I am performing principal component analysis (PCA) of the topographic data and soil properties in R using function prcomp(). And I standardized the data using function scale (data). But I am bit confused with the standardization of the variables like soil pH (which is negative logarithm) and aspect of the site. Is there any different method to standardize these variables?
Dear Paudel
You raised an interesting concern about standardizing pH. In my opinion standardization to zero mean and unit variance still makes sense. Basically it will tell you how different (i.e. how many standard deviation far) one site is from the average. In the book by Borcard et al. 2010 (Numerical Ecology with R), they do standardize pH (Chap 2, Pag 27).
When standardizing\transforming\normalizing variables, please consider also the function decostand() in the vegan package
Standardizing Aspect may be a bit tricky. Aspect is a circular variable, i.e. the value 359° is closer to 0° than for instance the value 10°. Treating this variables can be difficult.
There are some alternatives, although none is optimal.
1. Use aspect as a nominal variable (transforming the numerical value into e.g. 8 states: N, NW, W, SW, S etc. Of course if you do this, you won't be able to perform PCA anymore but you'll have to go through a PCoA. Furthermore, sites having N and NW aspect won't be treated as more similar than sites having N and S aspect.
You may not be willing to do this
2. Transform aspect into 2 variables: sin(Aspect) and cos(Aspect). This makes sense, since it take into account the circularity of the variable. Although, if you do so aspect will count twice in the PCA analysis. A linear combination of sin(a) and cos(a) is also an option. For instance sin(a)/cos(a)= tg(a). tg(a) is almost ideal. The only problem is that tg(+- 90°)= infinte. R won't be happy to have an Inf value in the PcA :-).
3. The best solution I found is using Aspect, together with slope and latitude to calculate the potential Annual solar radiation a plot is subject to (above canopy if you work with forests). This solution is nice especially when you work with plants, since aspect is just a proxy for the light and (in some circumstances) the heat stress that pertains a plot. You can do this either in ArcGIS, or numerically using the algorithm that was proposed by
McCune B, Keon D: Equations for potential annual direct incident radiation and heat load. J Veg Sci 2002, 13(4):603-606.
It works fine, and I used it in a couple of papers (for instance: Sabatini FM, Burrascano S, Tuomisto H, Blasi C: Ground Layer Plant Species Turnover and Beta Diversity in Southern-European Old-Growth Forests. PLoS ONE 2014, 9(4):e95244.)
Just, please be aware there is an error in the Excel script provided in the McCune's paper at pag 486. I prepared an Excel worksheet to do this (I can share it on private request).
I also decided to prepare an R function that you can find on my researchGate Page at:
https://www.researchgate.net/publication/262375438_SolarRad
I really hope this helps
Regards
F.
Data SolarRad
The centering operation is the removal of the average each variable. the
scale () function allows to perform this operation directly:
scale (XX, center = TRUE, scale = FALSE)
Centering and reduction is to focus the data values and divide by the standard deviation. The scale () function to perform this operation directly
scale (XX)
When doing a normalized PCA, working with the data after centering and
reduction.
Dear Paudel
You raised an interesting concern about standardizing pH. In my opinion standardization to zero mean and unit variance still makes sense. Basically it will tell you how different (i.e. how many standard deviation far) one site is from the average. In the book by Borcard et al. 2010 (Numerical Ecology with R), they do standardize pH (Chap 2, Pag 27).
When standardizing\transforming\normalizing variables, please consider also the function decostand() in the vegan package
Standardizing Aspect may be a bit tricky. Aspect is a circular variable, i.e. the value 359° is closer to 0° than for instance the value 10°. Treating this variables can be difficult.
There are some alternatives, although none is optimal.
1. Use aspect as a nominal variable (transforming the numerical value into e.g. 8 states: N, NW, W, SW, S etc. Of course if you do this, you won't be able to perform PCA anymore but you'll have to go through a PCoA. Furthermore, sites having N and NW aspect won't be treated as more similar than sites having N and S aspect.
You may not be willing to do this
2. Transform aspect into 2 variables: sin(Aspect) and cos(Aspect). This makes sense, since it take into account the circularity of the variable. Although, if you do so aspect will count twice in the PCA analysis. A linear combination of sin(a) and cos(a) is also an option. For instance sin(a)/cos(a)= tg(a). tg(a) is almost ideal. The only problem is that tg(+- 90°)= infinte. R won't be happy to have an Inf value in the PcA :-).
3. The best solution I found is using Aspect, together with slope and latitude to calculate the potential Annual solar radiation a plot is subject to (above canopy if you work with forests). This solution is nice especially when you work with plants, since aspect is just a proxy for the light and (in some circumstances) the heat stress that pertains a plot. You can do this either in ArcGIS, or numerically using the algorithm that was proposed by
McCune B, Keon D: Equations for potential annual direct incident radiation and heat load. J Veg Sci 2002, 13(4):603-606.
It works fine, and I used it in a couple of papers (for instance: Sabatini FM, Burrascano S, Tuomisto H, Blasi C: Ground Layer Plant Species Turnover and Beta Diversity in Southern-European Old-Growth Forests. PLoS ONE 2014, 9(4):e95244.)
Just, please be aware there is an error in the Excel script provided in the McCune's paper at pag 486. I prepared an Excel worksheet to do this (I can share it on private request).
I also decided to prepare an R function that you can find on my researchGate Page at:
https://www.researchgate.net/publication/262375438_SolarRad
I really hope this helps
Regards
F.
Data SolarRad
Standardization process is related to the norm (i.e. metric) used.
Hence, applying different methods of standardization before PCA will result in different type of ordination.
For more clarity on this matter, you can read the following comprehensive paper :
Legendre, P.and H. J. B. Birks. 2012
From classical to canonical ordination.Chapter 8, pp. 201-248
in:tracking Environmental Change using Lake Sediments, Volume
5: Data handling and numerical techniques.
H. J. B. Birks, A. F. Lotter, S. Juggins and J. P.Smoleds.].
Springer, Dordrecht, The Netherlands. xi + 716 pp.
available at http://biol09.biol.umontreal.ca/PLcourses/Ordination.pdf
Hello Paudel; Do you use the soil PH as raster or as a matrix of values?
Read the link
https://docs.google.com/a/koyauniversity.org/document/d/1x0A1nUz1WWtMCZb5oVzF0SVMY7a_58KQulqQVT8LaVA/edit#
Hi, if using function princomp(), parameter cor=TRUE authomatically makes metrics standard.
Check.
https://docs.tibco.com/pub/enterprise-runtime-for-R/4.0.2/doc/html/Language_Reference/stats/princomp.html
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