#' Fit a Gompertz Curve to Growth Data
#'
#' \code{fit_growth_gompertz} fits a Gompertz curve to a tidy growth data set
#' using nonlinear least squares
#'
#' @inheritParams fit_growth
#' @param ... Additional arguments to \code{\link[stats]{nls}}
#'
#' @seealso \url{https://en.wikipedia.org/wiki/Gompertz_function}
#' @return A \code{\link{growthcurve}} object
#'
#' @export
#'
#' @examples
#' \dontrun{
#' # Fit the data given in columns Time and OD600
#' fit_growth_gompertz(mydata, Time, OD600)}
#'
fit_growth_gompertz <- function(df, time, data, ...) {
fit_growth_gompertz_(
df = df,
time_col = lazyeval::lazy(time),
data_col = lazyeval::lazy(data),
...
)
}
#' @rdname fit_growth_gompertz
#' @inheritParams fit_growth_
#' @importFrom stats coef D
#' @export
#' @examples
#' \dontrun{
#' fit_growth_gompertz_(mydata, "Time", "OD600")
#' }
fit_growth_gompertz_ <- function(df, time_col, data_col, ...) {
growth_data <- lazyeval::lazy_eval(data_col, df)
time_data <- lazyeval::lazy_eval(time_col, df)
if (any(is.na(time_data))) stop("NAs in time data")
if (any(is.na(growth_data))) stop("NAs in growth data")
nlsmodel <- stats::nls(
growth_data ~ SSgompertz(time_data, Asym, b2, b3),
...
)
expr_gompertz <- expression(Asym * exp(-b2 * b3 ^ x))
yval <- function(x = time_data) {
eval_env(
expr_gompertz,
Asym = coef(nlsmodel)[["Asym"]],
b2 = coef(nlsmodel)[["b2"]],
b3 = coef(nlsmodel)[["b3"]],
x = x
)
}
# Find the time of maximum growth using the second derivative
fgompertzd2 <- function(x, Asym, b2, b3) -(Asym * (exp(-b2 * b3^x) * (b2 * (b3^x * log(b3) * log(b3))) - exp(-b2 * b3^x) * (b2 * (b3^x * log(b3))) * (b2 * (b3^x * log(b3)))))
max_rate_time <- stats::uniroot(
f = fgompertzd2,
interval = range(time_data),
Asym = coef(nlsmodel)[["Asym"]],
b2 = coef(nlsmodel)[["b2"]],
b3 = coef(nlsmodel)[["b3"]]
)$root
growthcurve(
type = "gompertz",
model = nlsmodel,
fit = list(
x = time_data,
y = stats::predict(nlsmodel),
residuals = stats::residuals(nlsmodel)
),
f = yval,
parameters = list(
asymptote = coef(nlsmodel)[["Asym"]],
max_rate = list(
time = max_rate_time,
value = yval(max_rate_time),
rate = eval_env(
D(expr = expr_gompertz, name = "x"),
Asym = coef(nlsmodel)[["Asym"]],
b2 = coef(nlsmodel)[["b2"]],
b3 = coef(nlsmodel)[["b3"]],
x = max_rate_time
)
),
augc = calculate_augc(time_data,
stats::predict(nlsmodel))
),
df = df,
time_col = as.character(time_col)[1],
data_col = as.character(data_col)[1]
)
}
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