Logistic regression - curve outside data

[constantin25]

Hello,
I have a dataset and I want to compute logistic regression but my curve is outside the data. My code is this
logistic_fun <- function(Obs.max, L, k, x0) {
L / (1 + exp(-k * (Obs.max - x0)))
}
fit <- nls(Note.jour ~ logistic_fun(Obs.max, L, k, x0), data = JOURSmv2, start = list(L = 10, k = 1, x0 = 1))
summary(fit)
coefs <- coef(fit)
JOURSmv2$predicted <- logistic_fun(JOURSmv3$Obs.max, coefs["L"], coefs["k"], coefs["x0"])

ggplot(JOURSmv2, aes(x = Obs.max, y = Note.jour)) +
geom_point() +
geom_line(aes(x = Obs.max, y = predicted), color = "red") +
ggtitle("Ajustement de la fonction logistique") +
xlab("Observation") +
ylab("Note")

And the result is this
Formula: Note.jour ~ logistic_fun(Obs.max, L, k, x0)

Parameters:
Estimate Std. Error t value Pr(>|t|)
L 10.01757 0.11349 88.270 < 2e-16 ***
k 0.55901 0.06675 8.374 1.23e-15 ***
x0 -1.90839 0.21019 -9.079 < 2e-16 ***

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.6446 on 362 degrees of freedom

Number of iterations to convergence: 9
Achieved convergence tolerance: 5.988e-06

It's not good. How to fix that ?

[startz]

One possibility is that nls() has converged to a local max. What happens if you start L at 8 instead of 10?

[constantin25]

This don't work because i have the same estimate for parameters.

[nirgrahamuk]

Consider providing a reprex.

[constantin25]

It's very strange because my formula and my regression are good. This is the result when I make my function in Geogebra !

[startz]

It is strange, but it's hard to give much advice without a reprex as @nirgrahamuk suggests.

[constantin25]

It's good finally !

ggplot(JOURSmv2, aes(x = Obs.max, y = Note.jour)) +
geom_point() +
ggtitle("Ajustement de la fonction logistique") +
xlab("Observation") +
ylab("Note") +
scale_x_continuous(breaks=c(-5,-2,0,2,4,6,8,10))+
geom_function(fun = function(x) 10.01756/(1 + exp(-0.559 * (x + 1.90831))), linetype = 1, color = "green4", linewidth = 1)+
theme_clean()