Logistic (5 Parameter)
The five-parameter logistic curve: an S-shaped step between two plateaus that can be asymmetric. With S = 1 it is the four-parameter Hill curve. Use it for dose–response and immunoassay standard curves whose two halves differ.
Parameters
- Plateau as x approaches 0, for positive B.
- Slope factor: how steep the step is.
- Location of the step. When S = 1, it is the midpoint, where y is halfway between A and D.
- Plateau as x becomes large, for positive B.
- Asymmetry factor. S = 1 gives the symmetric four-parameter form.
Tips
- Fit Hill Sigmoid (4 Parameter) first, and add S only if the residuals show an asymmetry. S is often strongly correlated with the other parameters.
- The halfway point is at x = C(2^(1/S) − 1)^(1/B); it equals C only when S = 1.
- Enter the dose or concentration itself, not its logarithm: x/C must stay positive when B can take non-integer values.
- Include points well into both plateaus.