[R] modelling 4-parameter curve in R does not match data - how to proceed?

[Duncan Murdoch]

On 17/03/2021 5:41 a.m., Luigi Marongiu wrote:
> Hello,
> I have a dataset from a polymerase chain reaction. I am using the
> equation given by Rutledge
> (https://pubmed.ncbi.nlm.nih.gov/15601990/) but the profile I get in R
> does not match the data. I ran the same thing in Desmos and instead
> the profile is correct (attached).
> Why do I not get the same matching model as in Desmos? I believe the
> formula in R is the same as the one in Desmos, and I am using the same
> parameters.
> Is there a procedure to debug models?
> Thanks
> 
> Here is the code:
> ```
> high <- c(120.64, 66.14, 34.87, 27.11, 8.87, -5.8, 4.52, -7.16, -17.39,
>         -14.29, -20.26, -14.99, -21.05, -20.64, -8.03, -21.56, -1.28, 15.01,
>         75.26, 191.76, 455.09, 985.96, 1825.59, 2908.08, 3993.18, 5059.94,
>         6071.93, 6986.32, 7796.01, 8502.25, 9111.46, 9638.01, 10077.19,
>         10452.02, 10751.81, 11017.49, 11240.37, 11427.47, 11570.07, 11684.96,
>         11781.77, 11863.35, 11927.44, 11980.81, 12021.88)
> plot(1:45, high, type = "l")
> rutledge <- function(p, x) {
>    m = p$half_fluorescence
>    s = p$slope
>    M = p$max_fluorescence
>    B = p$back_fluorescence
>    y = (M / ( 1 + exp(-(x-m)/s)) ) + B
>    return(y)
> }
> desmos <- rutledge(list(half_fluorescence = 27.1102, slope = 2.76798,
>                          max_fluorescence = 11839.8, back_fluorescence
> = -138.864) , high)
> 
> points(1:45, desmos, type="l", col="blue")


In your calculation of desmos, you are using the Y variable for x in the 
formula.  Calculate it this way instead:

desmos <- rutledge(list(half_fluorescence = 27.1102, slope = 2.76798,
                           max_fluorescence = 11839.8, back_fluorescence
  = -138.864) , 1:45)

Duncan Murdoch