I have a dataset with 11 variables and PCA (orthogonal) was done to reduce the data. Deciding on the number of components to keep it was evident for me from my knowledge about the subject and the scree plot (see below) that two principal components (PCs) were enough to explain the data and the remaining components were only less informative.
Scree plot with parallel analysis: observed eigenvalues (green) and simulated eigenvalues based on 100 simulations (red). Scree plot suggests 3 PCs, whereas parallel test suggests only the first two PCs.
As you can see only 48% of the variance could be captured by the first two PCs.
Plotting observations on the first plane made by the first 2 PCs revealed three different clusters using hierarchical agglomerative clustering (HAC) and K-means clustering. These 3 clusters turned out to be very relevant to the problem in question and were consistent with other findings as well. So except the fact that only 48% of variance was captured everything else was tremendously fine.
One of my two reviewers said: one cannot rely much on these findings as only 48% of variance could be explained and it is less than required.
Is there any required value of how much variance should be captured by PCA to be valid? Is it not dependent on the domain knowledge and methodology in use? Can anybody judge on the merit of the whole analysis just based on the mere value of the explained variance?
- Data are 11 variables of genes measured by a very sensitive methodology in molecular biology called Real-Time Quantitative Polymerase Chain Reaction (RT-qPCR).
- Analyses were done using R.
- Answers from data analysts based on their personal experience working on real-life problems in the fields of microarray analysis, chemometrics, spectometric analyses or alike are much appreciated.
- Please consider supporting you answer with references as much as possible.