interpret second matrix overlay on PCA

[benj...@isu.edu]

I am conducting a PCA of environmental variables that may help explain differnces in nutrient concentrations, which would be the response variable.  I put the environmental variables in the main matrix and nutrients in the second matrix.  I conducted a PCA  and then superimposed the second matrix.  Along PC-1 transient storage was driving the positive end.  Total nitrogen, which was in the second matrix, was related to PC-1, but the vecor was toward the negative end.  From this results, can I interpret that there is a potential for total nitrogen and transient strorage to be negatively related?  This makes biological sense. 

 

More specifically, I am curious how one would interpret the visual respresentation of the main matix being superimposed by the second matrix in a PCA?

 

Thanks,

 

joe

[Bruce McCune]

Joe, Let's say you are doing a joint plot with your second matrix variables superimposed on your ordination. The basis for interpretation is that the diagram is displaying the correlations between the individual variables in your second matrix and the PCA-based summary of covariation in your main matrix.

But your question raises another... It sounds like you chose to reduce your environmental matrix (explanatory variables) and superimpose your nutrient variables (response). Usually people would do the PCA on the response variables and superimpose the explanatory variables. But perhaps there are only a few of the nutrient variables? How did you decide which to use as the main matrix?

Bruce McCune

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[Joseph Benjamin]

Thanks for the response and good question.  As you suspected, I decided to use the environmental variables as the main matrix because I had 8 of them and only 2 nutrient variables of interest.  I am using PCA as an ad hoc exploratory tool to see if environmental differences among sites were mediating the response of nutrients to salmon carcasses added to half the reaches.  If this is the wrong approach, I would certainly entertain others.

 

joe

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