checkRd: (-1) DCchoice-package.Rd:134: Lost braces
   134 | in KG M\"{a}ler, JR Vincent (eds.), \emph{Handbook of Environmental Economics}. 
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checkRd: (-1) DCchoice-package.Rd:188: Lost braces
   188 | Kristr\"{o}m B (1990). 
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checkRd: (-1) KR.Rd:4: Lost braces
     4 | \title{Kristr\"{o}m's single-bounded dichotomous choice CVM data}
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checkRd: (-1) KR.Rd:7: Lost braces
     7 |     Kristr\"{o}m (1990).
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checkRd: (-1) KR.Rd:27: Lost braces
    27 |     the eleven virgin forests in Sweden. See Kristr\"{o}m (1990) 
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checkRd: (-1) KR.Rd:32: Lost braces
    32 |     The data are used in Kristr\"{o}m (1990). 
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checkRd: (-1) KR.Rd:35: Lost braces
    35 |     Professor Bengt Kristr\"{o}m, Swedish University of Agricultural Sciences.
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checkRd: (-1) KR.Rd:41: Lost braces
    41 | Kristr\"{o}m B (1990). 
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checkRd: (-1) dbchoice.Rd:155: Lost braces
   155 |   G, Mourato S, \"{O}zdemiro\={g}lu E, Pearce DW, Sugden R, Swanson J (eds.) (2002).
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checkRd: (-1) dbchoice.Rd:155: Lost braces
   155 |   G, Mourato S, \"{O}zdemiro\={g}lu E, Pearce DW, Sugden R, Swanson J (eds.) (2002).
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checkRd: (-1) dbchoice.Rd:161: Lost braces
   161 | in KG M\"{a}ler, JR Vincent (eds.), \emph{Handbook of Environmental Economics}. 
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checkRd: (-1) kristrom.Rd:7: Lost braces
     7 | The Kristr\"{o}m's nonparametric approach to analyze single-bounded dichotomous choice contingent valuation data
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checkRd: (-1) kristrom.Rd:12: Lost braces
    12 | of the Kristr\"{o}m's nonparametric method.
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checkRd: (-1) kristrom.Rd:32: Lost braces
    32 | valuation (CV) data on the basis of Kristr\"{o}m's nonparametric method (Kristr\"{o}m 1990).
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checkRd: (-1) kristrom.Rd:32: Lost braces
    32 | valuation (CV) data on the basis of Kristr\"{o}m's nonparametric method (Kristr\"{o}m 1990).
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checkRd: (-1) kristrom.Rd:64: Lost braces
    64 | \item{estimates}{a matrix of the estimated Kristr\"{o}m's survival probabilities.}
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checkRd: (-1) kristrom.Rd:67: Lost braces
    67 | and displays the estimated Kristr\"{o}m's survival probabilities. 
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checkRd: (-1) kristrom.Rd:69: Lost braces
    69 | The extractor function \code{summary()} is used to display the estimated Kristr\"{o}m's survival 
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checkRd: (-1) kristrom.Rd:88: Lost braces
    88 | Kristr\"{o}m B (1990). 
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checkRd: (-1) sbchoice.Rd:102: Lost braces
   102 |   G, Mourato S, \"{O}zdemiro\={g}lu E, Pearce DW, Sugden R, Swanson J (eds.) (2002).
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checkRd: (-1) sbchoice.Rd:102: Lost braces
   102 |   G, Mourato S, \"{O}zdemiro\={g}lu E, Pearce DW, Sugden R, Swanson J (eds.) (2002).
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checkRd: (-1) sbchoice.Rd:112: Lost braces
   112 | in KG M\"{a}ler, JR Vincent (eds.), \emph{Handbook of Environmental Economics}. 
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checkRd: (-1) spike.Rd:69: Lost braces
    69 | The functions \code{\link{sbspike}}, \code{\link{oohbspike}}, and \code{\link{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\"{o}m (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.
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checkRd: (-1) spike.Rd:75: Lost braces
    75 | The other difference is about an argument \code{formula}, which is assigned an object of the S3 class \code{'\link[Formula]{Formula}'}. For a model formula for the ordinary model functions, the left-handed side of the tilde (\code{~}) contains only response variable(s) (i.e., the response to SB DCCV question, \code{R1}, for \code{\link{sbchoice}}; the response to the first stage of OOHB/DB DCCV question, \code{R1}, and the second one, \code{R2}, for \code{\link{oohbchoice}} and \code{\link{dbchoice}}), while it contains both the response variable(s) and spike variable for the spike model functions. The spike variable, \code{S}, which must be set in the second part (after the vertical bar [\code{|}]) of the left-handed side of the tilde, takes the value of \code{1} if the respondent has a positive WTP for a good specified in the DCCV question and \code{0} otherwise. See Kristr\"{o}m (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:
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checkRd: (-1) spike.Rd:99: Lost braces
    99 | The spike model functions return an S3 \code{'spike'} class object. Various methods for the S3 \code{"spike"} class object are provided as follows: \code{print()} displays estimated coefficients; \code{summary()} extracts detailed information on the fitted model; \code{summary.print()} displays information extracted by \code{summary()}; \code{logLik()} extracts the value of a log-likelihood function at estimates; \code{vcov()} returns the variance-covariance matrix of the fitted model; and \code{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 \code{\link{sbchoice}}, \code{\link{oohbchoice}}, and \code{\link{dbchoice}}. Therefore, for details, see helps for the corresponding methods for ordinary DCCV functions. Note that the mean and median WTPs calculated by \code{summary()} for the spike model functions are defined as follows (see Kristr\"{o}m 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 \bold{x'b}, where \bold{x} is a row vector of covariates at the sample mean including the value of 1 for the constant, and \bold{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. 
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checkRd: (-1) spike.Rd:149: Lost braces
   149 | Kristr\"{o}m B. (1997) Spike models in contingent valuation. \emph{American Journal of Agricultural Economics} \bold{79}: 1013--1023.
       |         ^
checkRd: (-1) summary.kristrom.Rd:6: Lost braces
     6 | Summarizing the Kristr\"{o}m's nonparametric estimation of WTP
       |                         ^
checkRd: (-1) turnbull.Rd:119: Lost braces; missing escapes or markup?
   119 | $bid_{end}$, is found, it is straightforward to compute the triangular 
       |      ^
checkRd: (-1) turnbull.Rd:120: Lost braces; missing escapes or markup?
   120 | area by $0.5(bid_{end} - bid_{max})P_{max}$ where $bid_{max}$ is 
       |                  ^
checkRd: (-1) turnbull.Rd:120: Lost braces; missing escapes or markup?
   120 | area by $0.5(bid_{end} - bid_{max})P_{max}$ where $bid_{max}$ is 
       |                              ^
checkRd: (-1) turnbull.Rd:120: Lost braces; missing escapes or markup?
   120 | area by $0.5(bid_{end} - bid_{max})P_{max}$ where $bid_{max}$ is 
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checkRd: (-1) turnbull.Rd:120: Lost braces; missing escapes or markup?
   120 | area by $0.5(bid_{end} - bid_{max})P_{max}$ where $bid_{max}$ is 
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checkRd: (-1) turnbull.Rd:121: Lost braces; missing escapes or markup?
   121 | the maximum bid and $P_{max}$ is the acceptance probability for 
       |                        ^
checkRd: (-1) turnbull.Rd:122: Lost braces; missing escapes or markup?
   122 | $bid_{max}$, both of which are reported in the summarized output.
       |      ^