\name{epi.occc}

\alias{epi.occc}

\alias{print.epi.occc}

\title{
Overall concordance correlation coefficient (OCCC)
}

\description{
Overall concordance correlation coefficient (OCCC) for agreement on a continuous measure based on Lin (1989, 2000) and Barnhart et al. (2002).
}

\usage{
epi.occc(x, na.rm = FALSE, pairs = FALSE)

\method{print}{epi.occc}(x, ...)
}

\arguments{
  \item{x}{
    a matrix, or a matrix like object. Rows correspond to cases/observations, columns corresponds to raters/variables.
  }
  \item{na.rm}{
    logical. Should missing values (including \code{NaN}) be removed?
  }
  \item{pairs}{
    logical. Should the return object contain pairwise statistics? See Details.
  }
  \item{\dots}{
    further arguments passed to \code{print} methods.
  }
}

\details{
The index proposed by Barnhart et al. (2002) is the same as the index suggested by Lin (1989) in the section of future studies with correction of typographical error in Lin (2000).
}

\value{
An object of class 'occc' with the following list elements (notation follows Barnhart et al. 2002):

\itemize{
  \item{\code{occc}: }{the value of the overall concordance correlation coefficient
    (\eqn{\rho_{o}^{c}}{rho.o^c}),}

  \item{\code{oprec}: }{overall precision (\eqn{\rho}{rho}),}

  \item{\code{oaccu}: }{overall accuracy (\eqn{\chi^{a}}{chi^a}),}

  \item{\code{pairs}: }{a list with following elements (only if \code{pairs = TRUE}, otherwise \code{NULL};
    column indices for the pairs (j,k) follow lower-triangle column-major rule
    based on a \code{ncol(x)} times \code{ncol(x)} matrix),
    \itemize{
        \item{\code{ccc}: }{pairwise CCC values 
          (\eqn{\rho_{jk}^{c}}{rho_jk^c}),}
        \item{\code{prec}: }{pairwise precision values
          (\eqn{\rho_{jk}}{rho_jk}),}
        \item{\code{accu}: }{pairwise accuracy values
          \eqn{\chi_{jk}^{a}}{chi_jk^a}),}
        \item{\code{ksi}: }{pairwise weights (\eqn{\xi_{jk}}{ksi_jk}),}
        \item{\code{scale}: }{pairwise scale values 
          (\eqn{v_{jk}}{v_jk}),}
        \item{\code{location}: }{pairwise location values 
          (\eqn{u_{jk}}{u_jk}),}
    }
  }
  \item{\code{data.name}: }{name of the input data \code{x}.}
}
}

\references{
Barnhart H X, Haber M, Song J (2002). Overall concordance correlation coefficient for evaluating agreement among multiple observers. Biometrics 58: 1020 - 1027.

Lin L (1989). A concordance correlation coefficient to evaluate reproducibility. Biometrics 45: 255 - 268.

Lin L (2000). A note on the concordance correlation coefficient. Biometrics 56: 324 - 325.
}

\seealso{
  \code{\link[epiR]{epi.ccc}}
}

\author{
Peter Solymos, solymos@ualberta.ca
}

\examples{
## Generate some artificial ratings data:
set.seed(1234)
p <- runif(10, 0, 1)
(x <- replicate(5, rbinom(10, 4, p) + 1))
(z <- epi.occc(x, pairs = TRUE))
str(z)
}
\keyword{ htest }