使用高斯拟合 R 拟合和误差条

Question

I am trying to fit some data in R and so far I think I am doing an ok-job. My dataset is as follow (source:

x<-c(1:35)
y<-c(221,88,76,203,233,228,288,498,428,443,570,640,1145,1326,1598,
529,2076,2249,2116,2795,2853,2470,2989,2648,4480,4670,4821,
3957,3780,3612,3491,4492,4401,3651,3815)

data<-data.frame(x,y)
fitG =
   function(x,y,mu,sig,scale){
                f = function(p){
                  d = p[3]*dnorm(x,mean=p[1],sd=p[2])
                  sum((d-y)^2)
                  }
                 optim(c(mu,sig,scale),f)
   }

fitP=fitG(data$x, data$y, 35, 1, 6000)

plot(data$x, data$y)
p =fitP$par
lines(data$x, p[3]*dnorm(data$x, p[1], p[2]))

(source, http://www.protezionecivile.gov.it , i'm using the covid data as an example)

which fit the data quite nicely... but is there a way to

a) instead of using the plot function using the ggplot2 package which allows for more customization of the plot and b) I want to do a fitting for the data not shown here (ie extend the gaussian curve beyond the day 35), possibly adding an error bar that show the uncertainty over the fitting over time... I have tried to look up online but all the articles I've found assume that the reader have a strong statistical background... which I do not.

Answer 1

To use ggplot, you can do:

  data %>% 
  ggplot(aes(x=x, y=y))+
  geom_point()+
  geom_smooth()

And then customize as you wish.

Answer 2

You can add the fit onto the data.frame and plot:

library(ggplot2)
data$fitted = p[3]*dnorm(data$x, p[1], p[2])
ggplot(data,aes(x=x,y=y)) + 
geom_point() + 
geom_line(aes(y=fitted),col="blue")

Now as for the uncertainty, what you are fitting is not a conventional distribution (because you have a third parameter scale), and I don't see how a normal distribution can help you make predictions here.

What exactly do you mean by "possibly adding an error bar that show the uncertainty over the fitting over time" ? Although it's a lot of statistics, it can be simplified into this, what is the error do you want to show?

You can use the solution shown by @johnjohn, just bear in mind it is a gam which is fitting a spline and it's errors are estimated from the errors of the fit, you can see more about it maybe on this blog .