R/integratedetfct.logistic.R

In DistanceDevelopment/mrds: Mark-Recapture Distance Sampling

#' Integrate a logistic detection function
#'
#' Integrates a logistic detection function; a separate function is used because
#' in certain cases the integral can be solved analytically and also because
#' the scale trick used with the half-normal and hazard rate doesn't work
#' with the logistic.
#'
#' @param x logistic design matrix values
#' @param scalemodel scale model for logistic
#' @param width transect width
#' @param theta1 parameters for logistic
#' @param integral.numeric if \code{TRUE} computes numerical integral value
#' @param w design covariates
#'
#' @return vector of integral values
#' @author Jeff Laake
integratedetfct.logistic <- function(x,scalemodel,width,theta1,
                                     integral.numeric,w){
  # Functions Used: is.logistic.constant, integratelogistic,
  #                 integratelogistic.analytic

  # If the integrals are to be computed numerically use
  # integratelogistic function
  if(integral.numeric){
    # If all values are constant (no different covariates) then repeat
    # integral value for a single integration
    if(is.logistic.constant(x,scalemodel,width)){
      int1 <- rep(integratelogistic(x=x[1,], models=list(g0model=scalemodel),
                                    beta=theta1,width),nrow(x))
    }else{
      # Otherwise compute integrals for all different sets of covariates
      int1 <- NULL
      for(i in 1:(dim(x)[1])){
        int1 <- c(int1, integratelogistic(x=x[i,],
                                          models=list(g0model=scalemodel),
                                          beta=theta1,width))
      }
    }

  }else{
    # If not a numerical integral use integratelogistic.analytic to
    # compute analytically
    int1 <- integratelogistic.analytic(x, models=list(g0model=scalemodel),
                                       beta=theta1, width=width)
  }

  # Scale of logistic at x=0 to scale detection function to g(0)=1
  int1 <- int1/g0(beta=theta1,w[[2]])
  return(int1)
}