standardization for MRPP in conjunction with PCA

[Nina Nikolic]

Hi,

I have some non-species data, and I want to visualize the differences among 4 treatment groups by using PCA with correlation cross-product matrix.

Then, I wanted to use the T statistic from MRPP as a kind of measure how strong the separation (shown nicely graphically from PCA) of my 4 treatment groups is.

Now, the question is: if the PCA I used relies on standardized data, should I also standardize my data for MRPP (for this purpose)?

Thank you so much!

[Bruce McCune]

Nina, I am assuming that you are suggesting MRPP on the original data rather than on the PCA scores. If doing the MRPP on the original data, then yes, I would recommend standardizing the variables by their standard deviates (expressing each value as standard deviations from the mean of that variable), then choosing Euclidean distance for the MRPP. This would parallel the PCA.

Bruce McCune

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[Nina Nikolic]

Thank you dear Master,

that's exactly what I intended, but was not sure.

Please, two more points, briefly:

1. In the very same context (my "communities" are defined by concentrations of mineral nutrients in leaves instead by species; I use PCA with correlation cross-product matrix for data visualization, and T from MRPP -rel. by standard deviate- as an indicator of group separation), I am very interested in the interaction among my 2 treatment factors.

I noticed that if I use my original (raw) data on nutrient conc, I get different PerManova results as compared to when I run PerManova on data relativizied by standard devaite).

So, please, in this context, could you possibly give me any advice on whether to relativize, or not to relativize?

I do not know if in PerManova the calculations are such that variables expressed in large numerical values are bound to have a larger influence?

2. Is varimax rotation built-in in the Version 7, because I fail to find it as an option?

Thank you, the best Teacher in the world!

[Bruce McCune]

Nina, 

1. Because perMANOVA is based on a distance matrix and most distance measures do not standardize by the variables, the variables with large numerical values will tend to have more influence, as you suspected. So I would recommend standardizing the nutrient variables to put them on equal footing.

2. Varimax option is available in NMS but not PCA in v.7. But of course you can rotate a PCA solution any way you want after the fact in the Graph module.

Thanks for the nice comment. And I am guessing that you are one of the best learners in the world!

Bruce McCune

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[Nina Nikolic]

Excellent! Thank you so much.