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I have a plot like this.

enter image description here

I wish to apply a model to this, however, I guess a linear regression model won't work on this. What I did was plot it on logarithm x and logarithm y axis as well but it came out to be of no use.

With logarithm:

https://www.dropbox.com/s/vyzk4u26vnludoq/1.png?dl=0

I tried fitting in a model, but as expected, on plotting, the residual and fitted, it didn't turn out to be of much use:

https://www.dropbox.com/s/0uaf53bxdc3wd1l/3.png?dl=0

What else can I do? Anything that someone can suggest? Also, I wish to know how can I apply a non linear regression model?

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  • $\begingroup$ Don't take log(modularity)! That does entirely the wrong thing. Taking log(size) would be a good start, but on modularity it looks like you have an upper bound of 1; possibly a logit transform may help clarify the form of relationship if there are no actual "1" values -- but I wouldn't necessarily model the relationship this way. ... Which variable do you regard as the response here (if any)? $\endgroup$
    – Glen_b
    Commented Aug 28, 2014 at 22:58
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    $\begingroup$ Do you have any substantive knowledge about these variables? There is a very large space of "possible models" for bivariate data, but chances are there is a much smaller subspace of "reasonable models" for your bivariate data. $\endgroup$
    – shadowtalker
    Commented Aug 29, 2014 at 0:00
  • $\begingroup$ Refering to your very first plot: It looks like your dependent is a probability (e.g., will always be in the interval [0,1]). If that's the case you could use logistic regression. $\endgroup$
    – Roland
    Commented Aug 29, 2014 at 7:46

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As I suggested in comments, in order to see the relationships more clearly, something like the logit and log transforms on mods and sizes respectively at least lets you see more clearly what's happening when "mods" is jammed right up the high end:

enter image description here

This may not be linear, even on this scale; while there's a clear indication that at least that it continues to increase as "sizes" goes up, there's perhaps some suggestion of a kink somewhere around sizes of 70 to 80, after which it increases more slowly, and on this scale it looks almost flat by the largest values of size:

enter image description here

That kind of discussion shouldn't drive your model!

That should come from considerations of what these variables actually are, how they should be related, what might be meaningful for your application.

So:

What are the variables? How are they measured? Why should they be related? Which is the "response", if any? What's the aim of the analysis? What do you need to say about your data and how will you use it?

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  • $\begingroup$ Modularity basically tells us about the communities in a graph. Whereas, the size basically tells us the size of different graphs that I made. If modularity is on the higher side, I can say that there is a higher tendency of forming communities. I somehow want to link the size to the modularity. $\endgroup$
    – bjohn
    Commented Aug 29, 2014 at 5:15
  • $\begingroup$ Hmm. But in that application there are other important variables other than size, surely. If you're not sampling over them appropriately, you would need to control for them or you'll run into bias -- maybe even Simpson's paradox. $\endgroup$
    – Glen_b
    Commented Aug 29, 2014 at 5:27
  • $\begingroup$ What other important variables you think there can be which I can capture? And if I am trying to fit a model only on the basis of size, how can I do it? I mean, a model which perfectly describes it? $\endgroup$
    – bjohn
    Commented Aug 29, 2014 at 5:35
  • $\begingroup$ "What other important variables you think there can be which I can capture?" -- you should be telling me, but I'd guess some kind of measure of average connections per node would be an example of a potentially important variable. "I mean, a model which perfectly describes it?" -- this question makes no sense to me. If there's more than one potential variable that impact the outcome and you use only one how could you have a perfect description? $\endgroup$
    – Glen_b
    Commented Aug 29, 2014 at 8:32
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    $\begingroup$ If your question is "how do I model two variables without any in-domain information about how they should be related or the properties we require the model to have" then that's a question whose answer could fill many books - in fact, it does. You might consider nonparametric methods, for example (which fills books on its own) but if you need a succinct equation for the mean that approach may be unsatisfying. I would say if you're going to do model selection, estimation and assessment all on one set of data, then you should be aware of the problems with that. ... (ctd) $\endgroup$
    – Glen_b
    Commented Aug 29, 2014 at 21:35

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