Problem with 4 parameter logistic fit for immunoassay

[FDS]

I found an (old) pdf file on the web that uses a 4 parameter logistic fit for immunoassay. Unfortunately I must be overlooking something as it does not work in MC15. Are there more elegant ways to do this 4 parameter logistic fit?

Thanks in advance

[Werner_E]

Sure you can find a fit using a solve block with minerr and ever so often this has some advantages over using the built in "genfit" function.

But I doubt that the approach as posted by you ever worked in older Mathcad versions. We had to see the pdf to judge though.

Here is an approach using "genfit":

[Werner_E · Accepted solution]

Here is an approach using "minerr"

[FDS]

Werner, thank you so much. Very helpful as usual.

[FDS]

I am sorry but there is still something wrong when I use a slightly different 4 parameter logistic fit in combination with real data. Could you have a second look?

[Werner_E]

Not sure why the solve block fails.

It may be due to the fact, that the x-values are not in sequence so I guess you cannot expect your function to follow that zigzag behavior of your data. (EDIT: No, thats not the case)

It may be because the function you like to fit (you changed the function definition) is not suitable for that data set (Probably true, but a normal logistic fit at least gives us a bad fit)

It may be due to bad guess values. If you plot your fit function using your guess values, the graph is way away from your data. If you put your x-values in this function, you get values bigger than 10^307 which throws an error. This may be the reason why genfit fails and throws the "this value must be real" error. (EDIT: no, the "not real" error has to be something else).

The solve block with minerr fails in your sheet because of the missing guess value for k.

I guess the problem are the guess values.

I played around with a normal three parameter logistic fit and got a (not so pretty good) solution. I am not sure  about your function an why you call it a logistic one. Maybe your function type is not adequate for this data or maybe its suitable for logarithmic data - not sure, just poking around.

Why do you think your function type and your guess values are suitable for your data set (the combination of function and guesses sure is not - just plot it to see)

WE

[Werner_E]

Here are suitable guess values for your function type.

The reason for the "not real value" seems o be that d (starting with the guess) has to be negative!

[Werner_E]

Here is a completely different solution found with the minerr solve block

[VladimirN]

Please find in the attachment another approximating model for your data.

[FDS]

Werner and Vladimir, thank you for your help. Fitting data to a standard in ELISA testing can be quite challenging so I appreciated all input.