How to fit a smooth curve to my data in R

Question

I m trying to draw a smooth curve in R  I have the following simple toy data    gt  x   1   1  2  3  4  5  6  7  8  9 10  gt  y   1   2  4  6  8  7 12 14 16 18 20   Now when I plot it with a standard command it looks bumpy and edgy  of course    gt  plot x y  type  l   lwd 2  col  red     How can I make the curve smooth so that the 3 edges are rounded using estimated values  I know there are many methods to fit a smooth curve but I m not sure which one would be most appropriate for this type of curve and how you would write it in R

User · Answer

The other answers are all good approaches. However, there are a few other options in R that haven't been mentioned, including lowess and approx, which may give better fits or faster performance.

The advantages are more easily demonstrated with an alternate dataset:

sigmoid <- function(x)
{
  y<-1/(1+exp(-.15*(x-100)))
  return(y)
}

dat<-data.frame(x=rnorm(5000)*30+100)
dat$y<-as.numeric(as.logical(round(sigmoid(dat$x)+rnorm(5000)*.3,0)))

Here is the data overlaid with the sigmoid curve that generated it:

This sort of data is common when looking at a binary behavior among a population. For example, this might be a plot of whether or not a customer purchased something (a binary 1/0 on the y-axis) versus the amount of time they spent on the site (x-axis).

A large number of points are used to better demonstrate the performance differences of these functions.

Smooth, spline, and smooth.spline all produce gibberish on a dataset like this with any set of parameters I have tried, perhaps due to their tendency to map to every point, which does not work for noisy data.

The loess, lowess, and approx functions all produce usable results, although just barely for approx. This is the code for each using lightly optimized parameters:

loessFit <- loess(y~x, dat, span = 0.6)
loessFit <- data.frame(x=loessFit$x,y=loessFit$fitted)
loessFit <- loessFit[order(loessFit$x),]

approxFit <- approx(dat,n = 15)

lowessFit <-data.frame(lowess(dat,f = .6,iter=1))

And the results:

plot(dat,col='gray')
curve(sigmoid,0,200,add=TRUE,col='blue',)
lines(lowessFit,col='red')
lines(loessFit,col='green')
lines(approxFit,col='purple')
legend(150,.6,
       legend=c("Sigmoid","Loess","Lowess",'Approx'),
       lty=c(1,1),
       lwd=c(2.5,2.5),col=c("blue","green","red","purple"))

As you can see, lowess produces a near perfect fit to the original generating curve. Loess is close, but experiences a strange deviation at both tails.

Although your dataset will be very different, I have found that other datasets perform similarly, with both loess and lowess capable of producing good results. The differences become more significant when you look at benchmarks:

> microbenchmark::microbenchmark(loess(y~x, dat, span = 0.6),approx(dat,n = 20),lowess(dat,f = .6,iter=1),times=20)
Unit: milliseconds
                           expr        min         lq       mean     median        uq        max neval cld
  loess(y ~ x, dat, span = 0.6) 153.034810 154.450750 156.794257 156.004357 159.23183 163.117746    20   c
            approx(dat, n = 20)   1.297685   1.346773   1.689133   1.441823   1.86018   4.281735    20 a  
 lowess(dat, f = 0.6, iter = 1)   9.637583  10.085613  11.270911  11.350722  12.33046  12.495343    20  b

Loess is extremely slow, taking 100x as long as approx. Lowess produces better results than approx, while still running fairly quickly (15x faster than loess).

Loess also becomes increasingly bogged down as the number of points increases, becoming unusable around 50,000.

EDIT: Additional research shows that loess gives better fits for certain datasets. If you are dealing with a small dataset or performance is not a consideration, try both functions and compare the results.

User · Answer

LOESS is a very good approach  as Dirk said   Another option is using Bezier splines  which may in some cases work better than LOESS if you don t have many data points   Here you ll find an example  http   rosettacode org wiki Cubic bezier curves R    x  y  the x and y coordinates of the hull points   n  the number of points in the curve  bezierCurve  lt - function x  y  n 10            outx  lt - NULL     outy  lt - NULL      i  lt - 1     for  t in seq 0  1  length out n                     b  lt - bez x  y  t          outx i   lt - b x         outy i   lt - b y          i  lt - i 1                return  list x outx  y outy          bez  lt - function x  y  t            outx  lt - 0     outy  lt - 0     n  lt - length x -1     for  i in 0 n                    outx  lt - outx   choose n  i    1-t   n-i   t i x i 1          outy  lt - outy   choose n  i    1-t   n-i   t i y i 1                 return  list x outx  y outy            Example usage x  lt - c 4 6 4 5 6 7  y  lt - 1 6 plot x  y   o   pch 20  points bezierCurve x y 20   type  l   col  red

User · Answer

Maybe smooth spline is an option  You can set a smoothing parameter  typically between 0 and 1  here  smoothingSpline   smooth spline x  y  spar 0 35  plot x y  lines smoothingSpline    you can also use predict on smooth spline objects  The function comes with base R  see   smooth spline for details

User · Answer

I like loess   a lot for smoothing   x  lt - 1 10 y  lt - c 2 4 6 8 7 12 14 16 18 20  lo  lt - loess y x  plot x y  lines predict lo   col  red   lwd 2    Venables and Ripley s MASS book has an entire section on smoothing that also covers splines and polynomials -- but loess   is just about everybody s favourite

User · Answer

In ggplot2 you can do smooths in a number of ways  for example   library ggplot2  ggplot mtcars  aes wt  mpg     geom point       geom smooth method    gam   formula   y   poly x  2    ggplot mtcars  aes wt  mpg     geom point       geom smooth method    loess   span   0 3  se   FALSE

User · Answer

I didn t see this method shown  so if someone else is looking to do this I found that ggplot documentation suggested a technique for using the gam method that produced similar results to loess when working with small data sets    library ggplot2  x  lt - 1 10 y  lt - c 2 4 6 8 7 8 14 16 18 20   df  lt - data frame x y  r  lt - ggplot df  aes x   x  y   y     geom smooth method    gam   formula   y   s x  bs    cs    geom point   r   First with the loess method and auto formula Second with the gam method with suggested formula

User · Answer

the qplot   function in the ggplot2 package is very simple to use and provides an elegant solution that includes confidence bands   For instance   qplot x y  geom  smooth   span  0 5    produces

User · Answer

In order to get it REALLY smoooth     x  lt - 1 10 y  lt - c 2 4 6 8 7 8 14 16 18 20  lo  lt - loess y x  plot x y  xl  lt - seq min x  max x    max x  - min x   1000  lines xl  predict lo xl   col  red   lwd 2    This style interpolates lots of extra points and gets you a curve that is very smooth   It also appears to be the the approach that ggplot takes  If the standard level of smoothness is fine you can just use   scatter smooth x  y

[r] How to fit a smooth curve to my data in R?

Examples related to r

Examples related to plot

Examples related to curve-fitting