#' cummulative_rate
#' @importFrom dplyr mutate lag
#' @importFrom rlang enquo :=
#' @param data A \code{data.frame} object with interaction information
#' @param id Row id of incidence
#' @param incidence The incidence of interaction in the data \code{data.frame}
#' @param cummulativesum cummulative counted incidences
#' @param accuracy of the derivate of the rate
#' @return A \code{data.frame} with the rate of change from fractional cuumlative incidence
#' and the first and second derivates of the rate
#' @export
#'
#' @examples
#' library(ecointeraction)
#' data <- acummulate_incidence(mammalvirus, mammal_species, incidence)
#' cumrateData <- cummulative_rate(data, id, incidence, cummulativesum)
cummulative_rate <- function(data, id = id, incidence = incidence, cummulativesum = cummulativesum, accuracy = 4){
id <- rlang::enquo(id)
incidence <- rlang::enquo(incidence)
cummulativesum <- rlang::enquo(cummulativesum)
cummulativesum_frac <- "cummulativesum_frac"
rate <- "rate"
id_fraction <- "id_fraction"
ratediff <- "ratediff"
ratediffdiff <- "ratediffdiff"
data %>%
dplyr::mutate(!! cummulativesum_frac := !! cummulativesum/sum(!! incidence)) %>%
dplyr::mutate(!! id_fraction := !! id/max(!! id) ) %>%
dplyr::mutate(!! rate := id_fraction/cummulativesum_frac ) %>%
dplyr::mutate(!! ratediff := log(rate - dplyr::lag(rate))) %>%
dplyr::mutate(!! ratediffdiff := round( round(ratediff - dplyr::lag(ratediff), 3)^2, accuracy ))
}
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