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I'm working on a continuous set of data that tries to identify upward spikes in trends. The way I'm identifying these "spikes" are comparing the goodness of fit of the data on a linear, exponential, and logistic regression.

How would I compare these goodness' of fit? Or like: does the dataset resemble more of a linear, exponential, or sigmoid function?

(I'm no statistician, so please correct me of any improper vocabulary). Based on some Google searches, using $r^2$ for everything isn't the best so I tried to divvy up some tests with variances of residuals, but it seems like $r^2$ shouldn't even be used for logistic regression.

Edit: I tried to conceal the model of the data, but I suppose it won't really help if I keep it secret.

The data is modeled over something like a social media site that has tags/hashtags and the number of posts that use those tags/hashtags per hour. The continuity of data sources from the posts that users continuously generate, but the reason for identifying is for identifying which tags are trending. It's like primitive machine learning, in which getting an exponential goodness of fit being the best fit is what I'd consider as trending, at least for my code base. (There are some other logic that I've implemented, but that's the gist of it.)

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Please consider the underlying model: what generated the data and what is a likely cause-to-effect relation, and in particular asymptotic behavior. (I prefer not to advise analytical heuristics or blind tests to favor one model or the other.)

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    $\begingroup$ Hey, I've edited the question summary as to (self-)answer why I wanted to do a blind test. $\endgroup$
    – Yoomama
    Dec 23, 2019 at 13:58
  • $\begingroup$ @Yoomama: I don't really follow your explanations. If this is purely empirical, use the best correlation coefficient. And add any model that you want. $\endgroup$
    – user65203
    Dec 23, 2019 at 14:18
  • $\begingroup$ thanks! Wouldn't just analyzing correlation coefficient be inaccurate in some cases? Something about residuals (but I suppose, these numbers are to be calculated within a second...) is some visual way of identifying bias? $\endgroup$
    – Yoomama
    Dec 23, 2019 at 14:45
  • $\begingroup$ @Yoomama: inaccurate with respect to what ? $\endgroup$
    – user65203
    Dec 23, 2019 at 16:10

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