I've got 16 sites (groundwater, streams, wetlands) that I'm using PCA to help discriminate the grouping of sites based on their water quality (26 variables).
First issue: 3 of the 16 sites have much higher conductivity, alkalinity etc readings such that only 2 of the variables are normally distributed before transformation. After log or square root transformation, only 8 of the 26 variables are considered normally distributed (either a Shapiro Wilk value >0.85 or p>0.05). Do I have to remove these vastly different sites or remove the worst of the non-normal variables? Any ideas on the impact on the resulting PCA?
Second issue: The conductivity is highly correlated to a number of other variables such as (Total Alkalinity, Hardness, Total dissolved solids, Total dissolved ions, Calcium, Sodium, Chloride, Manganese, Magnesium). Leaving all these highly correlated variable will/do heavily weigh the PCA in the favour of the PC1 (dominated by all of these variables) because the PCA is maximising the variance explained. Has anyone got any references that discuss this and provide advice on approach?
Thanks
Andrew
PCA with water samples is always tricky considering that the variance in the data is usually very high. Thus the categorization and identifying Principal components is complicated. In one of my research with around 250 samples I had to first remove the ones in which the ions balances was not within the error range of +- 5% , then I could see a much clearer pattern. If you have already done that, and still you are seeing only very obvious correlations, you could try marking different areas with different colors or legends, and possibly see some significant spatial patterns.
You might want to try some methods with relaxed assumptions for non-parametric data, like cluster analysis, NMDS, or a version of CART (classification and regression trees) analysis. Cluster analysis and NMDS should give you some visual insight regarding spatial patterns at least.
If you have the uncertainty data for each element, I will advise that you use PMF.
Thanks all. I will probably remove the one site that is extremely different to all others and is causing the PCA plot to be dominated. I had already done this based on its effect on the PCA and its different chemistry.
Alana - I have also run through NMDS and Cluster analysis - both give generally a similar picture to the PCA - but I believe that they give a better clustering of what I believe are similar sites when compared to the PCA.
Environmnetal data usually do not show a normal distribution. Therefore, this is a normal case a you do not have to remove those variables. Apart from trying to normalize them with different transformatios (log or square root as you have already done) it is more important to center and scale the data before the PCA analysis. Statistical software normally have these options.
Hi Andrew:
I'd remove any of the unstable parameters (EC, pH, temp, DO) from the analysis. They're so variable that they can throw off a whole analysis.
I'd also consider using compositional data analysis first as it can help remove spurious results. See Buccianti & Grunsky 2014, van den Boogart & Tolosana-Delgado 2013, R Development Core Team 2011, van den Boogart 2015.
Hi Andrew,
Principally I agree with Jose Antonio. We have to look at this problem with the eye of the analyst/chemist and not only as a statistician. The parameters mentioned above are important parameters to estimate the quality of the waters even if they have a kind of uncertainty and non normal distribution. I'd just leave out the site with the extreme parameters.
Regarding the second problem I would not be worried because of the high correlation, PCA will handle this by "melting" the correlated variables to one PC.
Please send me your email address for that paper y9u requested.
Angela
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