A self-starting nonlinear regression function for the four-parameter
logistic function. The parameters to be fit are A, B, ld50, and
scale. An expression for the model is
USAGE:
fpl(conc, A, B, ld50, scal)
REQUIRED ARGUMENTS:
conc:
the "independent" variable - usually concentration or time.
A:
the parameter giving the asymptotic response as conc goes to
infinity. It has the same units as the response.
B:
the parameter giving the response at zero conc. It has the same
units as the response.
ld50:
the parameter giving the log of the value of conc which gives a
response midway between A and B.
scal:
a scale parameter. When conc is ld50 + scal the response is
roughly three quarters of the way between A and B.
VALUE:
The predicted responses are returned. The gradient attribute is
a length(conc) by 4 matrix containing the derivatives of the predicted
responses with respect to the parameters A, B, ld50, and scal.
DETAILS:
The function was created by applying deriv() to the expression
A + (B - A)/(1 + exp(-(log(conc) - ld50)/scal)). An initial
attribute was added to calculate the starting estimates for the
parameters automatically.