Your example doesn't run because it uses a variable `cyc` which you
didn't include.
But in general, I think you are mixing up two separate problems here.
The first problem is creating a function of x (which is Cycles in your
dataset). You used the predictions from a glm() to do this.
That's a reasonable way to create a function with a range of 0 to 1, but
you want a function with a different range. Dividing by the max is one
way to get it, but there are others. I'd say a better approach would be
to think about the problem from a subject matter point of view and
determine a class of functions that match your needs. After you've done
that, you might use glm() to find the particular version of that
function (i.e. the unknown parameters), or maybe some other method.
The second problem is finding where that function intersects a line. In
your sample code, you were trying to intersect a horizontal line. If
that's always the case, then it's a problem of inverting the function
from the first problem. Just write out y = f(x) and solve for x =
f^-1(y). If the formula isn't convenient, you can approximate the
answer using the R function uniroot().
Duncan Murdoch
On 2025-04-11 11:53 a.m., Luigi Marongiu wrote:
I am trying to predict the intersection value between a curve and a line.
I can fit a logistic model to the data by converting the data to the
range 0-1. How can I determine the intersection with a line?
Also, is there a way to do the same without converting the data?
Here is an example:
```
val = 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,
12058.35, 12100.63,
12133.57, 12148.89, 12137.09)
df = data.frame(Cycles = 1:35, Values = val[1:cyc])
M = max(df$Values)
df$Norm = df$Values/M
df$Norm[df$Norm<0] = 0
b_model = glm(Norm ~ Cycles, data=df, family=binomial)
x = 0.15
plot(Norm ~ Cycles, df, main="Normalized view",
xlab=expression(bold("Amplification cycle")),
ylab=expression(bold("Fluorescence (normalized)")),
type="l", lwd=3, col="blue")
lines(b_model$fitted.values ~ df$Cycles, col="red", lwd=2, lty=2)
abline(h=x, col="green", lwd=2)
```
Thank you
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