CODEWITHSUNDEEP
rsmoothing
J. Win.
J. Win.

Reputation: 6771

fitting a smooth line, with limits from 0 to 1

Apologies for the noobish question, my R seems to have gone very rusty since last time I was here. I have several series of ratio data taken over time, like so:

years <- c(1890, 1891, 1894, 1896, 1899, 1905, 1917)
ratio <- c(0.8,   0.9,  0.5, 0.25,  0.1, 0.02,    0)
plot(ratio~years)

Superimposed on the scatterplot I need a smoothish line that is respectful of the 0 to 1 limits of ratio data. Straight-up lines(predict(loess(ratio~years))~years) is a little too jerky, and a few methods I tried of smoothing it dip below zero sometimes with my real data. What function do I need here?

Upvotes: 1

Views: 490

Answers (1)

Andrie
Andrie

Reputation: 179468

It seems like you your model is exponential decay. You can estimate this with non-linear least squares regression, using nls():

fit <- nls(ratio ~ exp(-b*(years-1890)), start=list(b=0.5))
fit

Nonlinear regression model
  model:  ratio ~ exp(-b * (years - 1890)) 
   data:  parent.frame() 
     b 
0.2051 
 residual sum-of-squares: 0.05669

Number of iterations to convergence: 5 
Achieved convergence tolerance: 5.016e-06

Now plot the results:

plot(ratio~years, ylim=c(0,1))
newdata <- data.frame(years=1890:1917)
lines(newdata$years, predict(fit, newdata=newdata), col="red")

enter image description here

Upvotes: 4

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