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Chunk #99 — Methods (full – for online materials) — Inferring regulatory architectures by multiple linear regression

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An atlas of active enhancers across human cell types and tissues.
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r2 and multiple linear regression R2, for each enhancer among the ten considered for each TSS. This measure yielded highly similar ranking results of enhancers as the R2 contribution averaged over orderings among regressors67,68 and R2 decorrelation decomposition67,69 (data not shown), implemented in the ‘relaimpo’ R package37,69 (lmg and car methods, respectively). We used ranking of enhancers according to proportional contribution and within-model enhancer-enhancer correlations to identify TSSs with different enhancer architectures. Redundant enhancers were identified for TSSs that had enhancers that were, by proportional contribution, ranked second and onwards with at least some proportional contribution (>0.2) and high correlation (Pearson's r>0.7) with any other of the nine enhancers in the model. Patterning architectures were considered for enhancers in non-redundant models that were, by proportional contribution, ranked second and onwards with at least some proportional contribution (>0.2) and low correlation (Pearson's r<0.3) with all other of the nine enhancers in the model. Penalized lasso-based regression was used to reduce the number of enhancers in the models. The optimal models were selected using 100-fold cross validation and the largest value of lambda such that the mean squared error was within one standard error of the minimum, using the R package glmnet29,37