You can compare non-nested nls fits using the AIC command. Although
that does not give a formal hypothesis test there are rules of thumb for
using the AIC.
On Tue, Aug 12, 2008 at 2:13 AM, Nazareno Andrade
<[EMAIL PROTECTED]> wrote:
> Dear R-helpers,
>
> I am trying to check whether a model of the form y(t) = a/(1 +b*t) fits the
> curve of downloads per day of a file in a specific online community better
> than a model of the form y(t) = a*exp(-b*t). For that, I used nls to fit
> both models and I am now trying to compare the fits with anova. The problem
> I find is that anova does not report an F statistic or a p-value when I
> compare these two models.
>
> The data for a file is typically the following:
>> d
> V1 V2
> 1 1 293
> 2 2 101
> 3 3 63
> 4 4 53
> 5 5 42
> 6 6 19
> 7 7 28
> 8 8 23
> 9 9 18
> 10 10 17
> 11 11 14
> 12 12 18
> 13 13 5
> 14 14 9
> 15 15 10
> 16 15 0
>
> My code:
>
> d <-
> read.table(url("http://ece.ubc.ca/~nazareno/85247.arrivalRates<http://ece.ubc.ca/%7Enazareno/85247.arrivalRates>
> "))
> plot(d)
> f.exp.nw <- nls(V2 ~ a. * exp(-b. * V1), data = d, list( a. = d$V2[1], b. =
> 0.05))
> f.exp5.nw <- nls(V2 ~ a. / (1+ b. *V1), data = d, list( a. = d$V2[1], b. =
> 2))
> lines(d$V1, predict(f.exp.nw), col = "royalblue")
> lines(d$V1, predict(f.exp5.nw), col = "orange")
>
> anova(f.exp.nw, f.exp5.nw)
>
> However, the output from anova.nls is:
>
> Analysis of Variance Table
>
> Model 1: V2 ~ a. * exp(-b. * V1)
> Model 2: V2 ~ a./(1 + b. * V1)
> Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
> 1 13 4994.9
> 2 13 314.7 0 0.0
>
> and I cannot interpretate the lack of an F value. Looking at the
> implementation of the anova.nls() function, this seems to be related to the
> fact that the residuals' degrees of freedom are the same, but I could not
> find anywhere more information on whether they were required to be
> different. Thus, I'd greatly appreciate if you could spot any mistakes I
> might be doing or a (preferably online) reference for more on this issue.
>
>
> As a side question, it would be great also if someone with more experience
> on this matter could confirm with me that the proper direction for checking
> whether "the y(t) = a/(1 +b*t) form models more precisely the behavior of
> downloads of files in this communtiy" by quantifying for how many files it
> outperforms the exponential model.
>
> thank you very much in advance,
> Nazareno
>
> [[alternative HTML version deleted]]
>
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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
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