How to compare the fitting of function?

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How to compare the fitting of function?

Luigi
Hello,
I have fitted two curves to the data. How can I tell which one is more
fitted? By eye (see plot underneath) I would say that the function
Gompertz is better than the function Holling type III; how can I give
a number to this hunch?
This is an example:
```
# functions
holling = function(a, b, x) {
  y = (a * x^2) / (b^2 + x^2)
  return(y)
}
gompertz = function(a, b, c, x) {
  y = a * exp(-b * exp(-c * x))
  return(y)
}
# data
actual <- c(8,  24,  39,  63,  89, 115, 153)
holling <- c(4.478803,  17.404533,  37.384128,  62.492663,  90.683630,
120.118174, 149.347683)
gompertz <- c(11.30771,  22.39017,  38.99516,  61.19318,  88.23403,
118.77225, 151.19849)
# plot
plot(1:length(actual), actual, lty = 1 , type = "l", lwd = 2,
     xlab = "Index", ylab = "Values")
points(1:length(actual), holling, lty = 2, type = "l", col = "red")
points(1:length(actual), gompertz, lty = 3, type = "l", col = "blue")
legend("bottomright",
       legend = c("Actual values", "Holling III", "Gompertz"),
       lty = c(1, 2, 3), lwd = c(2, 1,1), col = c("black", "red", "blue"))
```
Thank you

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Re: How to compare the fitting of function?

Ivan Krylov
On Tue, 7 Jul 2020 08:57:28 +0200
Luigi Marongiu <[hidden email]> wrote:

>I would say that the function Gompertz is better than the function
>Holling type III; how can I give a number to this hunch?

There are many different goodness-of-fit measures; typically,
regression problems are solved by minimising the sums of squared
residuals, so you can just take a look at those (sum((y.predicted -
y.reference)^2)). Root-mean-square-error [*] is another widely used
metric. When comparing different methods, one should be aware of
multiple comparisons problem [**] and potential for overfitting [***].

All this and more is discussed in books on statistics and regression,
such as Regression Modeling Strategies by Frank E. Harrell, Jr.
[doi:10.1007/978-3-319-19425-7]. For more advice on statistics,
consider dedicated communities such as
<https://stats.stackexchange.com/>, since statistics advice is
considered off-topic here in R-help.

--
Best regards,
Ivan

[*] https://en.wikipedia.org/wiki/RMSE

[**] https://en.wikipedia.org/wiki/Multiple_testing

[***] https://en.wikipedia.org/wiki/Overfitting

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Re: How to compare the fitting of function?

Luigi
Thank you. The problem was the implementation of the goodness-of-fit
in R (any method, really).
regards

On Tue, Jul 7, 2020 at 1:31 PM Ivan Krylov <[hidden email]> wrote:

>
> On Tue, 7 Jul 2020 08:57:28 +0200
> Luigi Marongiu <[hidden email]> wrote:
>
> >I would say that the function Gompertz is better than the function
> >Holling type III; how can I give a number to this hunch?
>
> There are many different goodness-of-fit measures; typically,
> regression problems are solved by minimising the sums of squared
> residuals, so you can just take a look at those (sum((y.predicted -
> y.reference)^2)). Root-mean-square-error [*] is another widely used
> metric. When comparing different methods, one should be aware of
> multiple comparisons problem [**] and potential for overfitting [***].
>
> All this and more is discussed in books on statistics and regression,
> such as Regression Modeling Strategies by Frank E. Harrell, Jr.
> [doi:10.1007/978-3-319-19425-7]. For more advice on statistics,
> consider dedicated communities such as
> <https://stats.stackexchange.com/>, since statistics advice is
> considered off-topic here in R-help.
>
> --
> Best regards,
> Ivan
>
> [*] https://en.wikipedia.org/wiki/RMSE
>
> [**] https://en.wikipedia.org/wiki/Multiple_testing
>
> [***] https://en.wikipedia.org/wiki/Overfitting



--
Best regards,
Luigi

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