I have percentage data and would like to see if these different variables have an affect on certain factors;

i.e., I have different habitats of an area e.g., improved grassland: 40%, arable: 15%, urban: 15%, woodland: 30% (these may not add up to 100% as I have removed certain habitats which I am not interested in). I want to see if any of these habitats have an effect on a) the density of bird species with in an area and b) the bird species richness.

So, my data looks something like this:

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My question is: what is the best way to analyse this data? I have tried running a generalised linear model, but as many of the habitats come out as significant, it seems that I am almost picking and choosing my result. Also, and more significantly, there seems to be an issue with Simpson's paradox (e.g., there is a significant main effect of improved grassland, but a negative interaction when I look at two different types of sites (urban VS countryside sites); please see here). I then decided to run separate GLMs for each habitat, but this doesn't seem the most efficient way.

Would it be sensible to run a PCA? Or would this not be suitable due to a) them being percentages, and b) the fact that the habitats are already linked in some way?

  • $\begingroup$ In general, in a first step I would transform my numbers from % to values between 0 and 1. $\endgroup$ – Qaswed Jul 12 '16 at 9:09
  • $\begingroup$ Second hint: if your variables add up to 1, one variable is redundant and probably shouldn't be in the model. $\endgroup$ – Qaswed Jul 12 '16 at 9:18
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    $\begingroup$ My first concern would focus on the potentially strong nonlinear relationships between these percentages and the response. It would be worth a lot of exploratory effort to find ways to express all the variables that can lead to approximate linear relationships. Only then would it make sense, and be useful, to apply procedures like PCA or multiple regression. Such re-expressions of the explanatory variables often alleviate or even remove collinearity problems. $\endgroup$ – whuber Jul 12 '16 at 14:12

There are, I think, two problems here. The first is collinearity and the second is that the percentages add up to different amounts.

There are many ways of dealing with collinearity - e.g. ridge regression (which may be the simplest). Another possibility is to do a cluster analysis on the types of environment and see if there are meaningful clusters of habitats (but that may not be what you want).

The varying totals may not be a problem, it depends on what exactly you are after. But I think it would be better to include all the types of environment - it makes things neater.

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    $\begingroup$ Thanks for your help. I thought there might be an issue with multi-collinearity, but I tested for this using SPSS and shows not to be an issue. Cluster analysis (if I understand it correctly) is not what I am after, as I want to see what effects the individual habitats have. Rather than adding all of the habitats in to one GLM, would it be suitable to run separate GLMs for each habitat, or is this typically not an acceptable way due to the inefficiency? Thanks $\endgroup$ – EsFaKe Jul 12 '16 at 13:21
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    $\begingroup$ Including all the totals guarantees perfect collinearity. The software therefore will have to throw out at least one variable. Let's take control and decide which one(s) to use, rather than leaving it to the software. In particular, by far the most meaningful choice is the one already made: don't include the percentages for the habitats that are not of interest. $\endgroup$ – whuber Jul 12 '16 at 13:31

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