Hey everyone, I hope someone can help me. Please!
I've carried out a spatial PCA using the adegenet package in R, following Dr. Jombart's tutorial (i.e. NAs in data replaced to mean allele frequency, etc.). My problem is with the interpretation of the variance explained by each component... Obviously it's not like a regular PCA where you need all the components together in order to explain 100% of the variance in data.
Here in sPCA it's easy to see (in the screeplot for example) that combining just a couple of principal components exceeds 100% of the variance.
Showing the summary for the sPCA:
[Call: spca.genind(obj = mi_genind, xy = mi_genind$other$xy, cn = data.graph,
scannf = FALSE, nfposi = 2, nfnega = 0)]
Scores from the centred PCA
_________var___________cum___________ratio____________moran
Axis 1___1.184406_____1.184406_____0.07550004____0.3562353
Axis 2___1.022800_____2.207206_____0.14069851____0.1799373
sPCA eigenvalues decomposition:
___________eig_______________var_______________moran
Axis 1_____0.15675044______1.0088656_______0.6214918
Axis 2_____0.08220275______0.7455009_______0.4410605
###################################################
So I want to have some sort of idea whether this analysis is meaningful to explain the pattern in variability. As Jombart says in the tutorial: "The maximum attainable variance by a linear combination of alleles is the one from an ordinary PCA, indicated by the vertical dashed line on the right [of the screeplot]". I could take that value as my 100% variance and calculate the percentage explained by my Axis 1 on the sPCA... but I'm still confused because doing this to just a couple of principal components and then combining them would exceed 100% of variance explained.
Thanks for any help you can give me!
Each principal component(PC) has a corresponding eigenvalue of the variance-covariance matrix or the correlation matrix. The first PC corresponds with the highest eigenvalue. The sum of the eigenvalues is the variance. The proportion of the variance accounted for by the first PC is the ratio of the highest eigenvalue to the sum of the eigenvalues, and so on.
The principal components (PCs) with the largest Eigen value are the most important and explain the larger variation in the data set. The eigen value is the measure of importance of the PCs. The first and second PC usually accounted for the total variance in the entire data set. You can equally consider the eigen vectors of the variables under the PCs to determine and evaluate the parameter loading/significance.
Kindly go through the attached article for your reference purpose.
Thank you Ette Etuk and Isa Baba Koki for your kind contributions!
I understand those concepts in a normal PCA, but I've read papers more related to my particular case (spatial PCA) where authors directly take the value "variance" from the table I've shown (for my case in the first axis "1.0088656", as shown in the original post) and consider that as the proportion of variance explained. The thing is, my first axis is explaining more than 100% of the variance, which doesn't make any sense. Principal components in spatial PCA are not the same as in regular PCA, as they are a product of variance and autocorrelation.
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