\name{fitted.ppm}
\alias{fitted.ppm}
\title{
  Fitted Conditional Intensity for Point Process Model
}
\description{
  Given a point process model fitted to a point pattern,
  compute the fitted conditional intensity of the model
  at the points of the pattern,
  or at the points of the quadrature scheme used to fit the model.
}
\usage{
  \method{fitted}{ppm}(object, \dots, type="lambda", dataonly=FALSE,
check=TRUE, repair=TRUE)
}
\arguments{
  \item{object}{
    The fitted point process model (an object of class \code{"ppm"})
  }
  \item{\dots}{
    Ignored.
  }
  \item{type}{
    String (partially matched) indicating whether the fitted value is the
    conditional intensity (\code{"lambda"}) or the trend
    (\code{"trend"}).
  }
  \item{dataonly}{
    Logical. If \code{TRUE}, then values will only be computed
    at the points of the data point pattern. If \code{FALSE}, then
    values will be computed at all the points of the quadrature scheme
    used to fit the model, including the points of the data point pattern.
  }
  \item{check}{
    Logical value indicating whether to check the internal format
    of \code{object}. If there is any possibility that this object
    has been restored from a dump file, or has otherwise lost track of
    the environment where it was originally computed, set
    \code{check=TRUE}. 
  }
  \item{repair}{
    Logical value indicating whether to repair the internal format
    of \code{object}, if it is found to be damaged. 
  }
}
\value{
  A vector containing the values of the fitted conditional intensity
  or (if \code{type="trend"}) the fitted spatial trend.
  
  Entries in this vector correspond to the quadrature points (data or
  dummy points) used to fit the model. The quadrature points can be
  extracted from \code{object} by \code{union.quad(quad.ppm(object))}.
}
\details{
  The argument \code{object} must be a fitted point process model
  (object of class \code{"ppm"}). Such objects are produced by the 
  model-fitting algorithm \code{\link{ppm}}).

  This function evaluates the conditional intensity
  \eqn{\hat\lambda(u, x)}{lambdahat(u,x)}
  or spatial trend \eqn{\hat b(u)}{bhat(u)} of the fitted point process
  model for certain locations \eqn{u},
  where \code{x} is the original point pattern dataset to which
  the model was fitted.

  The locations \eqn{u} at which the fitted conditional intensity/trend
  is evaluated, are the points of the
  quadrature scheme used to fit the model in \code{\link{ppm}}.
  They include the data points (the points of the original point pattern
  dataset \code{x}) and other ``dummy'' points 
  in the window of observation.

  Use \code{\link{predict.ppm}} to compute the fitted conditional
  intensity at other locations or with other values of the
  explanatory variables.
}
\references{
  Baddeley, A., Turner, R., Moller, J. and Hazelton, M. (2005).
  Residual analysis for spatial point processes (with discussion).
  \emph{Journal of the Royal Statistical Society, Series B}
  \bold{67}, 617--666.
}
\seealso{
 \code{\link{ppm.object}},
 \code{\link{ppm}},
 \code{\link{predict.ppm}}
}
\examples{
    data(cells)
    str <- ppm(cells, ~x, Strauss(r=0.15))
    lambda <- fitted(str)

    # extract quadrature points in corresponding order
    quadpoints <- union.quad(quad.ppm(str))

    # plot conditional intensity values
    # as circles centred on the quadrature points 
    quadmarked <- setmarks(quadpoints, lambda)
    plot(quadmarked)
}
\author{Adrian Baddeley
  \email{adrian@maths.uwa.edu.au}
  \url{http://www.maths.uwa.edu.au/~adrian/}
  and Rolf Turner
  \email{r.turner@auckland.ac.nz}
}
\keyword{spatial}
\keyword{methods}
\keyword{models}