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This should be very basic and I hope someone can help me. I ran a principal component analysis with the following call:
pca <- princomp(....)
summary(pca)
Summary pca returns this description:
PC1 PC2 PC3
Standard deviation 2.8788 2.7862 2.1845
Proportion of Variance 0.1977 0.1549 0.07831
Look at the second line which shows the variance explained by each PC. How can I programmatically extract this vector in my script from the variable pca. I have done enough search and cannot find an answer.
914
In simple regression, the proportion of variance explained is equal to r2; in multiple regression, it is equal to R2. where N is the total number of observations and p is the number of predictor variables.
“Proportion of variance” is a generic term to mean a part of variance as a whole. For example, the total variance in any system is 100%, but there might be many different causes for the total variance — each of which have their own proportion associated with them.
The Proportion of Variance Explained The first principal component in our example therefore explains 62% of the variability, and the second principal component explains 25%. Together, the first two principal components explain 87% of the variability.
The total variance is the sum of variances of all individual principal components. The fraction of variance explained by a principal component is the ratio between the variance of that principal component and the total variance. For several principal components, add up their variances and divide by the total variance.
Proportion of Variance is nothing else than normalized standard deviations. You can calculate them as PoV <- pca$sdev^2/sum(pca$sdev^2)
81
Just:
summary(pc)$importance[2,]
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