We plotted the first (PC1) and second (PC2) principal components for each imputed GRM matrix in R (Team RC 2012).
Each metabolite in the imputed data matrix was normalized to the median concentration measured in both strains at the first sampling point and then converted to log2 scale.
We applied our method to this EMAP data, denoted as X, to obtain two matrices, a low-rank matrix L and a sparse matrix S. X ^ = L + S is the new complete data matrix with imputed missing entries.
By moving the genes whose missing values have been imputed to the complete matrix, the previous target genes with imputed values can be utilized for the missing value estimation of the following target gene.
The combined matrix with imputed missing values was then used to compute a phylogeny using Neighbor Joining.
Substituting equation (18) for g2= T2 α in equation (15) gives: 19 20 where,,, J2=− 1,, The matrix of imputed marker covariates can be obtained efficiently, using partitioned inverse results, by solving the easily formed very sparse system [see Additional file 1]: 21 where A i j are partitions of A−1 that correspond to partitioning g into g1 and g2.
Univariate outliers (boxplots) were eliminated from the data matrix and missing values were filled in using multiple imputation (5 imputed data sets) using the Marco Chain Monte Carlo (MCMC) method [ 56].
In the first comparison, the separate analysis treated the mRNA, miRNA and protein datasets as separate matrices and imputed them separately in the pipeline FA+LDA, this outputs, for each omic layer a combination of tissue-specific factors.
Once the complete SNP matrix was established (supporting information, File S1), the missing data were imputed using the realized relationship matrix method multivariate normal expectation maximization (MVN-EM) described by Poland et al. (2012b) with the R environment (R Development Core Team 2008) package rrBLUP (Endelman 2011).
For all algorithms, we imputed a M × N matrix of M individuals and N markers whose data points, defined in {0,1,2,NA}, represented the three possible genotypes and the missing value, respectively.
