How to calculate confidence intervals for Nonlinear Least Squares in r?

Question

I'm having some trouble to predict confidence intervals ros an nls in r.

pl <- ggplot(data) +  geom_point(aes(x=date, y=cases),size=2, colour="black") + xlab("Date") + ylab("Cases")  
model = nls(cases ~ SSlogis(log(date), Asym, xmid, scal), data= data )


new.data = data.frame(date=c(1:100))
interval <- predict(model, newdata = new.data, se.fit = TRUE, interval = "confidence", level= 0.9)

new.data[c("fit","lwr.conf", "upr.conf")] <- interval 

pl +   
  geom_ribbon(data=new.data, aes(x=date, ymin=lwr.pred, ymax=upr.pred), alpha=0.05, inherit.aes=F, fill="blue")

When I run it, it shows no error, but the interval I get is just a vector whith the fit, no the upper and lower confidence intervals.

Alsacelorraine

Can you post sample data? Please edit the question with the output of dput(data). Or, if it is too big with the output of dput(head(data, 20)). – Overijssel

The documentation of predict.nls says of argument se.fit the following: "At present this argument is ignored.". – Overijssel

Yeah, I know, I just put it just in case – Alsacelorraine

Answer 1

There are 3 ways I know how to do this one of them described in the other answer. Here are some other options. This first one uses nls() to fit the model and investr::predFit to make the predictions and CI:

 library(tidyverse)
 library(investr)
 data <- tibble(date = 1:7,
                cases = c(0, 0, 1, 4, 7, 8.5, 8.5))

    model <- nls(cases ~ SSlogis(log(date), Asym, xmid, scal), data= data )
    new.data <- data.frame(date=seq(1, 10, by = 0.1))
    interval <- as_tibble(predFit(model, newdata = new.data, interval = "confidence", level= 0.9)) %>% 
      mutate(date = new.data$date)

    p1 <- ggplot(data) +  geom_point(aes(x=date, y=cases),size=2, colour="black") + xlab("Date") + ylab("Cases")  

    p1+
      geom_line(data=interval, aes(x = date, y = fit ))+
      geom_ribbon(data=interval, aes(x=date, ymin=lwr, ymax=upr), alpha=0.5, inherit.aes=F, fill="blue")+
      theme_classic()

Another option is to do both the model fitting and predicting with the 'drc' pacakge (aka dose-response curves). This package uses built in starter functions that need to be used (or created), but an object of class 'drc' has many helpful methods that can utilized - one of them being predict.drc which supports confidence intervals (albeit for only some of built-in self-starters). Example with package 'drc':

library(drc)
model_drc <- drm(cases~date, data = data, fct=LL.4())
predict_drc <- as_tibble(predict(model_drc, newdata = new.data, interval = "confidence", level = 0.9)) %>% 
  mutate(date = new.data$date)

p1+
  geom_line(data=predict_drc, aes(x = date, y = Prediction ))+
  geom_ribbon(data=predict_drc, aes(x=date, ymin=Lower, ymax=Upper), alpha=0.5, inherit.aes=F, fill="red")+
  ggtitle("with package 'drc'")+
  theme_classic()

More info on the 'drc' package: journal paper, blog article describing custom self-starts for drc, and the package docs

Terrie

Answer 2

Nonlinear confidence intervals can be obtained by simulation with package propagate:

library("propagate")

x  <- c(25, 25, 10, 10, 5, 5, 2.5, 2.5, 1.25, 1.25)
y <- c(0.0998, 0.0948, 0.076, 0.0724, 0.0557,
       0.0575, 0.0399, 0.0381, 0.017, 0.0253)

m <- nls(y ~ SSmicmen(x, Vm, K), trace = TRUE)

x1 <- seq(0, 25, length = 100)
plot(x, y, xlim = c(0, 25), ylim = c(0, 0.1))
lines(x1, predict(m, data.frame(S = x1)), col = "red")

y.conf <- predictNLS(m, newdata=data.frame(x=x1), interval="confidence", alpha=0.05, nsim=10000)$summary
y.pred <- predictNLS(m, newdata=data.frame(x=x1), interval="prediction", alpha=0.05, nsim=10000)$summary

matlines(x1, y.conf[,c("Sim.2.5%", "Sim.97.5%")], col="red", lty="dashed")
matlines(x1, y.pred[,c("Sim.2.5%", "Sim.97.5%")], col="blue", lty="solid")

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