Dear collegues,
I am runing a network analysis for microbial community composition, but one set of my samples has Node Degrees that does not follow power laws (R² = 0.3 at most). Also, some metrics do not differ from a random network. While finding this random network is a result of my research by itself, I am still trying to figure out how I can justifiably trim the data so I can actually find a pattern and explore the network with solid statistics.
What are my options to improve the fit to a power law? or even, should I try such a thing at all?
My data input is the frequency of different bacterial taxa. So far I tried taking out some 6 out of 30 samples from the analysis, changing the minimal amount of occurences of a taxa (varies from 1-800), and varying the minimal amount of times a taxa must be found to be computed (between 5 and 15 in 30 samples).
Hi Pedro,
I'm not a biologist, but I was wondering whether you may want to try a hybrid approach? that is, fitting a distribution that is a mix between a random network and a network generated by a power law. It is quite used in economics and sociology, but I have no idea about biology. Have a look at this paper http://www.jstor.org/stable/30035025 . (again, it's from another field and assumptions may be not valid or plausible in yours, but still worthwhile)
Best,
While I dont fully understand your area, I think the gist of your question is --- am I making a mistake in my fitting process or are these data really not a good fit to the various power law scenarios. So, to FIT the model correctly you have to be able to look at all the cases and somehow organize the data so that there are scores for the ranked outcomes, ... so rank 1, score = 50, rank 2, score = 48 etc... Clearly such a data structure will be non-increasing .... higher ranks, lower scores. THEN, if you look at the ranks on the x-axis you have your observations arrayed from 1, ...., m ..... from rank one to the number of the smallest sample (m). Recognize that several observations may have a tied data values, but again they will be non-increasing in rank. NOW, log both the y axis "values" and the ranks, and regress.
Is your resultant anywhere close to a good linear fit?
What is the regression coefficient for the slope?
There is a small amount of algebra to get the slope of the power law. I can go into detail with a specific example if you are stuck.
Suppose the slope from the log-log regression is = -0.998.
This is consistent with a power law shape parameter of (1 + 1/0.998) = 2.002.
See paper where this example is discussed:
Article Network Hub Structure and Resilience
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