Given a SummarizedExperiment container, what is the quickest way to identify a batch effect from one of the covariates found within the DataFrame in the colData slot? Right now I am plotting the principal components and colouring the samples by each of the covariates. I then have to check the first few components for any separation and colour by the covariates to see which is responsible. I have a large number of libraries I have to check and was wondering if there was a Bioconductor package to perform this step? I've looked at svaseq and RUVseq but I can't see that they produce any QC plots which will tell me if an effect is present and which covariate is responsible?
Two methods are best used for analysis of batch effects.

1. PCA with annotation - as you are doing, but relies on manual visual analysis
2. PVCA - https://www.bioconductor.org/packages/release/bioc/html/pvca.html - this fits a mixed effects model to the principle components then looks at effects of various co variates, quantitatively. It is called principle variance components analysis.

Update: I highly recommend https://github.com/dswatson/bioplotr/blob/master/R/plot_drivers.R, this function it makes a great plot for examining for batch effects and more.