with Discrete Responses”, American Journal of Agricultural Economics, 66(2), 332–341.
Hanemann M, Kanninen B (1999). “The Statistical Analysis of Discrete-Response CV Data.”, in IJ Bateman, KG Willis (eds.), Valuing Environmental Preferences: Theory and Practice of the Contingent Valuation Methods in the US, EU, and Developing Countries, 302–441. Oxford University Press, New York.
Hanemann WM, Loomis JB, Kanninen BJ (1991). “Statistical Efficiency of Double-Bounded Dichotomous Choice Contingent Valuation.” American Journal of Agricultural Economics, 73(4), 1255–1263.
summary.dbchoice, krCI, bootCI,
sbchoice, turnbull.db, NaturalPark,
glm, optim, formula
## Examples are based on a data set NaturalPark in the package ## Ecdat (Croissant 2011): DBDCCV style question for measuring ## willingness to pay for the preservation of the Alentejo Natural ## Park. The data set (dataframe) contains seven variables: ## bid1 (bid in the initial question), bidh (higher bid in the follow-up ## question), bidl (lower bid in the follow-up question), answers ## (response outcomes in a factor format with four levels of "nn", ## "ny", "yn", "yy"), respondents' characteristic variables such ## as age, sex and income (see NaturalPark for details). data(NaturalPark, package = "Ecdat") head(NaturalPark) ## The variable answers are converted into a format that is suitable for the ## function dbchoice() as follows: NaturalPark$R1 <- ifelse(substr(NaturalPark$answers, 1, 1) == "y", 1, 0) NaturalPark$R2 <- ifelse(substr(NaturalPark$answers, 2, 2) == "y", 1, 0) ## We assume that the error distribution in the model is a ## log-logistic; therefore, the bid variables bid1 is converted ## into LBD1 as follows: NaturalPark$LBD1 <- log(NaturalPark$bid1) ## Further, the variables bidh and bidl are integrated into one ## variable (bid2) and the variable is converted into LBD2 as follows: NaturalPark$bid2 <- ifelse(NaturalPark$R1 == 1, NaturalPark$bidh, NaturalPark$bidl) NaturalPark$LBD2 <- log(NaturalPark$bid2) ## The utility difference function is assumed to contain covariates (sex, age, and ## income) as well as two bid variables (LBD1 and LBD2) as follows: fmdb <- R1 + R2 ~ sex + age + income | LBD1 + LBD2 ## Not run: ## The formula may be alternatively defined as fmdb <- R1 + R2 ~ sex + age + income | log(bid1) + log(bid2) ## End(Not run) ## The function dbchoice() with the function fmdb and the dataframe ## NP is executed as follows: NPdb <- dbchoice(fmdb, data = NaturalPark) NPdb NPdbs <- summary(NPdb) NPdbs ## The confidence intervals for these WTPs are calculated using the ## function krCI() or bootCI() as follows: ## Not run: krCI(NPdb) bootCI(NPdb) ## End(Not run) ## The WTP of a female with age = 5 and income = 3 is calculated ## using function krCI() or bootCI() as follows: ## Not run: krCI(NPdb, individual = data.frame(sex = "female", age = 5, income = 3)) bootCI(NPdb, individual = data.frame(sex = "female", age = 5, income = 3)) ## End(Not run) ## The variable age and income are deleted from the fitted model, ## and the updated model is fitted as follows: update(NPdb, .~. - age - income |.) ## The bid design used in this example is created as follows: bid.design <- unique(NaturalPark[, c(1:3)]) bid.design <- log(bid.design) colnames(bid.design) <- c("LBD1", "LBDH", "LBDL") bid.design ## Respondents' utility and probability of choosing Yes-Yes, Yes-No, ## No-Yes, and No-No under the fitted model and original data are ## predicted as follows: head(predict(NPdb, type = "utility", bid = bid.design)) head(predict(NPdb, type = "probability", bid = bid.design)) ## Utility and probability of choosing Yes for a female with age = 5 ## and income = 3 under bid = 10 are predicted as follows: predict(NPdb, type = "utility", newdata = data.frame(sex = "female", age = 5, income = 3, LBD1 = log(10))) predict(NPdb, type = "probability", newdata = data.frame(sex = "female", age = 5, income = 3, LBD1 = log(10))) ## Plot of probabilities of choosing yes is drawn as drawn as follows: plot(NPdb) ## The range of bid can be limited (e.g., [log(10), log(20)]): plot(NPdb, bid = c(log(10), log(20)))## Examples are based on a data set NaturalPark in the package ## Ecdat (Croissant 2011): DBDCCV style question for measuring ## willingness to pay for the preservation of the Alentejo Natural ## Park. The data set (dataframe) contains seven variables: ## bid1 (bid in the initial question), bidh (higher bid in the follow-up ## question), bidl (lower bid in the follow-up question), answers ## (response outcomes in a factor format with four levels of "nn", ## "ny", "yn", "yy"), respondents' characteristic variables such ## as age, sex and income (see NaturalPark for details). data(NaturalPark, package = "Ecdat") head(NaturalPark) ## The variable answers are converted into a format that is suitable for the ## function dbchoice() as follows: NaturalPark$R1 <- ifelse(substr(NaturalPark$answers, 1, 1) == "y", 1, 0) NaturalPark$R2 <- ifelse(substr(NaturalPark$answers, 2, 2) == "y", 1, 0) ## We assume that the error distribution in the model is a ## log-logistic; therefore, the bid variables bid1 is converted ## into LBD1 as follows: NaturalPark$LBD1 <- log(NaturalPark$bid1) ## Further, the variables bidh and bidl are integrated into one ## variable (bid2) and the variable is converted into LBD2 as follows: NaturalPark$bid2 <- ifelse(NaturalPark$R1 == 1, NaturalPark$bidh, NaturalPark$bidl) NaturalPark$LBD2 <- log(NaturalPark$bid2) ## The utility difference function is assumed to contain covariates (sex, age, and ## income) as well as two bid variables (LBD1 and LBD2) as follows: fmdb <- R1 + R2 ~ sex + age + income | LBD1 + LBD2 ## Not run: ## The formula may be alternatively defined as fmdb <- R1 + R2 ~ sex + age + income | log(bid1) + log(bid2) ## End(Not run) ## The function dbchoice() with the function fmdb and the dataframe ## NP is executed as follows: NPdb <- dbchoice(fmdb, data = NaturalPark) NPdb NPdbs <- summary(NPdb) NPdbs ## The confidence intervals for these WTPs are calculated using the ## function krCI() or bootCI() as follows: ## Not run: krCI(NPdb) bootCI(NPdb) ## End(Not run) ## The WTP of a female with age = 5 and income = 3 is calculated ## using function krCI() or bootCI() as follows: ## Not run: krCI(NPdb, individual = data.frame(sex = "female", age = 5, income = 3)) bootCI(NPdb, individual = data.frame(sex = "female", age = 5, income = 3)) ## End(Not run) ## The variable age and income are deleted from the fitted model, ## and the updated model is fitted as follows: update(NPdb, .~. - age - income |.) ## The bid design used in this example is created as follows: bid.design <- unique(NaturalPark[, c(1:3)]) bid.design <- log(bid.design) colnames(bid.design) <- c("LBD1", "LBDH", "LBDL") bid.design ## Respondents' utility and probability of choosing Yes-Yes, Yes-No, ## No-Yes, and No-No under the fitted model and original data are ## predicted as follows: head(predict(NPdb, type = "utility", bid = bid.design)) head(predict(NPdb, type = "probability", bid = bid.design)) ## Utility and probability of choosing Yes for a female with age = 5 ## and income = 3 under bid = 10 are predicted as follows: predict(NPdb, type = "utility", newdata = data.frame(sex = "female", age = 5, income = 3, LBD1 = log(10))) predict(NPdb, type = "probability", newdata = data.frame(sex = "female", age = 5, income = 3, LBD1 = log(10))) ## Plot of probabilities of choosing yes is drawn as drawn as follows: plot(NPdb) ## The range of bid can be limited (e.g., [log(10), log(20)]): plot(NPdb, bid = c(log(10), log(20)))
This function synthesizes responses to DCCV questions.
dccvResponse(bid, b, n, seed = NULL)dccvResponse(bid, b, n, seed = NULL)
bid |
a vector (for SBDC) or matrix (for DBDC) containing a bid design |
b |
a vector containing parameters of independent variables in the model |
n |
an integer value showing the number of respondents in the resultant dataset |
seed |
seed for a random number generator |
This function synthesizes response to SBDC- or DBDC-CV questions on the basis of the utility difference approach. See Aizaki et al. (2014) for detail on the model.
See the examples below for usage in detail.
This function returns a data frame, in which each row shows a single respondent. It contains the following variables.
For SBDC-CV,
R1 |
a response to a bid: 1 for "Yes", 0 for "No" |
bid1 |
the bid |
For DBDC-CV,
R1 |
the response in the first stage, which takes 1 for "Yes", 0 for "No" |
R2 |
the response in the second stage, which takes 1 for "Yes", 0 for "No" |
bid1 |
the bid in the first stage |
bid2 |
the bid in the second stage the respondent faced |
Aizaki H, Nakatani T, Sato K (2014). Stated Preference Methods Using R. CRC Press, Boca Raton, FL.
# SBDC-CV data(CarsonSB) CarsonSB CarsonSB[, 1] SB <- dccvResponse(bid = CarsonSB[, 1], b = c(0.64, -0.011), n = 1000) head(SB) sbchoice(R1 ~ 1|bid1, dist = "logistic", data = SB) # DBDC-CV data(CarsonDB) CarsonDB CarsonDB[, 1:3] DB <- dccvResponse(bid = data.matrix(CarsonDB[, 1:3]), b = c(0.7, -0.016), n = 1000) head(DB) dbchoice(R1 + R2 ~ 1|bid1 + bid2, dist = "logistic", data = DB)# SBDC-CV data(CarsonSB) CarsonSB CarsonSB[, 1] SB <- dccvResponse(bid = CarsonSB[, 1], b = c(0.64, -0.011), n = 1000) head(SB) sbchoice(R1 ~ 1|bid1, dist = "logistic", data = SB) # DBDC-CV data(CarsonDB) CarsonDB CarsonDB[, 1:3] DB <- dccvResponse(bid = data.matrix(CarsonDB[, 1:3]), b = c(0.7, -0.016), n = 1000) head(DB) dbchoice(R1 + R2 ~ 1|bid1 + bid2, dist = "logistic", data = DB)
A single-bounded dichotomous choice CVM data analyzed in Kristr\"om (1990).
data(KR)data(KR)
A data frame of single-bounded dichotomous choice contingent valuation survey data. The number of observations is 562.
a vector of bids expressd in SEK.
a vector of binary dummies equal to 1 if the bid is accepted and 0 otherwise.
The data consist of the responses to the single-bounded dichotomous choice survey for a sample of 562 Swedes regarding preservation of the eleven virgin forests in Sweden. See Kristr\"om (1990) for more details.
The data are used in Kristr\"om (1990).
The data are bundled in this package under kind permission from Professor Bengt Kristr\"om, Swedish University of Agricultural Sciences.
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.
This function calculates confidence intervals for WTP using the method of Krinsky and Robb (1986, 1990).
krCI(obj, nsim = 1000, CI = 0.95, individual = NULL) ## S3 method for class 'krCI' print(x, ...)krCI(obj, nsim = 1000, CI = 0.95, individual = NULL) ## S3 method for class 'krCI' print(x, ...)
obj |
an S3 class object |
nsim |
the number of draws of the parameters. |
CI |
a percentile of the confidence intervals to be estimated. |
individual |
a data frame containing covariates that show an individual of which to estimate WTP. |
x |
an object of class |
... |
optional arguments. Currently not in use. |
In the method of Krinsky and Robb (1986, 1990), a set of parameters is drawn nsim times
from a multivariate normal distribution with a vector of the parameter estimates as a mean
and the variance-covariance matrix of the parameter estimates. Then, various WTPs are computed for
each draw of simulated parameters. As a result, we are able to build an empirical distribution
of the WTPs concerned, and hence the confidence intervals. For each WTP, and when nsim = 1000,
the lower and the upper bound of the 95% confidence interval (CI = 0.95) correspond to
the 26th and the 975th sorted estimates, respectively.
Confidence intervals based on the bootstrap method are calculated by bootCI.
Hole (2007) conducted simulation experiments to compare the performance of the method of Krinsky and Robb (1986, 1990) with the bootstrap one.
A WTP of a specific individual (e.g., a representative respondent) can be estimated
when assigning covariates to individual. See Example for details.
The function krCI() returns an object of S3 class "krCI".
An object of "krCI" is a list with the following components.
out |
the output table with simulated confidence intervals as well as the four type of WTP estimates (mean, truncated mean, truncated mean with adjustment and median) from the ML estimation. |
mWTP |
a vector of simulated mean WTP. When |beta| < 1, this item is set
to |
tr.mWTP |
a vector of simulated mean WTP truncated at the maximum bid. |
adj.tr.mWTP |
a vector of simulated mean WTP truncated at the maximum bid with the adjustment. |
medWTP |
a vector of simulated median WTP. |
When the parameter estimate on the bid does not satisfy the condition for the existence
of the finite mean WTP (|beta|>1), the values of the lower and the upper bound of the
confidence interval are coerced to set to -999.
The table contains the confidence intervals for the four types (mean, truncated mean, truncated mean with adjustment and median) of WTP estimate from the ML estimation. The adjustment for the truncated mean WTP is implemented by the method of Boyle et~al.(1988).
The generic function print() is available for the object of class
"krCI" and displays the table of simulated confidence intervals.
Boyle KJ, Welsh MP, Bishop RC (1988). “Validation of Empirical Measures of Welfare Change: Comment.” Land Economics, 64(1), 94–98.
Hole AR (2007). “A Comparison of Approaches to Estimating Confidence Intervals for Willingness to Pay Measure.” Health Economics, 16, 827–840.
Krinsky I, Robb AL (1986). “On Approximating the Statistical Properties of Elasticities.” The Review of Economics and Statistics, 68, 715–719.
Krinsky I, Robb AL (1990). “On Approximating the Statistical Properties of Elasticities: A Correction.” The Review of Economics and Statistics, 72, 189–190.
## See Examples in dbchoice and sbchoice.## See Examples in dbchoice and sbchoice.
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, ...)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 |
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 |
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.
Croissant Y (2011). Ecdat: Data Sets for Econometrics, R package version 0.1-6.1, https://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)## 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)
This function analyzes one-and-one-half-bound dichotomous choice contingent valuation (CV) data on the basis of the utility difference approach.
oohbchoice(formula, data, subset, na.action = na.omit, dist = "log-logistic", par = NULL, ...)oohbchoice(formula, data, subset, na.action = na.omit, dist = "log-logistic", par = NULL, ...)
formula |
an object of S3 class |
data |
a data frame containing the variables in the model formula. |
subset |
an optional vector specifying a subset of observations. |
na.action |
a function which indicates what should happen when the data contains |
dist |
a character string setting the error distribution in the model, which
takes one of |
par |
a vector of initial parameters over which the optimization is carried out. |
... |
optional arguments. Currently not in use. |
One-and-one-half-bound dichotomous choice contingent valuation (OOHBDC-CV), which was developed by Cooper et al. (2002), is an intermediate CV format between single-bounded dichotomous choice (SBDC) CV format and double-bounded dichotomous choice (DBDC) CV format.
On the basis of an example of environmental valuation study, we will explain differences in question format among SBDC-CV, DBDC-CV, and OOHBDC-CV below.
In any of three CV surveys, two situations are firstly explained to the respondents: the current situation and the improved situation where an environmental improvement plan is assumed to be implemented. Question following the explanation of situations differs according to CV types.
In an SBDC-CV survey, after the explanation of situation mentioned above, the respondents are asked whether they would be willing to pay a certain amount of money toward the implementation of the plan. Therefore, there are two possible responses to the SBDC-CV survey: "yes (agree)," and "no (disagree)." The amounts (bids) that respondents are requested to contribute toward the plan are listed in advance. Each respondent is requested to answer a question randomly assigned with one of the listed bids.
In a DBDC-CV survey, the CV question consists of two stages: after answering the SBDC-CV style question mentioned above (the first stage), the respondents are also asked to answer an additional SBDC-CV style question (the second stage). The bid in the second stage varies according the response in the first stage: a higher bid is displayed in the second stage if the response in the first stage is "yes," whereas a lower bid is displayed when the response in the first stage is "no." Therefore, there are four possible responses to the DBDC-CV survey: "yes-yes" ("yes" in the both stages), "yes-no" ("yes" and "no" in the first and second stages, respectively), "no-yes" ("no" and "yes" in the first and second stages, respectively), and "no-no" ("no" in the both stages).
In the OOHBDC-CV survey, after answering the first SBDC-CV style question (the first stage), only respondents who satisfy certain conditions are requested to answer an additional SBDC-CV style question (the second stage). Details in the OOHBDC-CV survey are as follows: Step 1) A list of bid ranges [BLj, BHj] (j = 1, 2, ..., J), where BLj < BHj, are decided: i.e., [BL1, BH1], [BL2, BH2], ..., and [BLJ, BHJ]. Step 2) One of the bid ranges is randomly presented to respondents (e.g., a bid range of [BL3, BH3] for j = 3). Step 3) One of the two bids presented to the respondents is selected randomly (i.e., BL3 or BH3 in the case of step 2 example) and then the respondents are asked whether they would be willing to pay the amount of the bid selected (the first stage). Step 4) The respondents are asked to answer the second stage if they satisfy either condition: (a) their answer in the first stage is "yes" when the lower bid is presented in the first stage, or (b) their answer in the first stage is "no" when the higher bid is presented in the first stage. Therefore, there are six possible responses to the OOHBDC-CV survey: "no", "yes-no", and "yes-yes" when the lower bid is shown in the first stage; and "yes", "no-yes", and "no-no" when the higher bid is shown in the first stage. Refer to Cooper et al. (2002) for detailed explanation of OOHBDC-CV, including the example CV questions.
The function oohbchoice() implements an analysis of OOHBDC-CV responses (data) on the basis of the utility difference approach (Hanemann, 1984).
The function returns an object of S3 class oohbchoice (see below for details), which inherits from an S3 class dbchoice. The generic functions for the S3 class dbchoice such as print(), summary(), vcov(), logLik(), plot(), and update(), are available for the S3 class oohbchoice. In addition, the two functions krCI() and bootCI() are available to compute the confidence intervals for the estimates of willingness-to-pays (WTPs): krCI() implements simulations to construct empirical distributions of the WTP, while bootCI() carries out nonparametric bootstrapping (see the package DCchoice for details).
Although oohbchoice() has six arguments, a basic generic call to oohbchoice() is given as follows:
oohbchoice(formula, data, dist = "log-logistic")
The argument formula defines the response variables and covariates (see below for details on the formula). The argument data specifies the data frame containing the variables in the model. The argument dist sets the error distribution: one of "logistic", "normal", "log-logistic" (default value), "log-normal", or "weibull" is available. The difference between normal and log-normal models or between logistic or log-logistic ones is how the bid variable is incorporated into the model to be estimated. For the Weibull model, the bid variable must be entered in the natural log. Therefore, the user must be careful in defining the model formula that is explained in details below.
A typical structure of the formula for oohbchoice() is defined as follows:
R1 + R2 ~ (the names of the covariates) | BL + BH
The formula is an object of S3 class Formula and specifies the model structure. It has to be written in a symbolic expression in R. The formula consists of three parts as follows.
The first part, the left-hand side of the tilde sign (~), must contain the response variables for the suggested prices in the first and the second stage of CV questions. In the example below, R1 denotes a binary or two-level factor response variable for a bid in the first stage and R2 for a bid in the second stage. R1 contains yes or no to the bid in the first stage or 1 for yes and 0 for no. R2 contains yes, no, none to the bid in the second stage or 1 for yes, 0 for no, and -9 for none. The value of none (-9) means that the respondents have no second stage: the respondents are asked to answer the second stage question only if they satisfy either condition: (a) they answer yes in the first stage when the lower bid is shown in the first stage, or (b) they answer no in the first stage when the higher bid is shown in the first stage.
The covariates are defined in the second part of the formula in the place of (the names of the covariates). Each covariate is connected with the arithmetic operator + and (the names of the covariates) in the above syntax should be replaced with var1 + var2 and the like. The plus sign is nothing to do with addition of the two variables in the symbolic expression. When the covariate contains only a constant term, a value of 1 is set as the covariate: R1 + R2 ~ 1 | BL + BH (see the examples section below)
The last part of the formula starts after the vertical bar (|). The names of the two variables (BL and BH) containing suggested lower and higher prices in OOHBDC-CV question are specified in this part. The two variables are also connected with the arithmetic operator (+).
According to the structure of the formula, a data set (data frame) consists of three parts. An example of the data set (first six rows) is as follows (gender and age are respondents' characteristics and assumed to be covariates):
id |
R1 |
R2 |
gender |
age |
BL |
BH |
1 |
no |
none |
male |
51 |
2000 |
2500 |
2 |
yes |
no |
male |
30 |
500 |
1000 |
3 |
yes |
yes |
female |
25 |
500 |
1000 |
4 |
yes |
none |
male |
48 |
1000 |
1500 |
5 |
no |
yes |
male |
60 |
1000 |
1500 |
6 |
no |
no |
female |
34 |
2500 |
3000
|
Respondent 1 faced a bid range [2000, 2500]; respondents 2 and 3 faced a bid range [500, 1000]; respondents 4 and 5 faced a bid range [1000, 1500]; and respondent 6 faced [2500, 3000]. Respondent 1 answered no in the first stage of CV question and had no the second stage; respondent 2 answered yes and no in the first and second stage, respectively; respondent 3 answered yes and yes in the both stages; respondent 4 answered yes in the first stage and had no the second stage; respondent 5 answered no and yes in the first and second stage; and respondent 6 answered no in the both stages.
Note that BL and BH are NOT the first stage bid and the second stage bid, respectively. The function oohbchoice() understands which bids (BL and BH) are presented in the first stage and second stage, respectively, on the basis of values of variables R1 and R2.
Nonparametric analysis of OOHBDC-CV data can be done by turnbull.oohb.
The function returns an S3 class object oohbchoice, which inherits from the S3 class dbchoice. See dbchoice() for the details on the S3 object dbchoice.
We would like to thank Dr. Joseph C. Cooper and Dr. Giovanni Signorello for their kindness.
Cooper JC, Hanemann M, Signorello G (2002). “One-and-one-half-bound dichotomous choice contingent valuation”, The Review of Economics and Statistics, 84, 742–750.
Hanemann WM (1984). “Welfare Evaluations in Contingent Valuation Experiments with Discrete Responses”, American Journal of Agricultural Economics, 66(2), 332–341.
summary.dbchoice, oohbsyn, krCI, bootCI,
turnbull.oohb, Formula
## See oohbsyn.## See oohbsyn.
Dataset created artificially for the examples section of the function oohbhoice().
data(oohbsyn)data(oohbsyn)
A data frame with 80 observations on the following variables.
a vector of the identification number of the respondent.
a vector containing the gender of the respondent, taking male or female.
a vector containing the age of the respondent.
a vector of lower bid.
a vector of higher bid.
a vector of response to the first stage CV question, taking a value of 1 if the bid is accepted, and 0 otherwise.
a vector of response to the second stage CV question, taking a value of 1 if the bid is accepted, 0 if the bid is not accepted, and -9 if the respondent has no the second stage question.
## Parametric model data(oohbsyn) oohb1 <- oohbchoice(R1 + R2 ~ 1 | log(BL) + log(BH), data = oohbsyn) summary(oohb1) oohb2 <- oohbchoice(R1 + R2 ~ age + gender | log(BL) + log(BH), data = oohbsyn) summary(oohb2) ## Non-parametric model oohb3 <- turnbull.oohb(R1 + R2 ~ BL + BH, data = oohbsyn) summary(oohb3) plot(oohb3)## Parametric model data(oohbsyn) oohb1 <- oohbchoice(R1 + R2 ~ 1 | log(BL) + log(BH), data = oohbsyn) summary(oohb1) oohb2 <- oohbchoice(R1 + R2 ~ age + gender | log(BL) + log(BH), data = oohbsyn) summary(oohb2) ## Non-parametric model oohb3 <- turnbull.oohb(R1 + R2 ~ BL + BH, data = oohbsyn) summary(oohb3) plot(oohb3)
Plotting method for objects of class "dbchoice".
## S3 method for class 'dbchoice' plot(x, type = NULL, main = NULL, sub = NULL, xlab = NULL, ylab = NULL, lwd = NULL, lty = NULL, xlim = NULL, ylim = NULL, bid = NULL, ...)## S3 method for class 'dbchoice' plot(x, type = NULL, main = NULL, sub = NULL, xlab = NULL, ylab = NULL, lwd = NULL, lty = NULL, xlim = NULL, ylim = NULL, bid = NULL, ...)
x |
an object of class |
type |
type of plot. |
main |
the main title of the plot. If unspecified, no main title is displayed. |
sub |
the sub-title of the plot. If unspecified, no sub-title is displayed. |
xlab |
the x label of the plot. If missing, |
ylab |
the y label of the plot. If missing, |
lwd |
the line width for the plot. If missing, |
lty |
the line type for the plot. If missing, |
xlim |
the x limits of the plot. |
ylim |
the y limits of the plot. |
bid |
the bid limits should be drawn. If missing, the minimum and maximum values of the bid variable(s) in the original dataset is used. |
... |
optional arguments. |
The function plot() draws choice probabilities of yes according to
the range of bid (covariates are set on average). Choice probabilities are
calculated according to the relevant single-bounded dichotomous choice model.
## See Examples in dbchoice.## See Examples in dbchoice.
kristrom objects
Plotting method for objects of class "kristrom". The empirical survival curve
is plotted.
## S3 method for class 'kristrom' plot(x, main = NULL, sub = NULL, xlab = NULL, ylab = NULL, lwd = NULL, lty = NULL, ...)## S3 method for class 'kristrom' plot(x, main = NULL, sub = NULL, xlab = NULL, ylab = NULL, lwd = NULL, lty = NULL, ...)
x |
an object of class |
main |
the main title of the plot. If unspecified, no main title is displayed. |
sub |
the sub-title of the plot. If unspecified, no sub-title is displayed. |
xlab |
the x label of the plot. If missing, |
ylab |
the y label of the plot. If missing, |
lwd |
the line width for the plot. If missing, |
lty |
the line type for the plot. If missing, |
... |
optional arguments. Currently not in use. |
Plotting method for objects of class "sbchoice".
## S3 method for class 'sbchoice' plot(x, type = NULL, main = NULL, sub = NULL, xlab = NULL, ylab = NULL, lwd = NULL, lty = NULL, xlim = NULL, ylim = NULL, bid = NULL, ...)## S3 method for class 'sbchoice' plot(x, type = NULL, main = NULL, sub = NULL, xlab = NULL, ylab = NULL, lwd = NULL, lty = NULL, xlim = NULL, ylim = NULL, bid = NULL, ...)
x |
an object of class |
type |
type of plot. |
main |
the main title of the plot. If unspecified, no main title is displayed. |
sub |
the sub-title of the plot. If unspecified, no sub-title is displayed. |
xlab |
the x label of the plot. If missing, |
ylab |
the y label of the plot. If missing, |
lwd |
the line width for the plot. If missing, |
lty |
the line type for the plot. If missing, |
xlim |
the x limits of the plot. |
ylim |
the y limits of the plot. |
bid |
the bid limits should be drawn. If missing, the minimum and maximum values of the bid variable(s) in the original dataset is used. |
... |
optional arguments. |
The function plot() draws choice probabilities of yes according to
the range of bid (covariates are set on average).
## See Examples in sbchoice.## See Examples in sbchoice.
turnbull objects
Plotting method for objects of class "turnbull". The empirical survival curve and confidence interval (if computed) are plotted.
## S3 method for class 'turnbull' plot(x, main = NULL, sub = NULL, xlab = NULL, ylab = NULL, lwd = NULL, lty = NULL, plotCI = FALSE, ltyCI = 5, ...)## S3 method for class 'turnbull' plot(x, main = NULL, sub = NULL, xlab = NULL, ylab = NULL, lwd = NULL, lty = NULL, plotCI = FALSE, ltyCI = 5, ...)
x |
an object of class |
main |
the main title of the plot. If unspecified, no main title is displayed. |
sub |
the sub-title of the plot. If unspecified, no sub-title is displayed. |
xlab |
the x label of the plot. If missing, |
ylab |
the y label of the plot. If missing, |
lwd |
the line width for the plot. If missing, |
lty |
the line type for the plot. If missing, |
plotCI |
logical. If |
ltyCI |
a graphical parameter defining the line type of the confidence interval. By default, |
... |
optional arguments. Currently not in use. |
turnbull.sb, turnbull.db, summary.turnbull
Predicting method for objects of class "dbchoice".
## S3 method for class 'dbchoice' predict(object, newdata = NULL, type = c("utility", "probability"), bid = NULL, ...)## S3 method for class 'dbchoice' predict(object, newdata = NULL, type = c("utility", "probability"), bid = NULL, ...)
object |
an object of class "dbchoice". |
newdata |
a data frame containing new data to predict. If |
type |
type of prediction (utility or probability). |
bid |
a bid design needed to predict with original data. |
... |
optional arguments. Currently not in use. |
The function predict() for S3 object "dbchoice" calculates predicted values
according to the fitted model that is included in object. The values are
predicted with the original data used for fitting the model if newdata = NULL,
otherwise with a new data assigned to newdata. There are two notes for
dbchoice(): a bid design used for the fit must be assigned to bid,
when predicting with the original data; the predicted values are calculated according
to the relevant single-bounded dichotomous choice model, when predicting with a new
data. See examples for details.
The current function does not estimate standard errors of predicted values.
When newdata = NULL and type = utility, a matrix containing utility
values under first (f), second upper (u), and second lower (l) bids
is returned. When newdata = NULL and type = probability, a matrix
containing probabilities of choosing Yes-Yes (yy), No-No (nn), Yes-No (yn),
and No-Yes (ny) is returned. When a new data is assigned to newdata,
predictions are calculated according to the relevant single-bounded dichotomous choice
model, and a vector containing utility values of choosing yes (type = utility)
or probability of choosing yes (type = probability) is returned.
## See Examples in dbchoice.## See Examples in dbchoice.
Predicting method for objects of class "sbchoice".
## S3 method for class 'sbchoice' predict(object, newdata = NULL, type = c("utility", "probability"), ...)## S3 method for class 'sbchoice' predict(object, newdata = NULL, type = c("utility", "probability"), ...)
object |
an object of class "sbchoice". |
newdata |
a data frame containing new data to predict. If |
type |
type of prediction (utility or probability). |
... |
optional arguments. Currently not in use. |
The function predict() for S3 object "sbchoice" calculates predicted values
according to the fitted model that is included in object. The values are
predicted with the original data used for fitting the model if newdata = NULL,
otherwise with a new data assigned to newdata.
The current function does not estimate standard errors of predicted values.
When newdata = NULL and type = utility, a vector containing utility
values of choosing Yes under bid values is returned. When newdata = NULL
and type = probability, a vector containing probabilities of choosing Yes
is returned. When a new data is assigned to newdata, a vector containing
utility values of choosing Yes (type = utility) or probability of
choosing Yes (type = probability) under the new data is returned.
## See Examples in sbchoice.## See Examples in sbchoice.
This function analyzes single-bounded dichotomous choice contingent valuation (CV) data on the basis of the utility difference approach.
sbchoice(formula, data, subset, na.action = na.omit, dist = "log-logistic", ...) ## S3 method for class 'sbchoice' print(x, digits = max(3, getOption("digits") - 1), ...) ## S3 method for class 'sbchoice' vcov(object, ...) ## S3 method for class 'sbchoice' logLik(object, ...)sbchoice(formula, data, subset, na.action = na.omit, dist = "log-logistic", ...) ## S3 method for class 'sbchoice' print(x, digits = max(3, getOption("digits") - 1), ...) ## S3 method for class 'sbchoice' vcov(object, ...) ## S3 method for class 'sbchoice' logLik(object, ...)
formula |
an S3 class object |
data |
a data frame containing the variables in the model formula. |
subset |
an optional vector specifying a subset of observations. |
na.action |
a function which indicates what should happen when the data contains |
dist |
a character string setting the error distribution in the model, which takes one
of |
x |
an object of class |
digits |
a number of digits to display. |
object |
an object of class |
... |
optional arguments. Currently not in use. |
The function sbchoice() implements an analysis of single-bounded dichotomous choice
contingent valuation (CV) data on the basis of the utility difference approach
(Hanemann, 1984).
The extractor function summary() is available for a "sbchoice" class object.
Seesummary.sbchoice for details.
There are two functions available for computing the confidence intervals for the estimates of WTPs.
krCI implements simulations to construct empirical distributions of the WTP while
bootCI carries out nonparametric bootstrapping.
Most of the details of sbchoice() is the same as those of dbchoice(), a double-bounded
analogue of sbchoice. See the section Details in dbchoice. Differences between
the two functions are as follows:
In the model formula, the first part contains only one response variable (e.g., R1)
and the third part contains only one bid variable (e.g., BD1) because respondents are
requested to answer a CV question in the single-bounded dichotomous choice CV. The following
is a typical structure of the formula:R1 ~ (the names of the covariates) | BD1
The function sbchoice() analyzes the responses to single-bounded dichotomous choice CV
questions internally using the function glm() with the argument family = binomial(link = "logit")
orfamily = binomial(link = "probit").
When dist = "weibull", optimization is carried out using the optim() function
with a hard-coded log-likelihood function.
Outputs from sbchoice() are slightly different from those from dbchoice()
because the analysis in sbchoice() internally depends on the function glm()
for the (log-) normal or (log-) logistic distributions. (see the Value section).
Nonparametric analysis of single-bounded dichotomous choice data can be done by turnbull.sb
or by kristrom.
This function returns an object of S3 class "sbchoice" that is a list with the following components.
coefficients |
a named vector of estimated coefficients. |
call |
the matched call. |
formula |
the formula supplied. |
glm.out |
a list of components returned from |
glm.null |
a list of components returned from |
distribution |
a character string showing the error distribution used. |
nobs |
a number of observations. |
covariates |
a named matrix of the covariates used in the model. |
bid |
a named matrix of the bids used in the model. |
yn |
a named matrix of the responses to the CV question used in the model. |
data.name |
the data matrix. |
terms |
terms |
contrast |
contrasts used for factors |
xlevels |
levels used for factors |
Bateman IJ, Carson RT, Day B, Hanemann M, Hanley N, Hett T, Jones-Lee M, Loomes G, Mourato S, \"Ozdemiro\=glu E, Pearce DW, Sugden R, Swanson J (eds.) (2002). Economic Valuation with Stated Preference Techniques: A Manual. Edward Elger, Cheltenham, UK.
Boyle KJ, Welsh MP, Bishop RC (1988). “Validation of Empirical Measures of Welfare Change: Comment.” Land Economics, 64(1), 94–98.
Carson RT, Hanemann WM (2005). “Contingent Valuation.” in KG M\"aler, JR Vincent (eds.), Handbook of Environmental Economics. Elsevier, New York.
Croissant Y (2011). Ecdat: Data Sets for Econometrics, R package version 0.1-6.1, https://CRAN.R-project.org/package=Ecdat.
Hanemann, WM (1984). “Welfare Evaluations in Contingent Valuation Experiments with Discrete Responses”, American Journal of Agricultural Economics, 66(2), 332–341.
Hanemann M, Kanninen B (1999). “The Statistical Analysis of Discrete-Response CV Data.”, in IJ Bateman, KG Willis (eds.), Valuing Environmental Preferences: Theory and Practice of the Contingent Valuation Methods in the US, EU, and Developing Countries, 302–441. Oxford University Press, New York.
summary.sbchoice,
krCI, bootCI,
NaturalPark,
turnbull.sb, kristrom
glm, formula
dbchoice
## Examples for sbchoice() 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 sbchoice() as follows: NaturalPark$R1 <- ifelse(substr(NaturalPark$answers, 1, 1) == "y", 1, 0) NaturalPark$R2 <- ifelse(substr(NaturalPark$answers, 2, 2) == "y", 1, 0) ## We assume that the error distribution in the model is a log-logistic; ## therefore, the bid variables bid1 is converted into LBD1 as follows: NaturalPark$LBD1 <- log(NaturalPark$bid1) ## The utility difference function is assumed to contain covariates ## (sex, age, and income) as well as the bid variable (LBD1) as follows ## (R2 is not used because of single-bounded dichotomous choice CV format): fmsb <- R1 ~ sex + age + income | LBD1 ## Not run: ## The formula may be alternatively defined as fmsb <- R1 ~ sex + age + income | log(bid1) ## End(Not run) ## The function sbchoice() with the function fmsb and the data frame NP ## is executed as follows: NPsb <- sbchoice(fmsb, data = NaturalPark) NPsb NPsbs <- summary(NPsb) NPsbs ## Not run: ## Generic functions such as summary() and coefficients() work for glm.out summary(NPsb$glm.out) coefficients(NPsb$glm.out) ## The confidence intervals for these WTPs are calculated using the ## function krCI() or bootCI() as follows: krCI(NPsb) bootCI(NPsb) ## The WTP of a female with age = 5 and income = 3 is calculated ## using function krCI() or bootCI() as follows: krCI(NPsb, individual = data.frame(sex = "female", age = 5, income = 3)) bootCI(NPsb, individual = data.frame(sex = "female", age = 5, income = 3)) ## End(Not run) ## The variable age and income are deleted from the fitted model, ## and the updated model is fitted as follows: update(NPsb, .~. - age - income |.) ## Respondents' utility and probability of choosing Yes under ## the fitted model and original data are predicted as follows: head(predict(NPsb, type = "utility")) head(predict(NPsb, type = "probability")) ## Utility and probability of choosing Yes for a female with age = 5 ## and income = 3 under bid = 10 are predicted as follows: predict(NPsb, type = "utility", newdata = data.frame(sex = "female", age = 5, income = 3, LBD1 = log(10))) predict(NPsb, type = "probability", newdata = data.frame(sex = "female", age = 5, income = 3, LBD1 = log(10))) ## Plot of probabilities of choosing yes is drawn as drawn as follows: plot(NPsb) ## The range of bid can be limited (e.g., [log(10), log(20)]): plot(NPsb, bid = c(log(10), log(20)))## Examples for sbchoice() 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 sbchoice() as follows: NaturalPark$R1 <- ifelse(substr(NaturalPark$answers, 1, 1) == "y", 1, 0) NaturalPark$R2 <- ifelse(substr(NaturalPark$answers, 2, 2) == "y", 1, 0) ## We assume that the error distribution in the model is a log-logistic; ## therefore, the bid variables bid1 is converted into LBD1 as follows: NaturalPark$LBD1 <- log(NaturalPark$bid1) ## The utility difference function is assumed to contain covariates ## (sex, age, and income) as well as the bid variable (LBD1) as follows ## (R2 is not used because of single-bounded dichotomous choice CV format): fmsb <- R1 ~ sex + age + income | LBD1 ## Not run: ## The formula may be alternatively defined as fmsb <- R1 ~ sex + age + income | log(bid1) ## End(Not run) ## The function sbchoice() with the function fmsb and the data frame NP ## is executed as follows: NPsb <- sbchoice(fmsb, data = NaturalPark) NPsb NPsbs <- summary(NPsb) NPsbs ## Not run: ## Generic functions such as summary() and coefficients() work for glm.out summary(NPsb$glm.out) coefficients(NPsb$glm.out) ## The confidence intervals for these WTPs are calculated using the ## function krCI() or bootCI() as follows: krCI(NPsb) bootCI(NPsb) ## The WTP of a female with age = 5 and income = 3 is calculated ## using function krCI() or bootCI() as follows: krCI(NPsb, individual = data.frame(sex = "female", age = 5, income = 3)) bootCI(NPsb, individual = data.frame(sex = "female", age = 5, income = 3)) ## End(Not run) ## The variable age and income are deleted from the fitted model, ## and the updated model is fitted as follows: update(NPsb, .~. - age - income |.) ## Respondents' utility and probability of choosing Yes under ## the fitted model and original data are predicted as follows: head(predict(NPsb, type = "utility")) head(predict(NPsb, type = "probability")) ## Utility and probability of choosing Yes for a female with age = 5 ## and income = 3 under bid = 10 are predicted as follows: predict(NPsb, type = "utility", newdata = data.frame(sex = "female", age = 5, income = 3, LBD1 = log(10))) predict(NPsb, type = "probability", newdata = data.frame(sex = "female", age = 5, income = 3, LBD1 = log(10))) ## Plot of probabilities of choosing yes is drawn as drawn as follows: plot(NPsb) ## The range of bid can be limited (e.g., [log(10), log(20)]): plot(NPsb, bid = c(log(10), log(20)))
These functions implement a simple spike model analysis of single-, one-and-one-half-, and double-bounded dichotomous choice contingent valuation data using the maximum likelihood method.
## for the single-bounded data sbspike(formula, data, subset, na.action = na.omit, par = NULL, ...) ## for the one-and-one-half-bounded data oohbspike(formula, data, subset, na.action = na.omit, par = NULL, ...) ## for the double-bounded data dbspike(formula, data, subset, na.action = na.omit, par = NULL, ...) ## S3 method for class 'spike' print(x, digits = max(3, getOption("digits") - 1), ...) ## S3 method for class 'spike' summary(object, ...) ## S3 method for class 'summary.spike' print(x, digits = max(3, getOption("digits") - 1), ...) ## S3 method for class 'spike' logLik(object, ...) ## S3 method for class 'spike' vcov(object, ...) ## S3 method for class 'spike' plot(x, type = "l", main = NULL, sub = NULL, xlab = "Bid", ylab = "Probability", lwd = 3, lty = 1, xlim = c(0, max(x$bid)), ylim = c(0, 1), bid = c(0, max(x$bid)), ...)## for the single-bounded data sbspike(formula, data, subset, na.action = na.omit, par = NULL, ...) ## for the one-and-one-half-bounded data oohbspike(formula, data, subset, na.action = na.omit, par = NULL, ...) ## for the double-bounded data dbspike(formula, data, subset, na.action = na.omit, par = NULL, ...) ## S3 method for class 'spike' print(x, digits = max(3, getOption("digits") - 1), ...) ## S3 method for class 'spike' summary(object, ...) ## S3 method for class 'summary.spike' print(x, digits = max(3, getOption("digits") - 1), ...) ## S3 method for class 'spike' logLik(object, ...) ## S3 method for class 'spike' vcov(object, ...) ## S3 method for class 'spike' plot(x, type = "l", main = NULL, sub = NULL, xlab = "Bid", ylab = "Probability", lwd = 3, lty = 1, xlim = c(0, max(x$bid)), ylim = c(0, 1), bid = c(0, max(x$bid)), ...)
formula |
an object of S3 class |
data |
a data frame containing the variables in the model formula. |
subset |
an optional vector specifying a subset of observations. |
na.action |
a function which indicates what should happen when the data contains |
par |
a vector of initial parameters over which the optimization is carried out. |
x, object
|
an object of class |
digits |
the number of digits to display. |
type |
type of plot. |
main |
the main title of the plot. If unspecified, no main title is displayed. |
sub |
the sub-title of the plot. If unspecified, no sub-title is displayed. |
xlab |
the x label of the plot. The default is |
ylab |
the y label of the plot. The default is |
lwd |
the line width for the plot. The default is |
lty |
the line type for the plot. The default is |
xlim |
the x limits of the plot. The default is |
ylim |
the y limits of the plot. The default is |
bid |
the bid limits that should be drawn. The default is |
... |
optional arguments. |
The functions sbspike, oohbspike, and dbspike implement a spike model analysis of single-, one-and-one-half-, and double-bounded dichotomous choice contingent valuation (SB, OOHB, and DB DCCV) data, respectively. A simple spike model assumes a non-zero probability of zero willingness to pay (WTP) for a good/service and a zero probability of negative WTP. These functions are developed according to the original simplest spike model proposed by Kristr\"om (1997) and its follow-up studies (i.e., Yoo and Kwak (2002) for DB DCCV and Kwak et al. (2013) for OOHB DCCV). These functions use a maximum likelihood methods to fit the models with the CV data.
Since the usage of spike model functions sbspike, oohbspike, and dbspike are similar to the un-spike (the ordinary) DCCV model functions sbchoice, oohbchoice, and dbchoice, respectively, this help below explains only the differences in usage between the spike and ordinary model functions. We assume that you understand how to use the ordinary model functions sbchoice, oohbchoice, and dbchoice. If you are unfamiliar with the ordinary model functions, please refer to helps for these at first.
The first difference between the spike and ordinal model functions is that an argument distribution used in the ordinary model functions is not defined in the spike functions: the functions for spike models assume that the error distribution is only a logistic with a spike, and thus the other distributions (i.e., log-logistic, normal, log-normal, and Weibull) are not available to the spike model functions.
The other difference is about an argument formula, which is assigned an object of the S3 class 'Formula'. For a model formula for the ordinary model functions, the left-handed side of the tilde (~) contains only response variable(s) (i.e., the response to SB DCCV question, R1, for sbchoice; the response to the first stage of OOHB/DB DCCV question, R1, and the second one, R2, for oohbchoice and dbchoice), while it contains both the response variable(s) and spike variable for the spike model functions. The spike variable, S, which must be set in the second part (after the vertical bar [|]) of the left-handed side of the tilde, takes the value of 1 if the respondent has a positive WTP for a good specified in the DCCV question and 0 otherwise. See Kristr\"om (1997) for a question to measure whether the respondent has a positive WTP or not. A typical structure of the formula for spike model functions consists of the following four parts:
for sbspike(),
R1 | S ~ <the names of the covariates> | BD1
for dbspike(),
R1 + R2 | S ~ <the names of the covariates> | BD1 + BD2
and for oohbspike(),
R1 + R2 | S ~ <the names of the covariates> | BL + BH
where BD1 and BD2 are variables containing suggested prices in the first and second stages of the SB/DB DCCV question; and BL and BH are variables containing suggested lower and higher prices in the OOHB DCCV question.
According to the structure of the formula, a data set (data frame) consists of four parts. An example of the data set for dbspike is as follows (sex, age, and income are respondent characteristics and assumed to be covariates):
R1 |
R2 |
S |
sex |
age |
income |
BD1 |
BD2
|
Yes |
Yes |
1 |
Male |
20 |
Low |
100 |
250
|
Yes |
No |
0 |
Male |
30 |
Low |
500 |
1000
|
| ... |
The spike model functions fit the models with DCCV data using the function optim on the basis of the initial coefficients estimated from an un-spike (ordinary) binary logit model analysis of the response to the SB DCCV question, or the first-stage response to the OOHB/DB DCCV question. The binary logit model is estimated internally using the function glm with the argument family = binomial(link = "logit").
The spike model functions return an S3 'spike' class object. Various methods for the S3 "spike" class object are provided as follows: print() displays estimated coefficients; summary() extracts detailed information on the fitted model; summary.print() displays information extracted by summary(); logLik() extracts the value of a log-likelihood function at estimates; vcov() returns the variance-covariance matrix of the fitted model; and plot() draws an estimated survival distribution of the WTP according to the fitted model. These S3 methods correspond to those for the ordinary DCCV functions sbchoice, oohbchoice, and dbchoice. Therefore, for details, see helps for the corresponding methods for ordinary DCCV functions. Note that the mean and median WTPs calculated by summary() for the spike model functions are defined as follows (see Kristr\"om 1997): mean WTP = ln(1 + exp(A))/B if the parameter for a bid variable (B) is positive (A is the constant), and NA otherwise; median WTP = A/B if 1/(1 + exp(-A)) < 0.5, and 0 otherwise. When covariates are included in the fitted model, the constant in the mean and median WTPs is replaced with x'b, where x is a row vector of covariates at the sample mean including the value of 1 for the constant, and b is a column vector of estimates for covariates including the constant. See Yoo and Kwak (2009), Kwak et al. (2013), and Lee et al. (2010) for SB, OOHB, and DB spike models with covariates, respectively.
The existing functions bootCI and krCI, which compute the confidence intervals for the estimates of WTPs using non-parametric and parametric bootstrapping approaches respectively, were revised to handle an S3 'spike' class object. An existing function ct2df was also updated to handle a data set in contingency-table format for spike model functions.
Furthermore, a new function spikeCoef was developed to estimate a spike for the fitted model as 1/(1 + exp(A)), where A is the constant. This function returns the estimated spike, its standard error, and the corresponding z- and p-values under the null hypothesis where the spike is zero. The standard error is calculated using the delta method. When covariates are included in the fitted model, the constant in the formula is replaced with x'b as the mean and median WTP calculations. See the examples below, for details.
These spike model functions return an S3 class object 'spike', which is a list with the following components.
f.stage |
a list of components returned from the un-spike (ordinary) binary logit mode analysis using the function |
optim.out |
a list of components returned from the function |
coefficients |
a named vector of estimated coefficients. |
call |
the matched call. |
formula |
the formula supplied. |
Hessian |
an estimate of the Hessian. See also Hessian in |
loglik |
a value of the log likelihood at the estimates. |
convergence |
a logical code: |
niter |
a vector of two integers describing the number of calls to the object function and numerical gradient, respectively. See also counts in |
nobs |
a number of observations. |
covariates |
a named matrix of the covariates used in the model. |
bid |
a named matrix of the bids used in the model. |
yn |
a named matrix of the responses to the SB DCCV question or the first and second stage of the OOHB/DB DCCV question used in the model. |
data.name |
the data matrix. |
terms |
terms. |
contrast |
contrasts used for factors. |
xlevels |
levels used for factors. |
Kristr\"om B. (1997) Spike models in contingent valuation. American Journal of Agricultural Economics 79: 1013–1023.
Yoo S-H, Kwak S-J. (2002) Using a spike model to deal with zero response data from double bounded dichotomous choice contingent valuation surveys. Applied Economics Letters 9: 929–932.
Kwak S-J, Yoo S-H, Kim C-S. (2013) Measuring the willingness to pay for tap water quality improvements: results of a contingent valuation survey in Pusan. Water 5: 1638–1652.
Lee J-S, Yoo S-H, Kwak S-J. (2010) Public's willingness to pay for preventing climate change. Applied Economics Letters 17: 619–622.
Yoo S-H, Kwak S-Y. (2009) Willingness to pay for green electricity in Korea: a contingent valuation study. Energy Policy 37: 5408–5416.
sbchoice, oohbchoice, dbchoice,
ct2df, krCI, bootCI,
CarsonSB, CarsonDB, oohbsyn,
glm, optim,
Formula
# Example datasets were created by modifying CarsonSB, CarsonDB, and oohbsyn. # Spike SB Example sb <- data.frame( bid = c(10, 30, 60, 120), y = c(178, 138, 129, 88), ny = c(56, 45, 50, 76), nn = c(30, 84, 76, 93)) SB <- ct2df(sb, bid1 = "bid", type = "single", spike = TRUE) head(SB) dim(SB) SBout <- sbspike(R1 | S ~ 1 | bid1, data = SB) summary(SBout) spikeCoef(SBout) ## Not run: krCI(SBout) bootCI(SBout) ## End(Not run) plot(SBout, main = "Spike SB model") # Spike DB Example db <- data.frame( bidh = c(30, 60, 120), bid1 = c(10, 30, 60), bidl = c(5, 10, 30), yy = c(119, 69, 54), yn = c(59, 69, 75), ny = c(8, 31, 25), nny = c(47, 61, 35), nnn = c(31, 37, 66)) DB <- ct2df(x = db, type = "double", spike = TRUE) head(DB) dim(DB) DBout <- dbspike(R1 + R2 | S ~ 1 | bid1 + bid2, data = DB) summary(DBout) spikeCoef(DBout) ## Not run: krCI(DBout) bootCI(DBout) ## End(Not run) plot(DBout, main = "Spike DB model") # Spike OOHB Example oohb <- data.frame( bidl = c(2, 4, 6, 8), bidh = c(4, 6, 8, 10), yy = c(8, 6, 4, 2), yn = c(1, 3, 1, 1), n_y = c(1, 1, 4, 4), n_n = c(0, 1, 1, 3), y = c(7, 6, 3, 1), ny = c(2, 2, 3, 1), nn_y = c(1, 1, 2, 5), nn_n = c(0, 0, 2, 3)) OOHB <- ct2df(x = oohb, type = "oohb", spike = TRUE) head(OOHB) dim(OOHB) OOHBout <- oohbspike(R1 + R2 | S ~ 1 | BL + BH, data = OOHB) summary(OOHBout) spikeCoef(OOHBout) ## Not run: krCI(OOHBout) bootCI(OOHBout) ## End(Not run) plot(OOHBout, main = "Spike OOHB model")# Example datasets were created by modifying CarsonSB, CarsonDB, and oohbsyn. # Spike SB Example sb <- data.frame( bid = c(10, 30, 60, 120), y = c(178, 138, 129, 88), ny = c(56, 45, 50, 76), nn = c(30, 84, 76, 93)) SB <- ct2df(sb, bid1 = "bid", type = "single", spike = TRUE) head(SB) dim(SB) SBout <- sbspike(R1 | S ~ 1 | bid1, data = SB) summary(SBout) spikeCoef(SBout) ## Not run: krCI(SBout) bootCI(SBout) ## End(Not run) plot(SBout, main = "Spike SB model") # Spike DB Example db <- data.frame( bidh = c(30, 60, 120), bid1 = c(10, 30, 60), bidl = c(5, 10, 30), yy = c(119, 69, 54), yn = c(59, 69, 75), ny = c(8, 31, 25), nny = c(47, 61, 35), nnn = c(31, 37, 66)) DB <- ct2df(x = db, type = "double", spike = TRUE) head(DB) dim(DB) DBout <- dbspike(R1 + R2 | S ~ 1 | bid1 + bid2, data = DB) summary(DBout) spikeCoef(DBout) ## Not run: krCI(DBout) bootCI(DBout) ## End(Not run) plot(DBout, main = "Spike DB model") # Spike OOHB Example oohb <- data.frame( bidl = c(2, 4, 6, 8), bidh = c(4, 6, 8, 10), yy = c(8, 6, 4, 2), yn = c(1, 3, 1, 1), n_y = c(1, 1, 4, 4), n_n = c(0, 1, 1, 3), y = c(7, 6, 3, 1), ny = c(2, 2, 3, 1), nn_y = c(1, 1, 2, 5), nn_n = c(0, 0, 2, 3)) OOHB <- ct2df(x = oohb, type = "oohb", spike = TRUE) head(OOHB) dim(OOHB) OOHBout <- oohbspike(R1 + R2 | S ~ 1 | BL + BH, data = OOHB) summary(OOHBout) spikeCoef(OOHBout) ## Not run: krCI(OOHBout) bootCI(OOHBout) ## End(Not run) plot(OOHBout, main = "Spike OOHB model")
dbchoice estimation
Summary method for objects of class "dbchoice".
## S3 method for class 'dbchoice' summary(object, ...) ## S3 method for class 'summary.dbchoice' print(x, digits = max(3, getOption("digits") - 1), ...)## S3 method for class 'dbchoice' summary(object, ...) ## S3 method for class 'summary.dbchoice' print(x, digits = max(3, getOption("digits") - 1), ...)
object |
an object of class |
x |
an object of class |
digits |
a number of digits to display. |
... |
optional arguments. Currently not in use. |
The function summary.dbchoice() computes and returns a list of summary
statistics of the fitted model in object of the "dbchoice" class.
Some of the values are printed up to certain decimal places. Actual values of
individual components are displayed separately, for instance, by summary(object)$coefficients.
See the Value section for a list of components.
In addition to those available in the object of the "dbchoice" class,
the following list components are added.
medianWTP |
the estimated median WTP. |
meanWTP |
the estimated mean WTP. |
trunc.meanWTP |
the estimated mean WTP truncated at the maximum bid. |
adj.trunc.meanWTP |
the truncated mean WTP with the adjustment of Boyle et~al.(1988). |
LR.test |
a vector containing the likelihood ratio test statistic, the degrees of freedom and the associated p-value. The null is that all the parameters on the explanatory variables other than constant and the bid variable are jointly zero. |
coef |
a table of estimates including their s.e., z-value, and p-value. |
AIC |
information criterion (AIC and BIC). |
Boyle KJ, Welsh MP, Bishop RC (1988). “Validation of Empirical Measures of Welfare Change: Comment.” Land Economics, 64(1), 94–98.
Summary method for objects of class "kristrom".
## S3 method for class 'kristrom' summary(object, digits = max(3, getOption("digits") - 1), ...) ## S3 method for class 'summary.kristrom' print(x, digits = max(3, getOption("digits") - 1), ...)## S3 method for class 'kristrom' summary(object, digits = max(3, getOption("digits") - 1), ...) ## S3 method for class 'summary.kristrom' print(x, digits = max(3, getOption("digits") - 1), ...)
object |
an object of class |
x |
an object of class |
digits |
a number of digits to display. |
... |
optional arguments. Currently not in use. |
plot.kristrom, kristrom,
NaturalPark, sbchoice
sbchoice estimation
Summary method for objects of class sbchoice.
## S3 method for class 'sbchoice' summary(object, ...) ## S3 method for class 'summary.sbchoice' print(x, digits = max(3, getOption("digits") - 1), ...)## S3 method for class 'sbchoice' summary(object, ...) ## S3 method for class 'summary.sbchoice' print(x, digits = max(3, getOption("digits") - 1), ...)
object |
an object of class |
x |
an object of class |
digits |
a number of digits to display. |
... |
optional arguments. Currently not in use. |
The function summary.sbchoice() computes and returns a list of summary
statistics of the fitted model in object of the "sbchoice" class.
Some of the values are printed up to certain decimal places. Actual values of
individual components are displayed separately, for instance, by summary(object)$coefficients.
See the Value section for a list of components.
Since the model for the single-bounded dichotomous choice CV data is estimated by glm,
an object of class"summary.sbchoice" is constructed based on a "summary.glm"
class object. The summary of the "summary.glm" class object is available by
summary(object)$glm.summary. Other components computed by
summary.glm are also accessible. See summary.glm
for details.
In addition to those available in the object of the "sbchoice" class,
the following list components are added.
glm.summary |
a summary of the |
glm.null.summary |
a summary of the |
loglik |
the value of the log-likelihood of the model. |
loglik.null |
the value of the log-likelihood of the null model. |
psdR2 |
McFadden's pseudo-R2 measure. |
adjpsdR2 |
McFadden's pseudo-R2 measure adjusted for the degrees of freedom. |
medianWTP |
the estimated median WTP. |
meanWTP |
the estimated mean WTP. |
trunc.meanWTP |
the estimated mean WTP truncated at the maximum bid. |
adj.trunc.meanWTP |
the truncated mean WTP with the adjustment of Boyle et~al.(1988). |
LR.test |
a vector containing the likelihood ratio test statistic, the degrees of freedom and the associated p-value. |
AIC |
information criterion (AIC and BIC). |
Boyle KJ, Welsh MP, Bishop RC (1988). “Validation of Empirical Measures of Welfare Change: Comment.” Land Economics, 64(1), 94–98.
Summary method for objects of class "turnbull".
## S3 method for class 'turnbull' summary(object, printCI = TRUE, ...) ## S3 method for class 'summary.turnbull' print(x, digits = max(3, getOption("digits") - 1), ...)## S3 method for class 'turnbull' summary(object, printCI = TRUE, ...) ## S3 method for class 'summary.turnbull' print(x, digits = max(3, getOption("digits") - 1), ...)
object |
an object of class |
printCI |
an argument controlling whether the summary of confidence interval estimates are printed. The CIs are not summarized and printed unless |
x |
an object of class |
digits |
a number of digits to display. |
... |
optional arguments. Currently not in use. |
This function analyzes single-, one-and-one-half-, or double-bounded dichotomous choice contingent valuation (CV) data on the basis of the Kaplan-Meier-Turnbull method.
## for the single-bounded data turnbull.sb(formula, data, subset, conf.int = FALSE, B = 200, conf.level = 0.95, timeMessage = FALSE, seed = 19439101, ...) ## for the one-and-one-half-bound data turnbull.oohb(formula, data, subset, conf.int = FALSE, B = 200, conf.level = 0.95, timeMessage = FALSE, seed = 19439101, ...) ## for the double-bounded data turnbull.db(formula, data, subset, conf.int = FALSE, B = 200, conf.level = 0.95, timeMessage = FALSE, seed = 19439101, ...) ## S3 method for class 'turnbull' print(x, digits = max(3, getOption("digits") - 1), ...)## for the single-bounded data turnbull.sb(formula, data, subset, conf.int = FALSE, B = 200, conf.level = 0.95, timeMessage = FALSE, seed = 19439101, ...) ## for the one-and-one-half-bound data turnbull.oohb(formula, data, subset, conf.int = FALSE, B = 200, conf.level = 0.95, timeMessage = FALSE, seed = 19439101, ...) ## for the double-bounded data turnbull.db(formula, data, subset, conf.int = FALSE, B = 200, conf.level = 0.95, timeMessage = FALSE, seed = 19439101, ...) ## S3 method for class 'turnbull' print(x, digits = max(3, getOption("digits") - 1), ...)
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 |
conf.int |
logical. If |
B |
number of bootstrap resampling for confidence interval estimation. Defaulted to 200. |
conf.level |
a confidence coefficient. Defaulted to 0.95. |
timeMessage |
logical. If |
digits |
a number of digits to display. |
seed |
a seed for a random number generator. |
... |
optional arguments. Currently not in use. |
The functions turnbull.sb(), turnbull.oohb(), and turnbull.db() analyze single-,
one-and-one-half-, and double-bounded dichotomous choice contingent valuation (CV) data, respectively, on
the basis of the modified Kaplan-Meier-Turnbull method (Carson and Steinberg, 1990).
For single-bounded dichotomous choice data
Most of the details of turnbull.sb() is the same as those of turnbull.db().
See the subsequent section for details.
A difference between turnbull.sb() and turnbull.db() appears in the
definition of the model formula. In turnbull.sb(), the first part contains
only one response variable (e.g., R1) and the other part contains only one
bid variable (e.g., BD1) because respondents are requested to answer a CV
question in the single-bounded dichotomous choice CV. A typical structure of the
formula is given by
R1 ~ BD1
kristrom is an alternative nonparametric method for analyzing single-bounded
dichotomous choice data. A parametric analysis can be done by sbchoice.
For one-and-one-half-bound dichotomous choice data
The details of turnbull.oohb() is the same as those of turnbull.db().
See the the subsequent section for details.
A difference between turnbull.oohb() and turnbull.db() appears in the
definition of variables. See oohbchoice and oohbsyn
for the details of creating response and bid variables.
For double-bounded dichotomous choice data
A generic call to turnbull.db() is given by
turnbull.db(formula, data)
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 turnbull.db() is defined as follows:
R1 + R2 ~ BD1 + BD2
The formula consists of two parts. The first part, the left-hand side of the
tilde sign (~), must contain the response variables for the suggested
prices in the first and the second stage of CV questions. In the above example,
R1 denotes a binary or two-level factor response variable for a bid in
the first stage and R2 for a bid in the second stage. Each of R1
and R2 contains "Yes" or "No" to the bid or 1 for
"Yes" and 0 for "No".
The two variables are connected with the arithmetic operator (+). The other
part, which starts after the tilde sign, must contain bid variables (BD1,
BD2) containing suggested prices in the first and second stage of double-bounded
dichotomous choice CV question. The two variables are also connected with the
arithmetic operator (+).
A parametric approach for analyzing double-bounded dichotomous choice data can be
carried out by dbchoice.
The structure of data set which assigned to the argument data is the same as that
of dbchoice(). See dbchoice for details in the data set structure.
The confidence intervals are computed by the bootstrap method in icfit of the interval (Fay and Shaw, 2010) package. The arguments conf.int, B, conf.level and timeMessage are passed to icfit(). The bootstrap can be time consuming, so that it is in general not advisable to increase the number of bootstrap resamplint B. See the help of icfit for futher detail.
The generic function print() is available for a fitted model object
of class "turnbull" and displays simply estimated probabilities of
the distribution: this is the same as the element pf in the function
icfit of the interval (Fay and Shaw, 2010) package.
The extractor function summary() is also available for a fitted model
object of class "turnbull" and the generic function print.summary()
displays the survival probability and three types of WTP estimates (a Kaplan-Meier mean,
a Spearman-Karber mean, and median WTPs). In estimating the two types of mean WTP,
the area under the survivor function is truncated at the maximum bid because
there seems no unified approach to determine an ending point of bids at which
the acceptance probability is zero. Therefore, we leave the decision of how
the area is treated to the user. In practice, once the ending point,
$bid_end$, is found, it is straightforward to compute the triangular
area by $0.5(bid_end - bid_max)P_max$ where $bid_max$ is
the maximum bid and $P_max$ is the acceptance probability for
$bid_max$, both of which are reported in the summarized output.
Furthermore, the generic function plot() is available for a fitted model object
of class "turnbull" and displays the empirical survival function. See
plot.turnbull for details.
Both turnbull.db() and turnbull.sb() return an object of S3 class
"turnbull" that is a list with the following components.
left |
a vector of left endpoints of censored interval. The vector is
internally assigned to the argument |
right |
a vector of right endpoints of censored interval. The vector is
internally assigned to the argument |
turnbull |
a list of components returned from |
unq.dib |
a vector of unique bids including Inf. |
CI |
estimates for confidence intervals from |
Croissant Y (2011). Ecdat: Data Sets for Econometrics, R package version 0.1-6.1, https://CRAN.R-project.org/package=Ecdat.
Fay MP, Shaw PA (2010). “Exact and Asymptotic Weighted Logrank Tests for Interval Censored Data: The interval R Package”, Journal of Statistical Software, 36(2), 1-34. https://www.jstatsoft.org/v36/i02/.
Krinsky I, Robb AL (1986). “On Approximating the Statistical Properties of Elasticities.” The Review of Economics and Statistics, 68, 715–719.
Krinsky I, Robb AL (1990). “On Approximating the Statistical Properties of Elasticities: A Correction.” The Review of Economics and Statistics, 72, 189–190.
Turnbull BW (1976). “The Empirical Distribution Function with Arbitrarily Grouped, Censored and Truncated Data.” Journal of the Royal Statistical Society. Series B, 38(3), 290–295.
summary.turnbull, plot.turnbull, kristrom,
sbchoice, dbchoice, NaturalPark, glm,
icfit
## Examples are based on turnbull.db(). turnbull.sb() is similarly ## implemented. A difference appears in the definition of the model ## formula. See "Details" section of the help. ## A data set used here is NaturalPark in the package Ecdat (Croissant, ## 2011): double-bounded dichotomous choice CV style question for ## measuring willingness to pay for the preservation of the Alentejo ## Natural Park. The data frame contains seven variables: bid1 (bid in ## the initial question), bidh (higher bid in the follow-up question), ## bidl (lower bid in the follow-up question), answers (response ## outcomes in a factor format with four levels of "nn", "ny", "yn", "yy"), ## respondents' characteristic variables such as age, sex and income (see ## NaturalPark for details). data(NaturalPark, package = "Ecdat") ## The variable answers are converted into a format that is suitable for ## the function turnbull.db() as follows: NaturalPark$R1 <- ifelse(substr(NaturalPark$answers, 1, 1) == "y", 1, 0) NaturalPark$R2 <- ifelse(substr(NaturalPark$answers, 2, 2) == "y", 1, 0) ## The variables bidh and bidl are integrated into one variable (bid2) ## as follows: NaturalPark$bid2 <- ifelse(NaturalPark$R1 == 1, NaturalPark$bidh, NaturalPark$bidl) ## The formula for turnbull.sb and turnbull.db are defined respectively as follows: fmts <- R1 ~ bid1 fmtd <- R1 + R2 ~ bid1 + bid2 ## The function turnbull.db() with the formula fmtd and the data frame ## NaturalPark is executed as follows: NPts <- turnbull.sb(fmts, data = NaturalPark) NPts NPtss <- summary(NPts) NPtss plot(NPts) ## The function turnbull.db() with the formula fmtd and the data frame ## NaturalPark is executed as follows: NPtd <- turnbull.db(fmtd, data = NaturalPark) NPtd NPtds <- summary(NPtd) NPtds plot(NPtd)## Examples are based on turnbull.db(). turnbull.sb() is similarly ## implemented. A difference appears in the definition of the model ## formula. See "Details" section of the help. ## A data set used here is NaturalPark in the package Ecdat (Croissant, ## 2011): double-bounded dichotomous choice CV style question for ## measuring willingness to pay for the preservation of the Alentejo ## Natural Park. The data frame contains seven variables: bid1 (bid in ## the initial question), bidh (higher bid in the follow-up question), ## bidl (lower bid in the follow-up question), answers (response ## outcomes in a factor format with four levels of "nn", "ny", "yn", "yy"), ## respondents' characteristic variables such as age, sex and income (see ## NaturalPark for details). data(NaturalPark, package = "Ecdat") ## The variable answers are converted into a format that is suitable for ## the function turnbull.db() as follows: NaturalPark$R1 <- ifelse(substr(NaturalPark$answers, 1, 1) == "y", 1, 0) NaturalPark$R2 <- ifelse(substr(NaturalPark$answers, 2, 2) == "y", 1, 0) ## The variables bidh and bidl are integrated into one variable (bid2) ## as follows: NaturalPark$bid2 <- ifelse(NaturalPark$R1 == 1, NaturalPark$bidh, NaturalPark$bidl) ## The formula for turnbull.sb and turnbull.db are defined respectively as follows: fmts <- R1 ~ bid1 fmtd <- R1 + R2 ~ bid1 + bid2 ## The function turnbull.db() with the formula fmtd and the data frame ## NaturalPark is executed as follows: NPts <- turnbull.sb(fmts, data = NaturalPark) NPts NPtss <- summary(NPts) NPtss plot(NPts) ## The function turnbull.db() with the formula fmtd and the data frame ## NaturalPark is executed as follows: NPtd <- turnbull.db(fmtd, data = NaturalPark) NPtd NPtds <- summary(NPtd) NPtds plot(NPtd)
Updating and refitting method for object of class "dbchoice".
## S3 method for class 'dbchoice' update(object, new, evaluate = TRUE, ...)## S3 method for class 'dbchoice' update(object, new, evaluate = TRUE, ...)
object |
an object of class "dbchoice". |
new |
a new call. |
evaluate |
If |
... |
optional arguments. Currently not in use. |
The function update() for S3 object "dbchoice" updates a model used for
the fit that is included in object according to a new call assigned to
new, and then refits the updated model. The function returns the refitted
model object when evaluate = TRUE, otherwise the updated model call.
## See Examples in dbchoice.## See Examples in dbchoice.
Updating and refitting method for object of class "sbchoice".
## S3 method for class 'sbchoice' update(object, new, evaluate = TRUE, ...)## S3 method for class 'sbchoice' update(object, new, evaluate = TRUE, ...)
object |
an object of class "sbchoice". |
new |
a new call. |
evaluate |
If |
... |
optional arguments. Currently not in use. |
The function update() for S3 object "sbchoice" updates a model used for
the fit that is included in object according to a new call assigned to
new, and then refits the updated model. The function returns the refitted
model object when evaluate = TRUE, otherwise the updated model call.
## See Examples in sbchoice.## See Examples in sbchoice.