Estimating equation for 4-parameter log-logistic dose-response model

Implements the 4-parameter log-logistic model: $$R_i = \theta_0 + \frac{\theta_m - \theta_0}{1 + \exp[\theta_s (\log D_i - \log \theta_{50})]}$$

Usage

ee_loglogistic(theta, dose, response, loss = NULL, k = NULL)

Arguments

theta

Numeric vector of length 4: lower limit, upper limit, ED50, steepness.

dose

Numeric vector of n dose values.

response

Numeric vector of n response values.

loss

Optional character string for robust loss function.

k

Optional numeric tuning parameter for robust loss.

Value

A 4-by-n matrix, with rows named lower, upper, ed50, and steepness.

See also

ee_loglogistic_ed() for the effective dose at a given level, which is stacked with this equation to give it a sandwich standard error.

Examples

# Four-parameter log-logistic dose-response for the ryegrass data.
psi <- function(theta) {
  ee_loglogistic(theta, dose = inderjit$dose, response = inderjit$response)
}

# The default rootSolve solver does not converge here, so nleqslv is used.
m <- m_estimate(
  stacked_equations = psi,
  init = c(0.2, 8, 2, 1),
  solver = "nleqslv"
)

# Lower limit, upper limit, ED50, and steepness
coef(m)
#>     lower     upper      ed50 steepness 
#>  0.481410  7.792962  3.057955  2.982229