What's the most pain-free way to fit logistic growth curves in R?

Question

This isn't as easy to Google as some other things as, to be clear, I'm not talking about logistic regression in the sense of using regression to predict categorical variables.

I'm talking about fitting a logistic growth curve to given data points. To be specific, $x$ is a given year from 1958 to 2012 and $y$ is the estimated global CO2 ppm (parts per million of carbon dioxide) in November of year $x$.

Right now it's accelerating but it's got to level off at some point. So I want a logistic curve.

I haven't found a relatively straightforward way to do this yet.

A logistic curve isn't the only curve that 'levels off'. Indeed a multiple of any continuous cdf would satisfy that requirement. — Glen_b, Aug 23 '13 at 02:52
Nick, thank you very much for positng your code, I was just wondering how to write it as an equation? in the code the values C, a and K refer to which parameters? — , Oct 18 '13 at 13:26
Use the package grofit Makes use of spline and growth curves. — , Sep 02 '13 at 10:19
I think you are taking me to be @user2581681. I just edited their answer. — Nick Cox, Oct 18 '13 at 15:45

score 25 · Accepted Answer · answered Jan 15 '13 at 20:48

25

See the nls() function. It has a self starting logistic curve model function via SSlogis(). E.g. from the ?nls help page

> library("nls")
> DNase1 <- subset(DNase, Run == 1)
>      
> ## using a selfStart model
> fm1DNase1 <- nls(density ~ SSlogis(log(conc), Asym, xmid, scal), 
+                  DNase1)

I suggest you read the help pages for these functions and probably the linked references if possible to find out more.

answered Jan 15 '13 at 20:48

Gavin Simpson

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Hello. Seems that package nls was removed from cran. Are there any alternative solutions for those of us using r version 4.x? https://cran.r-project.org/web/packages/nls/ – Doug Fir Mar 19 '21 at 12:55
1

I think you could just use the `nls()` function that ships with R in the stats package (which is loaded automagically) – Gavin Simpson Mar 19 '21 at 17:44

score 12 · Answer 2 · edited Aug 22 '13 at 18:02

I had the same question a little while ago. This is what I found:

Fox and Weisberg wrote a great supplemental article using the nls function (both with and without the self-starting option mentioned by Gavin). It can be found here:

http://socserv.mcmaster.ca/jfox/Books/Companion/appendix/Appendix-Nonlinear-Regression.pdf

From that article, I ended up writing a function for my class to use when fitting a logistic curve to their data:

###Log fit - be sure to use quotes around the variable names in the call
log.fit <- function(dep, ind, yourdata){
#Self-starting...

y <- yourdata[, dep]
x <- yourdata[, ind]

log.ss <- nls(y ~ SSlogis(x, phi1, phi2, phi3))

#C
C <- summary(log.ss)$coef[1]
#a
A <- exp((summary(log.ss)$coef[2]) * (1/summary(log.ss)$coef[3]))
#k
K <- (1 / summary(log.ss)$coef[3])

plot(y ~ x, main = "Logistic Function", xlab=ind, ylab=dep)
lines(0:max(x), predict(log.ss, data.frame(x=0:max(x))), col="red")

r1 <- sum((x - mean(x))^2)
r2 <- sum(residuals(log.ss)^2)

r_sq <- (r1 - r2) / r1

out <- data.frame(cbind(c(C=C, a=A, k=K, R.value=sqrt(r_sq))))
names(out)[1] <- "Logistic Curve"

return(out)
}

What's the most pain-free way to fit logistic growth curves in R?

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