PCA was applied for the analysis of the data. PCA decomposes the variation of matrix X into scores T , loadings P , and a residuals matrix E . P is an I × A matrix containing the A selected loadings and T is a J × A matrix containing the accompanying scores.
X = PT T + E ,
whereP T P = I , the identity matrix.
The number of components used (A) in the PCA analysis was based on the scree plots and the score plots.
For ranking of the metabolites according to importance for the A selected PCs, the contribution r of all the variables to the effects observed in the A PCs was calculated
Here, r is the contribution of variable i to A components, λa is the singular value for the ath PC and pia is the value for the ith variable in the loading vector belonging to the ath PC. To allow for comparison between the different data pretreatment methods, the values for rA were sorted in descending order after which the comparisons were performed using the rank of the metabolite in the sorted list.
The measurement errors were analyzed by estimation of the standard deviation from the biological, analytical, and sampling repeats. The standard deviations were binned by calculating the average variance per 10 metabolites ordered by mean value [23 (link)].
The jackknife routine was performed according to the following setup. In round one experiments F1, G1, N1 were left out, in round two F2, G2, N1d were left out, and in round three F3, G3A, were left out. By selecting these experiments, the specific aspects of the experimental design were maintained.
where
The number of components used (A) in the PCA analysis was based on the scree plots and the score plots.
For ranking of the metabolites according to importance for the A selected PCs, the contribution r of all the variables to the effects observed in the A PCs was calculated
Here, r is the contribution of variable i to A components, λa is the singular value for the ath PC and pia is the value for the ith variable in the loading vector belonging to the ath PC. To allow for comparison between the different data pretreatment methods, the values for rA were sorted in descending order after which the comparisons were performed using the rank of the metabolite in the sorted list.
The measurement errors were analyzed by estimation of the standard deviation from the biological, analytical, and sampling repeats. The standard deviations were binned by calculating the average variance per 10 metabolites ordered by mean value [23 (link)].
The jackknife routine was performed according to the following setup. In round one experiments F1, G1, N1 were left out, in round two F2, G2, N1d were left out, and in round three F3, G3A, were left out. By selecting these experiments, the specific aspects of the experimental design were maintained.
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