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This question is mostly about another post here on stats.stackexchange. In general, VIM (Variability Independent of the Mean) is usually calculated, as the name suggests, to calculate the variability in a series of numbers independent of their mean. In most of the references, VIM is calculated by: VIM = SD / mean ^ x. In this formula, x is usually calculated by a fitting a non-linear model between mean and SD. For example, in R:

nls.vim = nls(sntd ~ k*avg^p, data=df, start=c(k=1,p=1))
summary(nls.vim)

In which x = p in the above model. Consequently, to my understanding, VIM should be calculated by fitting SD and mean of each individual and the acquired p:

VIM(i)=SD(i)/mean(i)^p

However, in the above mentioned post, VIM was calculated through the following formula (SD of each individual is raised to the power of p as well and the added constant k):

VIM(i)=k⋅(SD(i)/mean(i))^p

The code and the data and relevant references are already available in the linked post. Now I have three questions:

  1. Why is SD raised to the power of p as well as mean? We don't see this approach in any of the cited references.

  2. In some references,(including this one, also linked in the original post), the constant k is acquired by calculating the (mean of all means)^p. However, in the mentioned post, we see that he uses the k estimate from the summary of the non-linear model. Some references don't use a k at all. what is the difference between these calculations?

  3. Is the approach used in the original mentioned post statistically correct? why does it seem different compared to other references?

I would appreciate any help, as I am new to these concepts and this may well be a misunderstanding on my part, however, I can't seem to find any answers on my own.

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