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# tcplObjHill: Generate a hill model objective function to optimize
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#' @rdname Models
#'
#' @section Hill Model (hill):
#' \code{tcplObjHill} calculates the likelyhood for a 3 parameter Hill model
#' with the bottom equal to 0. The parameters passed to \code{tcplObjHill} by
#' \code{p} are (in order) top (\eqn{\mathit{tp}}), log AC50 (\eqn{\mathit{ga}}), hill
#' coefficient (\eqn{\mathit{gw}}), and the scale term (\eqn{\sigma}). The hill model
#' value \eqn{\mu_{i}}{\mu[i]} for the \eqn{i^{th}}{ith} observation is given
#' by:
#' \deqn{
#' \mu_{i} = \frac{tp}{1 + 10^{(\mathit{ga} - x_{i})\mathit{gw}}}
#' }{
#' \mu[i] = tp/(1 + 10^(ga - x[i])*gw)}
#' where \eqn{x_{i}}{x[i]} is the log concentration for the \eqn{i^{th}}{ith}
#' observation.
#'
#' @importFrom stats dt
#' @export
tcplObjHill <- function(p, lconc, resp) {
### This function takes creates an objective function to be optimized using
### the starting hill parameters, log concentration, and response.
###
### Arguments:
### p: a numeric vector of length 4 containg the starting values for
### the hill model, in order: top, log AC50, hill
### coefficient, and log error term
### lconc: a numeric vector containing the log concentration values to
### produce the objective function
### lresp: a numeric vector containing the response values to produce the
### objective function
###
### Value:
### An objective function for the hill model and the given conc-resp data
mu <- p[1]/(1 + 10^((p[2] - lconc)*p[3]))
sum(dt((resp - mu)/exp(p[4]), df = 4, log = TRUE) - p[4])
}
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