{"comment":{"url":"https://api.github.com/repos/bpbond/SpeciesRankSurface/comments/11141144","html_url":"https://github.com/bpbond/SpeciesRankSurface/commit/e6b64787e5d5f5f7edb40cb692db6f8fcc6d6a28#commitcomment-11141144","id":11141144,"user":{"login":"lsaravia","id":1203501,"avatar_url":"https://avatars.githubusercontent.com/u/1203501?v=3","gravatar_id":"","url":"https://api.github.com/users/lsaravia","html_url":"https://github.com/lsaravia","followers_url":"https://api.github.com/users/lsaravia/followers","following_url":"https://api.github.com/users/lsaravia/following{/other_user}","gists_url":"https://api.github.com/users/lsaravia/gists{/gist_id}","starred_url":"https://api.github.com/users/lsaravia/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/lsaravia/subscriptions","organizations_url":"https://api.github.com/users/lsaravia/orgs","repos_url":"https://api.github.com/users/lsaravia/repos","events_url":"https://api.github.com/users/lsaravia/events{/privacy}","received_events_url":"https://api.github.com/users/lsaravia/received_events","type":"User","site_admin":false},"position":45,"line":88,"path":"srsdq.md","commit_id":"e6b64787e5d5f5f7edb40cb692db6f8fcc6d6a28","created_at":"2015-05-11T19:29:42Z","updated_at":"2015-05-11T19:29:42Z","body":"Third intent:\r\n\r\nTo determine if a data set could be analyzed using multifractals there should be a linear relationship between $log(Z_q)$ versus $log(\\epsilon)$, but oscillations might be present and the data sets still qualify as self-similar [@Liebovitch1998]. For this reason it is difficult to use tests of quadratic trends as proposed by Yakimov et al.[-@Yakimov2008], because the curvature of a quadratic function can be fitted by a periodic function with the correct amplitude. To work around this problem, I used the coefficient of determination ($R^2$) as a measure of goodness of fit [@Borda-de-Agua2002]; in general this is not a good indicator of linearity, but since linearity is not exclusively required, I use it here in a descriptive way. The C++ source code to perform the multifractal analysis is available at <https://github.com/lsaravia/mfsba>."}}