1. ## Sigmoid curve

Hi,

Is it possible to linearise data for a sigmoid curve?
To be clear, I do not mean a logistic function! The data are not between 0 and 1!
I have have encountered this problem several times and I just can't find a solution. All books and sites mention logistic sigmoid curves.
For instance, if I have following data:
x y
0 0
1 2
2 4
3 6
4 7
5 8
6 8.5
7 9
8 9
9 9

Btw I use R.
Is there glm function i can use?

Thank you!

2. ## Re: Sigmoid curve

Hi, when I look at the data I dont think that they have a sigmoid shape.

3. ## Re: Sigmoid curve

Perhaps my definition of sigmoid is something different.
Doesn't matter, question remains. How can I linearise this data?

4. ## Re: Sigmoid curve

Can you describe your data little bit more?

5. ## Re: Sigmoid curve

Originally Posted by Dason
Can you describe your data little bit more?
Well for instance:

x = number of animals
y = the number of eaten prey

Thus if there are more animals present, predation will increase untill a certain upper limit is reached. To be clear, you cannot make a proportion of the y-axis! Otherwise I could do a logistic regression. That is the problem! How can I statistically analyse these data?

Thank you!

6. ## Re: Sigmoid curve

The question is what do want to know from your data? For your data with a saturation property for increasing x one typically uses a Michaelis-Menten model and therefore obtains access to some biological interpretable parameter.

7. ## Re: Sigmoid curve

“Is it possible to linearise data for a sigmoid curve? “
Don’t know.

“ question remains. How can I linearise this data?”
Maybe.

“How can I statistically analyse these data?”
The last question is very different from the first two. You asked for how to linearize. Maybe it is possible to linearize, I don’t know. But you can analyse it in a different way.

You can run non-linear regression. I had a quick look at your data and thought, just like Jacov, that maybe it would fit better with a Michaelis Menten model.

Code:
``````x <- c( 0,1,2,3,4 ,5 ,6 ,7 ,8 ,9)
y <- c( 0 , 2 , 4 , 6 , 7 , 8 , 8.5, 9  , 9  , 9  )

plot(x,y)

mod1 <- nls(y ~  vm*x/(k+x) , start = list(k= 5 , vm =10 ), trace = TRUE  )
summary(mod1)

# Formula: y ~ vm * x/(k + x)
#
# Parameters:
#    Estimate Std. Error t value Pr(>|t|)
# k    4.4894     0.8142   5.514 0.000564 ***
# vm  14.3585     1.1646  12.329 1.74e-06 ***
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
# Residual standard error: 0.4163 on 8 degrees of freedom

xvar <- seq(0,10,by =0.1)
yvar <-   14.3585*xvar/(4.4894 +xvar)

plot(x,y)
lines(xvar,yvar)``````
The model does not fit very well. The residuals deviate systematically. But it is not completely stupid.

I got this from a textbook about non-linear models.

If you google at “gompertz logistic model” or “bacterial growth logistic” then you will find a lot of growth curves.

I am sure that you are aware of the classical time series data from sales of fur from lynx and hare from trappers in Canada in the 19:th century. When there was a lot of lynx the number of hares decreased and then the lynx decreased. But that made the hares to increase so that the number of lynx could increase. If you make a diagram with lynx and hares on the x- and y-axes respectively then you can se a clock-wise movement. That data series started a subject called population dynamics.

Ritz C., Streibig J.C., Nonlinear Regression with R, Springer: 2008

8. ## Re: Sigmoid curve

I would like to give a general comment which actually fits very well to this thread.

First of all I am not a statistician but a modeler.

To my opinion the first question when analyzing data is not to find a model which describes the data best but to understand what the data describes and what one want to know from the data. If this is clarified then one starts to look for appropriate models.

The objective of modeling data is not to describe them. The aim is to get interpretable parameter.

It is no problem to find a function for your data which will perfectly fit and has therefore, a “perfect” AIC, BIC or
whatever. But personally, I am not a huge fan of this “competing model theory”.

What I want to say is, don't reject a realistic model because it does not really very well describe our data.

@rmoerken: So please first ask yourself, what is the aim of the whole project. If this is clarified then we could go through the list of models...

9. ## Re: Sigmoid curve

Yes, I agree what Jacov just said. But maybe we have lost rmoerken from this forum.

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