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When I try to fit an exponential decay and my x axis has decimal number, the fit is never correct. Here's my data below:

exp.decay = data.frame(time,counts)
   time counts
1   0.4   4458
2   0.6   2446
3   0.8   1327
4   1.0    814
5   1.2    549
6   1.4    401
7   1.6    266
8   1.8    182
9   2.0    140
10  2.2    109
11  2.4     83
12  2.6     78
13  2.8     57
14  3.0     50
15  3.2     31
16  3.4     22
17  3.6     23
18  3.8     20
19  4.0     19
20  4.2      9
21  4.4      7
22  4.6      4
23  4.8      6
24  5.0      4
25  5.2      6
26  5.4      2
27  5.6      7
28  5.8      2
29  6.0      0
30  6.2      3
31  6.4      1
32  6.6      1
33  6.8      2
34  7.0      1
35  7.2      2
36  7.4      1
37  7.6      1
38  7.8      0
39  8.0      0
40  8.2      0
41  8.4      0
42  8.6      1
43  8.8      0
44  9.0      0
45  9.2      0
46  9.4      1
47  9.6      0
48  9.8      0
49 10.0      1

fit.one.exp <- nls(counts ~ A*exp(-k*time),data=exp.decay, start=c(A=max(counts),k=0.1))
plot(exp.decay, col='darkblue',xlab = 'Track Duration (seconds)',ylab = 'Number of Particles', main = 'Exponential Fit')
lines(predict(fit.one.exp), col = 'red', lty=2, lwd=2)

I always get this weird fit. Seems to me that the fit is not recognizing the right x axis, because when I use a different set of data, with only integers in the x axis (time) the fit works! I don't understand why it's different with different units.

enter image description here

Cleb
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Paulo Caldas
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  • As it is your first question: Please don't forget to upvote helpful answers and accept the best one by clicking on the green check next to the answer; the check then turns green – Cleb Oct 26 '17 at 18:20

1 Answers1

2

You need one small modification:

lines(predict(fit.one.exp), col = 'red', lty=2, lwd=2)

should be

lines(exp.decay$time, predict(fit.one.exp), col = 'red', lty=2, lwd=2)

This way you make sure to plot against the desired values on your abscissa.

I tested it like this:

data = read.csv('exp_fit_r.csv')

A0 <- max(data$count)
k0 <- 0.1

fit <- nls(data$count ~ A*exp(-k*data$time), start=list(A=A0, k=k0), data=data)

plot(data)
lines(data$time, predict(fit), col='red')

which gives me the following output:

enter image description here

As you can see, the fit describes the actual data very well, it was just a matter of plotting against the correct abscissa values.

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Cleb
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